ArticlePDF Available

Examining the Mutual Relations Between Language and Mathematics: A Meta-Analysis

Psychological Bulletin

April 2020
146(7):595-643

DOI:10.1037/bul0000231

Authors:

Peng Peng

University of Texas at Austin

Xin Lin

University of Macau

Zehra Emine Unal

Intern @Stanford Medicine | Ph.D. Candiate @Mizzou Psychology

Kejin Lee

Pusan National University

Show all 7 authorsHide

This study presents a meta-analysis of the relation between language and mathematics. A moderate relation between language and mathematics was found in 344 studies with 393 independent samples and more than 360,000 participants, r = .42, 95% CI [.40, .44]. Moderation and partial correlation analyses revealed the following: (a) More complicated language and mathematics skills are associated with stronger relations between language and mathematics; after partialling out working memory and intelligence, rapid automatized naming showed the strongest relation to numerical knowledge; (b) The relation between language and mathematics was stronger among native language speakers than among second-language learners, but this difference was not found after partialling out working memory and intelligence; (c) Working memory and intelligence together explained over 50% of the variance in the relation between language and mathematics and explained more variance in such relations involving complex mathematics skills; (d) Language and mathematics predicted the development of one another even after controlling for initial performance. These findings suggest that we may use language as a medium to communicate, represent, and retrieve mathematics knowledge as well as to facilitate working memory and reasoning during mathematics performance and learning. With development, the use of language to retrieve mathematics knowledge may be more important for foundational mathematics skills, which in turn further strengthens linguistic thought processes for performing more advanced mathematics tasks. Such use of language may boost the mutual effects of cognition and mathematics across development.

Developmental Function Hypothesis of Language for Mathematics Note. A solid arrow means the impact is relatively stable with development; A dotted arrow with a "+" means the impact increases with development; A dotted arrow with a "-" means the impact decreases with development;

…

Description of Codes and Examples of Response Categories for Types Language and Mathematics Tasks

…

Moderation Analysis on the Relation Between Language and Calculations

…

Moderation Analysis on the Relation Between Language and Word Problems

…

Moderation Analysis on the Relation Between Language and Mathematics Controlling for Working Memory and Reasoning

…

Figures - uploaded by Peng Peng

Content may be subject to copyright.

Content uploaded by Peng Peng

Content may be subject to copyright.

Psychological Bulletin

Examining the Mutual Relations Between Language and

Mathematics: A Meta-Analysis

Peng Peng, Xin Lin, Zehra Emine Ünal, Kejin Lee, Jessica Namkung, Jason Chow, and Adam Sales

Online First Publication, April 16, 2020. http://dx.doi.org/10.1037/bul0000231

CITATION

Peng, P., Lin, X., Ünal, Z. E., Lee, K., Namkung, J., Chow, J., & Sales, A. (2020, April 16). Examining

the Mutual Relations Between Language and Mathematics: A Meta-Analysis. Psychological

Bulletin. Advance online publication. http://dx.doi.org/10.1037/bul0000231

Examining the Mutual Relations Between Language and Mathematics:

A Meta-Analysis

Peng Peng and Xin Lin

The University of Texas at Austin Zehra Emine U

¨nal

University of Missouri

Kejin Lee and Jessica Namkung

University of Nebraska–Lincoln Jason Chow

Virginia Commonwealth University

Adam Sales

The University of Texas at Austin

This study presents a meta-analysis of the relation between language and mathematics. A moderate

relation between language and mathematics was found in 344 studies with 393 independent samples and

more than 360,000 participants, r⫽.42, 95% CI [.40, .44]. Moderation and partial correlation analyses

revealed the following: (a) more complicated language and mathematics skills were associated with

stronger relations between language and mathematics; after partialing out working memory and intelli-

gence, rapid automatized naming showed the strongest relation to numerical knowledge; (b) the relation

between language and mathematics was stronger among native language speakers than among second-

language learners, but this difference was not found after partialing out working memory and intelli-

gence; (c) working memory and intelligence together explained over 50% of the variance in the relation

between language and mathematics and explained more variance in such relations involving complex

mathematics skills; (d) language and mathematics predicted the development of one another even after

controlling for initial performance. These findings suggest that we may use language as a medium to

communicate, represent, and retrieve mathematics knowledge as well as to facilitate working memory

and reasoning during mathematics performance and learning. With development, the use of language to

retrieve mathematics knowledge may be more important for foundational mathematics skills, which in

turn further strengthens linguistic thought processes for performing more advanced mathematics tasks.

Such use of language may boost the mutual effects of cognition and mathematics across development.

Public Significance Statement

We use language as a medium to communicate, represent, and retrieve mathematics knowledge, as

when we learn mathematics vocabulary, follow classroom instruction, and understand mathematics

texts. Meanwhile, we also use language to facilitate the processes of memory and reasoning during

mathematics performance and learning. With development, the use of language to retrieve mathe-

matics knowledge may become more important for foundational mathematics skills, which frees up

cognitive resources for more advanced mathematics performance; such use of language may boost

the mutual effects between cognition and mathematics during development.

Keywords: language, mathematics, mutualism, medium, development

Supplemental materials: http://dx.doi.org/10.1037/bul0000231.supp

XPeng Peng and Xin Lin, Department of Special Education, College of

Education, The University of Texas at Austin; Zehra Emine U

¨nal, Depart-

ment of Psychological Sciences, University of Missouri; XKejin Lee,

The Nebraska Center for Research on Children, Youth, Families and

Schools, University of Nebraska–Lincoln; Jessica Namkung, Department

of Special Education and Communication Disorders, University of

Nebraska–Lincoln; Jason Chow, School of Education, Virginia Common-

wealth University; Adam Sales, College of Education, The University of

Texas at Austin.

Correspondence concerning this article should be addressed to Peng Peng or

Xin Lin, Department of Special Education, College of Education, The Uni-

versity of Texas at Austin, SZB 408D, 1912 Speedway STOP D5300, Austin,

TX 78712. E-mail: kevpp2004@hotmail.com or lxjy1105@hotmail.com

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

Psychological Bulletin

ISSN: 0033-2909 http://dx.doi.org/10.1037/bul0000231

Language is a fundamental skill with which we express our

ideas, feelings, and queries to the world around us. It includes, but

is not limited to, phonological processing (manipulation and re-

trieval of sounds), vocabulary/morphology (the meaning of words),

and oral comprehension (making sense of oral discourse; see, e.g.,

Barre, Morgan, Doyle, & Anderson, 2011; Catts, Adlof, & Ellis

Weismer, 2006; Elbro, 1996; Language and Reading Research

Consortium, 2015; Wagner, Torgesen, Rashotte, & Pearson, 1999;

Zwaan & Radvansky, 1998). Language is also a critical skill for

academic performance, which includes reading and mathematics

(Chow & Wehby, 2018; Hoover & Gough, 1990; Kleemans,

Segers, & Verhoeven, 2011; LeFevre et al., 2010). The relation

between language and reading is well evidenced, such that word

decoding heavily involves phonological processing especially

early on, whereas reading comprehension is greatly influenced by

vocabulary and oral comprehension across one’s development

(Francis, Kulesz, & Benoit, 2018; Hjetland et al., 2019; Hoover &

Gough, 1990).

In contrast, findings on the relation between language and

mathematics remain mixed. Some have reported strong correla-

tions (rs⬎.70; e.g., Merz et al., 2015; Pind, Gunnarsdóttir, &

Jóhannesson, 2003), and others have found weak to nonsignificant

correlations (rs⬍.20; e.g., Mellard, Woods, & McJunkin, 2015;

Mestre, 1981). It is necessary to gain better insight into the relation

between language and mathematics, and the factors that influence

this relation. Such knowledge is important not only for theorists of

language and mathematical cognition, but also for educators so

that they can make informed decisions about how to use language

and to what degrees language should be emphasized in mathemat-

ics instruction.

To our knowledge, three reviews have specifically investigated

the relation between language and mathematics (Chow & Jacobs,

2016; de Araujo, Roberts, Willey, & Zahner, 2018; Koponen,

Georgiou, Salmi, Leskinen, & Aro, 2017). Chow and Jacobs

(2016) reviewed the relation between oral language and fraction

outcomes among school-age students. Based on three studies con-

ducted in the U.S., the authors suggested that oral language plays

a meaningful role in fraction performance, and that cognition may

partially explain the relation between oral language and fraction

performance. Koponen, Georgiou, Salmi, Leskinen, and Aro

(2017) investigated the relation between mathematics and rapid

automatized naming (RAN; one component of phonological pro-

cessing that mainly taps verbal retrieval abilities). Across 38

studies, Koponen et al. (2017) found a significant correlation

between RAN and mathematics, r⫽.37; 95% CI [.33, .42]. RAN

was more strongly correlated with calculations (e.g., solving stan-

dard arithmetic problems) than with general mathematics perfor-

mance. Among calculation tasks, RAN was more strongly corre-

lated with tasks that tap automatic fact retrieval (single-digit

calculations and mathematics fluency tasks). These findings sug-

gest that the relation between RAN and mathematics can be partly

explained by the retrieval of mathematics representations from

long-term memory (Georgiou, Wei, Inoue, & Deng, in press;

Koponen et al., 2017).

In the third review, de Araujo, Roberts, Willey, and Zahner

(2018) synthesized qualitative literature, with a focus on how

English language learners learn mathematics in a multilinguistic

educational setting. The authors suggest that language is a primary

medium for English language learners’ acquisition of mathematics

knowledge. That is, curricula incorporating a language component

and multimodal instruction such as visual presentations (to com-

pensate for limited English language proficiency) can facilitate

mathematics learning among English language learners. They also

suggested that it is important for English language learners to draw

on their first language in mathematics learning, because it is easier

to engage in mathematical reasoning in one’s first language than in

one’s second language (e.g., de Araujo et al., 2018; Martin &

Fuchs, 2019).

Taken together, the findings of these reviews shed some light on

the relation between language and mathematics. However, it re-

mains unclear whether different types of language skills might be

related to different types of mathematics skills in different ways—

whether these relations are influenced by task characteristics (e.g.,

measurement format) and sample characteristics (e.g., second-

language learning status), whether these relations may differ dur-

ing development, and how these relations may be influenced by

important cognitive skills such as working memory and intelli-

gence. The present study aims to contribute to the literature by

addressing these gaps.

The Language Function Hypothesis in Mathematics

This meta-analysis is guided by a general theoretical frame-

work: the function hypothesis of language, which suggests that

language serves many functions in our lives such as exchanging/

delivering messages/information, expressing our feelings and atti-

tudes, and informing our thoughts (Bruner, 1966; Fetzer & Tiede-

mann, 2018; Vygotsky, 1986). In these ways, language can lead to

the development of other skills such as mathematics. Among all

language functions, two that are fundamental to mathematics de-

velopment are language as a medium of exchange and language as

a means of thought (Bruner, 1966; Fetzer & Tiedemann, 2018).

Medium Function Hypothesis

The medium function hypothesis of language in mathematics

posits that we use language as a tool for communicating mathe-

matics knowledge with others, and building and retrieving repre-

sentations of mathematics knowledge from long-term memory,

implying a causal relation between language and subsequent math-

ematics development (Bruner, 1966; Dehaene, 1992; Dehaene &

Cohen, 1995; Fetzer & Tiedemann, 2018; Gersten et al., 2009;

LeFevre et al., 2010). More specifically, both general language and

mathematics-specific language (i.e., mathematics vocabulary such

as hexagon, dividend, and numerator, and mathematical expres-

sions such as the interior angle of a triangle) are used to commu-

nicate mathematical information in school settings (Gersten et al.,

2009; National Council of Teachers of Mathematics, 2006) and to

construct mathematical meanings in general, particularly when

paired with symbolic or other visual information (Chow & Wehby,

2019; O’Halloran, 2005).

Different types of language are important for constructing math-

ematical representations. In the pathways to mathematics model,

LeFevre et al. (2010) proposed and demonstrated that both pho-

nological processing and vocabulary serve as important mediums

to form visual and verbal representations of the meaning of num-

bers in early childhood. In the triple-code model of number pro-

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

2PENG ET AL.

cessing, Dehaene and colleagues (Dehaene, 1992; Dehaene &

Cohen, 1995) proposed that numerical tasks are supported by three

types of mental codes: the visual Arabic number code, the verbal

word code, and the analogue magnitude representation code. The

verbal word code is especially important at the beginning of formal

mathematics learning, linking the visual Arabic number code and

the analogue magnitude representation code (LeFevre et al., 2010).

Spelke (2017) proposed that children use language to learn to pair

number words with items in a set through the process of counting

to develop their abilities to represent exact numbers of unlimited

magnitude. Hecht, Torgesen, Wagner, and Rashotte (2001) sug-

gested that the quality of the phonological representations is im-

portant for arithmetic performance, such that children need to

transform numbers and operators into a speech-based code and use

phonological-based strategies such as counting to solve problems

(e.g., De Smedt et al., 2010).

Language also facilitates knowledge retrieval from long-term

memory during mathematics performance. It has been suggested

that arithmetic facts are stored in a language format (Spelke &

Tsivkin, 2001), and mathematics has specific vocabulary/expres-

sions that are also stored in a language format (O’Halloran, 2005).

Over the course of development, as students cumulatively build

their mathematics knowledge, the direct retrieval of arithmetic

facts and other mathematics knowledge (e.g., mathematics vocab-

ulary/expressions) from long-term memory can reduce cognitive

load (i.e., working memory demands) as they perform increasingly

difficult mathematics tasks (Koponen et al., 2017; Peng & Lin,

2019). In addition, many mathematics tasks consist of word prob-

lems, which also require general knowledge. The direct retrieval of

non-mathematics-specific knowledge from long-term memory can

facilitate the comprehension of word problems and reduce cogni-

tive load in solving them (Fuchs, Fuchs, Compton, Hamlett, &

Wang, 2015; Peng & Lin, 2019).

Thinking Function Hypothesis

In contrast to the medium function hypothesis, the thinking

function hypothesis of language for mathematics acknowledges

language as a medium for performing/learning mathematics, but

emphasizes that the use of language involves cognition (Daneman

& Merikle, 1996; Lombrozo, 2006; Peng, Wang, & Namkung,

2018; Vygotsky, 1986). That is, we use language to think about

more abstract mathematical concepts and relations between them,

as when we construct a schema and an equation in solving word

problems. We do this even for seemingly nonverbal mathematics

tasks, such as reasoning about orientation, locations, and patterns

in performing geometrical tasks (Bruner, 1966; Carruthers, 2002;

Fetzer & Tiedemann, 2018; Fuchs et al., 2015; Ingram, Andrews,

& Pitt, 2016; Sfard, 2008; Sidney, Hattikudur, & Alibali, 2015).

Even when we use language as a medium to share/learn mathe-

matics ideas with/from others or to construct mathematical mean-

ings, this use of language in turn affects our ideas about how to

make sense of mathematics problems (Fetzer & Tiedemann, 2018).

In comparison with the medium function hypothesis, which

implies that better language leads to better mathematics skills, the

thinking function hypothesis emphasizes that a third variable,

high-level cognition, underlies how we use language for mathe-

matics. Among many cognitive skills, working memory and intel-

ligence are human cognition’s core components (Ackerman, Beier,

& Boyle, 2005) that underlies the relation between language and

mathematics (e.g., as a third variable/confounder; see, e.g., Dane-

man & Merikle, 1996; Gathercole & Baddeley, 1990; Montgom-

ery, 2001; Peng, Wang, Wang, & Lin, 2019). The investigation of

whether working memory, intelligence, or both fully or partially

explain the relations between language and mathematics provides

not only relatively direct evidence on the thinking function of

language for mathematics, but also some indirect evidence on the

medium function of language for mathematics (i.e., the residual

variance on the relation between language and mathematics that is

not explained by working memory, intelligence, or both).

Working Memory

Working memory is the ability to simultaneously process and

store information (Baddeley, 1986). It is assumed to influence both

language and mathematics. Various language models agree that

language processing and development rely on working memory’s

limited capacity (Fedorenko, 2014; Gathercole & Baddeley, 1993;

Just & Carpenter, 1992). The ability to actively maintain and

integrate linguistic materials in working memory determines a

person’s success in learning, comprehending, and producing lan-

guage (Acheson & MacDonald, 2009; Baddeley, Gathercole, &

Papagno, 1998; Daneman & Carpenter, 1980; Ellis Weismer,

Evans, & Hesketh, 1999). Moreover, research on individuals with

specific language impairment (those with normal IQ but delayed

language development in the absence of any obvious cause) high-

lights that a deficit in working memory, across verbal and nonver-

bal domains, is one of the most distinctive markers of this group,

even when nonverbal cognitive skills are controlled for (Ellis

Weismer et al., 1999; Henry, Messer, & Nash, 2012; Im-Bolter,

Johnson, & Pascual-Leone, 2006; Marton, 2008; Marton &

Schwartz, 2003; Montgomery, Magimairaj, & Finney, 2010).

In mathematics, working memory is related to mathematics

performance both concurrently and prospectively (Bull & Lee,

2014; Geary, Nicholas, Li, & Sun, 2017; Lee & Bull, 2016). Many

mathematics tasks require individuals to actively maintain multiple

conceptions of mathematical expressions and intermediate num-

bers while solving problems, switching between strategies as ap-

propriate (e.g., Fuchs et al., 2005; Geary & Widaman, 1992; Peng,

Namkung, Barnes, & Sun, 2016; Raghubar, Barnes, & Hecht,

2010; Swanson & Beebe-Frankenberger, 2004). Especially for

more advanced mathematics tasks such as solving word problems,

working memory makes a unique contribution even after control-

ling for foundational mathematics skills (e.g., arithmetic; Swanson

& Sachse-Lee, 2001).

The effects of working memory on mathematics are not limited

to numerical processing (numerical working memory). Converging

evidence from behavioral and neuroimaging studies suggests that

verbal working memory is especially important for numerical

development (Menon, 2016; Raghubar et al., 2010) and for math-

ematics performance involving comprehension (e.g., word prob-

lems; Fuchs et al., 2015, 2018). Visuospatial working memory is

especially important for enhancing the proficiency of different

types of mathematics skills over time (Menon, 2016; Szucs,

Devine, Soltesz, Nobes, & Gabriel, 2014). Not surprisingly, work-

ing memory deficits across domains are often found to be the most

distinctive markers for children with various subtypes of mathematics

difficulties (Geary, 1993, 2004; Peng, Wang, & Namkung, 2018).

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

In addition to the conventional model of working memory that

emphasizes simultaneous information processing and storage, the

long-term working memory model provides further explanations

for the relation between language and mathematics (Baddeley,

2000; Ericsson & Kintsch, 1995; Peng et al., 2018). In this model,

working memory is an important part of executive function (Bad-

deley, 1986; Miyake & Friedman, 2012; Miyake et al., 2000),

which closely collaborates with long-term memory in academic

learning/performance (Peng et al., 2018). Long-term memory sup-

plements working memory such that working memory, as an

“executive commander,” helps one evaluate and integrate incom-

ing information through the retrieval of relevant information from

long-term memory (Kirschner, Sweller, & Clark, 2006; Miller-

Cotto & Byrnes, 2019). Given that many mathematics tasks rely

heavily on mathematics fact retrieval (Koponen et al., 2017),

working memory can influence the relation between language and

mathematics, even if tasks tap retrieval skills primarily (Friso-van

den Bos, van der Ven, Kroesbergen, & van Luit, 2013; Peng et al.,

2016).

Working memory, language, and mathematics also seem to

influence each other mutually. Research shows that the relation

between working memory and mathematics performance can be

partially explained by language (Peng & Lin, 2019). The effects of

language-centered mathematics instruction partly depend on chil-

dren’s working memory, such that children with very low working

memory benefit more from structured instruction that emphasizes

conceptual understanding than do those with relatively high work-

ing memory, potentially due to a reduced cognitive load (Fuchs et

al., 2016, 2014; Sweller, 1994). Mathematics difficulties among

children with language disorders can be partially explained by

their working memory abilities (Cross, Joanisse, & Archibald,

2019; Fyfe, Matz, Hunt, & Alibali, 2019). Furthermore, the rela-

tion between mathematics development and working memory

growth is influenced by language proficiency, especially among

second-language learners who perform mathematics in their sec-

ond language (Swanson, Kong, & Petcu, 2018). Taken together,

these findings further suggest that working memory may be a key

factor in explaining the relation between language and mathemat-

ics.

Intelligence

Intelligence refers to the reasoning capacity to solve novel

complex problems by means of mental operations, such as drawing

inferences, forming concepts, classifying, identifying relations,

finding solutions, and so forth (Cattell, 1963; Newton & McGrew,

2010). Obviously, such reasoning is heavily involved in both

language and mathematics (Lombrozo, 2006; Peng et al., 2019;

Wechsler, 2008). In this review, reasoning and intelligence refer to

the same construct and are used interchangeably. Although some

researchers consider intelligence to be strongly related to working

memory (Kane, Hambrick, & Conway, 2005), in the present meta-

analysis, we consider intelligence to be a relatively independent

cognitive skill of working memory (Ackerman et al., 2005) and

examine its role in the relation between language and mathematics.

Across different languages, there are rules about sound combi-

nations in phonological processing. Phonological tasks or decod-

ing tasks that involve phonological processing often require the

analysis and manipulation of sound structures, which involve

intelligence especially in early stages of reading development and

among children with intellectual/learning disabilities (Levy, 2011;

Peng et al., 2019; Tiu, Thompson, & Lewis, 2003). The acquisition

and use of vocabulary often involve reasoning. For example, when

they read books, children often learn new vocabulary by using

context clues and inference-making skills to decipher the clues

(Cain, Oakhill, & Lemmon, 2004). Direct vocabulary instruction

in schools often emphasizes the analysis of word roots and affixes

(suffixes and prefixes) and the use of categorization rules (e.g.,

synonyms and antonyms; National Reading Panel, 2000). In ad-

dition, the use of vocabulary in comprehending language often

draws on inference-making skills. It is suggested that not just

knowledge of individual word meanings but also rich semantic

networks with robust connections between the meanings of words

associated by topic are important for easy, accurate inference-

making during comprehension (Ahmed et al., 2016; Currie & Cain,

2015). Oral comprehension is structurally complicated, and accu-

rately comprehending orally presented sentences/passages requires

careful analyses and consistency checks. The involvement of rea-

soning in oral comprehension increases as sentences/passages be-

come longer and more complicated (Evans & Stanovich, 2013;

Mata, Schubert, & Ferreira, 2014).

The relation between mathematics and intelligence is well doc-

umented (Ackerman & Lohman, 2003; Blair, Gamson, Thorne, &

Baker, 2005; Deary, Strand, Smith, & Fernandes, 2007; Geary,

2011; Peng et al., 2019). For foundational mathematics skills (e.g.,

numerical knowledge and calculations), reasoning is involved in

the mastery of numerical symbols, their relations and applications

in the number system, and the rules and principles for calculations

(Fuchs et al., 2006; Östergren & Träff, 2013). Word problems,

fractions, and algebra are advanced mathematics skills that build

on foundational skills. Reasoning is highly involved in developing

conceptual and procedural understanding of these advanced skills.

For instance, we use reasoning to make sense of the magnitudes of

fractions based on our understanding of the magnitudes of whole

numbers (Stein, Grover, & Henningsen, 1996). In addition, math-

ematics tasks are often presented via word problems (Common

Core State Standards Initiative, 2010), and reasoning is often

required to construct problem models or schema to formalize

conceptual relations among quantities and guide the application of

strategies for solutions (e.g., Fuchs et al., 2015; Jordan et al., 2013;

Kaufmann & Schmalstieg, 2003; Namkung & Fuchs, 2016; Re-

uhkala, 2001).

The role of intelligence in the relation between language and

mathematics can also be understood from the perspective of school

instruction. In mathematics curricula and instruction across cul-

tures, students are often encouraged to “explain” the process of

solving mathematics problems to their peers and teachers (Ingram,

Andrews, & Pitt, 2019). This is commonly approached through

verbal explanation or by explaining an accurate solution in a

written form (e.g., in explaining how to solve a problem, con-

structing viable arguments, and critiquing the reasoning of others).

Such explanations and demonstrations require reasoning and log-

ical inferences (Horne, Muradoglu, & Cimpian, 2019). That is,

when children produce explanations and make causal attributions,

they need to make logical inferences (Griffiths & Tenenbaum,

2009), and the extent to which children provide favorite answers in

response to certain features (e.g., to achieve simplicity) requires

explanatory reasoning (Wilson & Keil, 1998).

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

4PENG ET AL.

Factors in the Language Function Framework

for Mathematics

Although the medium and thinking function hypotheses can

help explain how language is related to mathematics from a

theoretical perspective, these function-based hypotheses have

never been systematically investigated in mathematics learning

and performance, partly because the medium and thinking func-

tions of language are often considered “entangled” with each other

in the use of language (Carruthers, 2002). In the present meta-

analysis, we investigated several factors that may provide direct

and indirect evidence on the role of the medium and the thinking

functions of language in the relation between language and math-

ematics, respectively. These factors map directly onto this study’s

hypothesized moderators of the relation between language and

mathematics. We describe these factors as follows.

Types of Language/Mathematics

Different types of language skills may bear the medium function

to varying degrees in relation to different types of mathematics

tasks. For example, phonological processing (phonological aware-

ness and RAN) is often suggested to be heavily involved in

building numerical representations and retrieving mathematics

facts in long-term memory for numerical and calculation tasks

(e.g., Koponen et al., 2017; LeFevre et al., 2010; Singer, Strasser,

& Cuadro, 2019). By contrast, vocabulary and oral comprehension

are used in communicating mathematics knowledge in general

(Carey, 2009; Carruthers, 2002; Donlan, Cowan, Newton, &

Lloyd, 2007; Peng & Lin, 2019; Praet, Titeca, Ceulemans, &

Desoete, 2013; Singer et al., 2019). For example, oral comprehen-

sion may be generally important for the uptake of mathematics

instruction via receptive processes (e.g., syntax) that facilitate

comprehension of verbally delivered instruction (e.g., Chow &

Ekholm, 2019). Vocabulary and oral comprehension also play an

important role in developing/performing more advanced mathe-

matics skills such as solving word problems (Fuchs et al., 2015).

This may be because solving word problems differs from other

forms of mathematics competence in that it requires considerable

skills in reading comprehension, tapping vocabulary and oral com-

prehension to a greater extent (e.g., Cummins, Kintsch, Reusser, &

Weimer, 1988; Kintsch & Greeno, 1985).

Similarly, different types of language skills may bear the think-

ing function to varying degrees in relation to different types of

mathematics skills that also involve cognition to varying degrees.

According to the intrinsic cognitive load theory, an inherent level

of difficulty is associated with specific tasks (Chandler & Sweller,

1991; Sweller, 1994). Tasks with multiple interactive steps and

sequential thinking are assumed to be more difficult than tasks

involving fewer noninteractive steps. Thus, in comparison with the

relations between foundational language skills (e.g., phonological

processing and RAN) and foundational mathematics skills (e.g.,

numerical knowledge and calculations), the relations between

more complicated and semantically oriented language skills (e.g.,

vocabulary and oral language comprehension) and more compli-

cated mathematic skills such as solving word problems and frac-

tions may require more working memory and intelligence (Born-

stein, Hahn, Putnick, & Suwalsky, 2014; Chow & Jacobs, 2016;

Fuchs et al., 2015; Geary, 2004; Kintsch & Greeno, 1985; Lervåg,

Hulme, & Melby-Lervåg, 2018; Namkung & Fuchs, 2016).

Age (Development)

Mathematics development is accumulative, and the contribution

of cognitive skills and foundational mathematics skills to mathe-

matics performance varies with development. For example, lon-

gitudinal studies suggest that the importance of foundational

mathematics skills (numerical knowledge and calculations) in

subsequent mathematics achievement increases across elementary

and secondary grades, whereas cognitive skills are constantly

important for mathematic performance over time; cognitive skills

are more important than foundational mathematics skills for math-

ematics achievement only in early grades (Geary et al., 2017; Lee

& Bull, 2016). These findings likely reflect the increasingly im-

portant role of direct retrieval of mathematics knowledge from

long-term memory in partly reducing cognitive load on later math-

ematics performance (Geary et al., 2017; Peng & Lin, 2019).

Given such developmental features of mathematics, it is

reasonable to expect the relations between different language

skills and mathematics skills to vary with age under different

function hypotheses of language. For example, under the me-

dium function hypothesis of language, it is reasonable that the

relation between language and mathematics might not vary with

age, except with respect to foundational mathematics skills.

That is, numerical knowledge and calculations may be more

strongly related to phonological processing, especially RAN,

because performing these foundational tasks taps more

retrieval-based processes as children become more proficient

and automatic through development.

In contrast, under the thinking function hypothesis of language,

it is reasonable that the relations between different language skills

and different mathematics skills might vary with age. The relations

between phonological processing/vocabulary (relatively founda-

tional language skills) and various mathematics skills may de-

crease with age. The relation between oral comprehension and

mathematics, especially advanced mathematics skills such as word

problems, fractions, and algebra that require oral comprehension,

may stay stable or increase with age. Correspondingly, age may

not influence the impact of working memory and intelligence on

the relation between phonological processing and mathematics,

whereas working memory and intelligence may account for more

variance in the relation between oral comprehension and mathe-

matics with age.

Mutualism

Examining developmental relations may also help in further

testing of the thinking function of language in mathematics. Recent

research and reviews suggest that the relation between high-level

cognitive skills and academic performance is reciprocal, such that

both working memory/reasoning and academic skills influence

each other mutually during development (e.g., Kievit et al., 2017;

McArdle, Hamagami, Meredith, & Bradway, 2000; Peng et al.,

2019; Peng et al., 2018; Rindermann, Flores-Mendoza, & Mansur-

Alves, 2010; Van Der Maas et al., 2006). One rationale for the

impact of academic skills on cognition is that learning and per-

forming academic tasks often involve a constant use of working

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

memory and intelligence, which to some extent may serve as a

“long-term intervention” for these cognitive skills (Peng & Kievit,

2020; Peng et al., 2019; Peng et al., 2018). Moreover, the accu-

mulation of academic knowledge in long-term memory can further

strengthen the efficiency of using cognitive skills associated with

academic performance (Peng et al., 2018). Thus, if language

primarily serves the thinking function in mathematics, based on

mutualism, we would expect that language and mathematics pre-

dict each other from a longitudinal perspective.

Language Measurement

How language is measured may influence the evaluation of

cognitive load’s involvement in language skills. Language can be

measured in terms of reception or expression (Language and

Reading Research Consortium, 2015), respectively tapping one’s

ability to understand words, sentences, and passages or one’s

ability to put information into words and sentences grammatically

(Gleason & Ratner, 2005). Working memory is generally consid-

ered to show stronger relations with language expression or pro-

duction than with language reception because more information

(especially syntactic and grammatical knowledge) is simultane-

ously activated, processed, and stored in language production

(Acheson & MacDonald, 2009). This is especially so among

children, such that children with better working memory can

produce language that is more grammatically complex, contains a

richer array of words, and includes longer utterances than can

children with poorer working memory (Adams & Gathercole,

1995).

Second-Language Learning Status

Second-language learning status (using a second language to

learn/perform mathematics vs. using one’s first language to learn/

perform mathematics) may influence the medium function of

language in mathematics. Many studies have investigated how

English-language learners (those for whom English is a second

language) learn and perform mathematics in an English-speaking

environment (de Araujo et al., 2018). This research has adopted

various sociocultural models that emphasize the medium effect of

the English language on learning/performing mathematics in

English-language learners. It suggests that learning mathematics

requires the expression of mathematics in mathematics-specific

vocabulary and syntax (Pimm, 1987) and that English-language

learners need to be able to use English efficiently to acquire and

use mathematics-specific language in learning and performing

mathematics (Schleppegrell, 2007). English-language learners

who import meanings of mathematics vocabulary from their first

language to English often interpret them differently than intended

(Kazima, 2007). In addition, English-language learners can use

English to better communicate in mathematics-specific language

during mathematics instruction (e.g., Moschkovich, 2002;

Schleppegrell, 2007). All this evidence, taken together, suggests

that the medium function of language in mathematics may be

particularly important among second-language learners.

Research Questions

To summarize, this meta-analysis addresses four major ques-

tions.

Question 1: Is there a significant relation between language

and mathematics, and if so, what is the magnitude of this

relation?

Question 2: Does the relation between language and mathe-

matics vary as a function of types of language skills (i.e.,

phonological processing, vocabulary, oral comprehension,

comprehensive language ability), types of mathematics (i.e.,

numerical knowledge, calculations, word problems, fractions,

algebra, geometry, comprehensive mathematics skills),

second-language learning status (using a second language to

learn/perform mathematics vs. using the first language to

learn/perform mathematics), language measurement type (re-

ceptive vs. expressive), and age?

Question 3: What is the role of working memory and intelli-

gence in the relation between language and mathematics?

Specifically, is there a relation between language and mathe-

matics after controlling for working memory, intelligence, or

both? If so, how much variance can working memory, intel-

ligence, and both explain? Is the partial correlation between

language and mathematics, controlling for working memory

and intelligence, influenced by types of language skills, types

of mathematics, second-language learning status, and age?

Question 4: What is the longitudinal relation between lan-

guage and mathematics? Specifically, does language predict

mathematics after controlling for initial mathematics skills,

and does mathematics predict language after controlling for

initial language skills? What are the predictive powers of

different types of early language/mathematics on later

mathematics/language?

Method

Literature Search

Articles for this meta-analysis were identified in three ways.

First, the Communication & Mass Media Complete, Education

Source, ERIC, PsycINFO, and Medline databases were searched

for literature from the earliest possible start date until October

2018. Titles, abstracts, and keywords were searched using the

following terms: (language OR vocabulary OR linguistics OR

“listening comprehension” OR phonolog

ⴱ

OR morpholog

ⴱ

syntax OR semantics OR OR “rapid naming” OR “rapid automat

ⴱ

naming” OR RAN) AND (math

ⴱ

OR arithmetic OR “number

sense” OR numerical OR calcul

ⴱ

OR computation OR “word

problem

ⴱ

” OR algebra OR geometry OR calculus OR fraction).

The asterisk enables the inclusion of different forms of search

terms (e.g., calcul

ⴱ

can include calculation and calculating). Sec-

ond, we searched unpublished literature through the Dissertation

and Masters Abstract indexes in ProQuest and the Cochrane Da-

tabase of Systematic Reviews. Third, we searched in previous

relevant reviews and also contacted researchers to request corre-

lation tables not provided in their reported studies. The initial

search yielded 22,828 studies. Three authors of this study then

reviewed all studies by titles and abstracts. After excluding 682

duplicate and 19,990 irrelevant articles, the remaining 2,156 were

closely reviewed using specific criteria (see Figure 1 for a flow

diagram of the inclusion of studies).

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

6PENG ET AL.

First, studies had to include at least one quantitative task mea-

suring language and at least one quantitative task measuring math-

ematics. Language measures refer to the tasks that tap three lan-

guage skills: phonological processing including phonological

awareness (speech sound manipulation and short-term memory at

the word, onset-rime, syllable, and phonemic levels) and RAN

(phonological retrieval); vocabulary (expressive and receptive vo-

cabulary tasks; morphological and grammatical tasks targeting

only the vocabulary/word level); and oral comprehension (mor-

phological and grammatical tasks involving sentences, syntactic

judgment tasks, sentences/passages listening comprehension/re-

tell). Because we did not want to confound language skills with

writing/reading skills, we did not include language measures that

required substantial writing and reading (e.g., spelling, writing

down sentences/passages to answer oral comprehension ques-

tions). We also did not include measures of mathematics language

(e.g., mathematics vocabulary), because such measures are often

specific to a certain domain of mathematics (e.g., “pentagon” for

geometry; “dividend” for calculations) and are likely to be

confounded with general language and mathematics skills; this

might bias the relation between language and mathematics. For

this study, mathematics measures refer to the tasks that tap one

of the following: numerical knowledge (e.g., counting, subitiz-

ing, number comparison), calculations, solving of word prob-

lems, fractions, algebra, and geometry (see Table 1 for defini-

tions of different language and mathematics skills and examples

of tasks). Second, studies had to report at least one correlation

(r) between any measure of language and any measure of

mathematics.

Coding

Studies were coded according to their characteristics, samples,

and tasks used to measure language and mathematics. Among the

coded variables, we included some as covariates that were con-

trolled in our moderation analyses: publication type (peer-

reviewed vs. other), language type (alphabetic vs. nonalphabetic),

sample status (typically developing vs. atypically developing), and

socioeconomic status (SES; coded as low or middle, based on two

resources from the original studies: direct report of family SES

from the study and relevant SES information such as parental

education level, years of education, income level, and free-reduced

lunch status; studies that did not specify SES were coded as

general/unspecified SES). The moderator variables included types

of language skills (phonological awareness, RAN, vocabulary, oral

comprehension, and comprehensive language skills), second-

language learning status (using one’s second language vs. using

one’s first language to learn/perform mathematics), language mea-

surement type (expressive vs. receptive), types of mathematics

skills (numerical knowledge, calculations, word problems, frac-

tions, geometry, algebra, and comprehensive mathematics skills),

and age. We also coded working memory and intelligence (if

provided by the included studies) and the materials used to mea-

sure those cognitive skills (verbal, nonverbal, mixed verbal and

nonverbal). For measures of intelligence, we included only non-

verbal reasoning tasks or composite reasoning tasks. We excluded

reasoning tasks that were based only on verbal/numerical materials

that are often confounded with vocabulary/mathematics skills. In

addition to these variables, we also coded the number of partici-

pants for each correlation, which was needed to weight each effect

size, so that correlations obtained from larger samples were given

more weight in the analysis than were those from smaller samples.

The important features of individual studies are provided in online

supplemental materials. The variables were discussed until a con-

sensus was reached between the first and second authors. Then,

using the same coding system, the second author and a trained

research assistant (with a master’s degree in education) each

independently coded all included studies. The interrater reliability

between the two coders was .87⬃.99 for all variables of interest.

Articles are excluding duplicates

(n=22,145)

Initial

Screening

Eligibility

Included

Records identified through database search and previous

reviews

(n=22,828)

Articles based on titles and abstracts

(n=2,115)

Duplicate articles

removed

(n=683)

Titles and abstracts were

not related to the research

topic

(n=19,990)

Articles included in the current meta-analysis

(n=344)

Full-text articles excluded

(n=1,811)

1472: No objective language

measures

312: No objective

mathematics measures

27: No correlation data

Figure 1. Flow diagram for the inclusion of studies for the current review.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

Any disagreements were resolved by consulting the original article

or by discussion.

Missing Data

Not all studies provided sufficient information on the vari-

ables of interest for the present study. In case of insufficient

information, authors were contacted to obtain missing informa-

tion. However, if missing data could not be retrieved, especially

when data were missing for moderator variables, the studies

were excluded from the moderator analyses for which data were

missing but were included in all moderator analyses for which

data were provided.

Analytic Strategies

The effect size index used for all outcome measures is Pearson’s

r, for the correlation between language and mathematics. We

considered all eligible effect sizes in each study. That is, studies

could contribute multiple effect sizes as long as the sample for

each effect size was independent. For studies that reported multiple

effect sizes from the same sample, we accounted for the statistical

dependencies by using the random effects robust standard error

estimation technique developed by Hedges, Tipton, and Johnson

(2010). This analysis allowed for the clustered data (i.e., effect

sizes nested within samples) by correcting studies’ standard errors

to take into account correlations between effect sizes from the

same sample. The robust standard error technique requires that an

estimate of the mean correlation (␳) between all pairs of effect

sizes within a cluster be estimated for calculating the between-

study sampling variance estimate, ␶

. In all analyses, we estimated

␶

with ␳⫽.80; sensitivity analyses showed that the findings were

robust across different reasonable estimates of ␳.

Analyses were based on Borenstein, Hedges, Higgins, and Roth-

stein’s (2005) recommendations: We converted correlation coef-

Table 1

Description of Codes and Examples of Response Categories for Types Language and Mathematics Tasks

Types of skills Definition Examples of response categories

Types of language skills

Phonological processing Phonological Awareness: Tasks that tap the ability

to identify, manipulate, and temporally

memorize units of oral language parts (words,

syllables, onsets and rimes, and phonemes).

Identify the rhyme of words; identify initial sounds or

final sounds in words; identify medial sounds in

words; segment words into their component

syllable/sound; delete/add sounds from/to words;

Sound blending; Pseudoword repetition

Rapid Automatized Naming (RAN): Phonological

codes retrieval efficiency

Name letters/digits/colors/objects rapidly

Vocabulary Tasks that require individuals to point to a picture

corresponding to a word or explain what a word

means

Peabody Picture Vocabulary Test, Wechsler

Abbreviated Scale of Intelligence-Vocabulary,

Nelson Reading Skills Test-Vocabulary, Word

production fluency (e.g., say words that start with

letter B); Extended Range Vocabulary Test

Oral comprehension Tasks that require individuals to comprehend a

passage in an oral format (listening

comprehension)

Passage listening comprehension; Oral syntax

judgement; WAIS-Information/Comprehension;

Sentence repetition; Retell

Types of mathematics skills

Numerical knowledge Questions that tap numerosity (i.e., cardinality) as

well as the relation between numbers (i.e.,

ordinality), counting words, and Arabic digits

(i.e., symbolic knowledge)

Counting; seriation; classification of numbers; number

comparison; compare pairs of piles of objects;

quantity estimation; number line; number

identification/naming; Early Numeracy Test; place

value; transcoding from Arabic to verbal numerals

Calculations Single-digit or multidigit addition, subtraction,

multiplication, and division

Addition (e.g., 2 ⫹1⫽;20⫹60 ⫽); subtraction

(e.g., 6 ⫺4⫽;20⫺15 ⫽); division (e.g., 6/2 ⫽;

20/10 ⫽); multiplication (e.g., 2 ⫻4⫽;20⫻

12 ⫽); WJ-Math Fluency; CBM-Calculation;

WRAT-4-Math; WIAT-Arithmetic

Word problems Questions that involves the ability to understand

the problem narrative, focus on relevant and

ignore irrelevant information, construct a

number sentence, and solve for the missing

number to find the answer

WISC-Word Problem; Arithmetic Word Problems

(e.g., John had nine pennies. He spent three

pennies at the store. How many pennies did he

have left?); key-math problem solving

Fractions Questions that tap the understanding of the part-

whole relation, measurement interpretation of

fractions, and math problems that involve

fractional quantities

Fractions calculations (e.g., ¼ ⫹½); fractions

comparisons (e.g., ¼ ___ ½); NAEP-Fraction;

symbol-picture correspondence; calculations and

word problem-solving involving fractions;

fractional estimate

Geometry Questions that involves the properties and

relations of points, lines, surfaces, solids, and

higher dimensional analogs.

The MT advanced geometry task; the intuitive

geometry task.

Algebra Problems that can be solved by prelearned symbol

manipulation algorithms that are taught in many

algebra curricula

Algebra problem solving (e.g., if x ⫹2⫽3, then

x⫺5⫽); algebra judgement (e.g., 3y ⫹2⫽20;

y⫽2)

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

8PENG ET AL.

ficients to Fisher’s Zscale, and all analyses were performed using

transformed values. The results, such as the summary effect and its

confidence interval, were then converted back to correlation coef-

ficients for presentation. Also, because we hypothesized that this

body of research reports a distribution of correlation coefficients

with significant between-studies variance, as opposed to a group of

studies that attempts to estimate one true correlation, a random-

effects model was appropriate for the present study (Lipsey &

Wilson, 2001). Weighted random-effects metaregression models

using Hedges et al.’s (2010) corrections were run with

ROBUMETA in Stata (Hedberg, 2014) to summarize correlation

coefficients and to examine potential moderators.

We first estimated only the overall weighted mean correlation

between language and mathematics. Then, subgroup analyses were

used to examine the relation between language and mathematics

for each subgroup of each moderator. Metaregression analyses

were used to examine whether types of language skills, types of

mathematics skills, second-language status, language measure-

ment type, and age moderated the relation between language and

mathematics. For the moderation analysis, all moderators were

entered into the model simultaneously, with publication type, SES,

language type, and sample status as covariates in the model as

well. For categorical moderators, we created dummy coded vari-

ables to examine comparisons among categories (Cohen, Cohen,

West, & Aiken, 2013). Because there were multiple subgroups for

some moderators (e.g., types of language/mathematics), we ap-

plied the Benjamini-Hochberg procedure to those categorical mod-

erators in the metaregression models to reduce Type I errors.

To examine the influence of working memory and intelligence

on the relation between language and mathematics, we calculated

correlations between mathematics and language, partialing out

working memory, intelligence, and both. The calculation of the

partial correlation was based on the correlation matrices retrieved

from the original studies (e.g., if a study provided two measures of

mathematics, two measures of language, and two measures of

working memory, we would calculate all possible eight correla-

tions between [the two] mathematics measures and [the two]

language measures, partialing out [the two] working memory

measures). To calculate the correlation between language and

mathematics partialing out both working memory and intelligence,

we used the cor2pcor function from the corpcor package in R. We

then synthesized these partial correlations to indicate whether the

relation between language and mathematics was influenced by

working memory, intelligence, or both. We also calculated the

proportion of variance in the relation between language and math-

ematics that was explained by working memory, intelligence, or

both, based on the formula: 1 ⫺(r

partial

/r) (Huang, Sivaganesan,

Succop, & Goodman, 2004; Preacher & Kelley, 2011), where

partial

represents the partial correlation between language and

mathematics, partialing out working memory, intelligence, or both,

and rrepresents the correlation between language and mathemat-

ics.

To examine the relation between language and mathematics

longitudinally, we calculated (a) the correlations between mathe-

matics measured at Time 1 and language measured at Time 2 (a

later time point), partialing out their relations with language mea-

sured at Times 1; and (b) the correlations between language

measured at Time 1 and mathematics measured at Time 2, partial-

ing out their relations with mathematics measured at Times 1. The

partial correlation was based on the correlation matrices retrieved

from the original studies. We then synthesized these partial cor-

relations to indicate whether mathematics measured earlier pre-

dicted language later or vice versa. For all partial correlation

synthesis, we accounted for the statistical dependencies of multiple

partial correlations from one study using the random effects robust

standard error estimation technique developed by Hedges et al.

(2010) as mentioned earlier.

Publication bias (the problem of selective publication, in which

the decision to publish a study is influenced by its results) was

examined using the method of Egger, Davey Smith, Schneider, and

Minder (1997) and funnel plots (we aggregated all effect sizes for

each independent sample, as there are currently no funnel plots that

handle dependency with ROBUMETA). We did not find signifi-

cant publication bias based on Egger et al.’s (1997) statistics (i.e.,

the standard errors of correlations did not significantly predict

correlations among studies with ROBUMETA in Stata) for the

correlations between language and calculations/fractions/algebra,

or correlations between language and mathematics partialing out

intelligence/working memory, or the longitudinal correlations for

earlier language predicting later mathematics, ps⬎.05. However,

we found that Egger et al.’s (1997) test was significant for the

correlation between language and overall mathematics/numerical

knowledge/word problems/geometry, the relations between lan-

guage and mathematics partialing out working memory, and the

longitudinal correlations for earlier mathematics predicting later

language. Further examination of the funnel plots of the correla-

tions with Egger et al.’s (1997) test did not reveal any obvious

asymmetrical patterns, except that the funnel plot for the correla-

tion between language and geometry indicated that there were not

many studies with big sample sizes (probably due to the fact that

there were only 10 effect sizes available). That said, we considered

both published and unpublished literature for the present meta-

analysis, we included a large number of studies and effect sizes,

and we were thus not very concerned about publication bias,

particularly because there is some evidence that correlational

meta-analyses are less susceptible to bias due to the publication

process (Chow & Ekholm, 2018). In addition, we controlled for

publication type (peer-reviewed vs. other types of publication) in

all metaregression analyses.

Results

Based on our inclusion criteria, 344 studies (including 54 non-

peer reviewed articles) involving 393 independent samples,

368,268 participants, and 2,831 correlations between language and

mathematics were included for the final analyses.

Question 1: Is There a Significant Relation Between

Language and Mathematics?

The overall magnitude of the relation between language and

mathematics was r⫽.42, 95% CI [.40, .44]. As Table 2 shows, the

average correlation between different language skills and different

mathematics types was moderate and significant, rs⫽.29⬃.51,

ps⬍.05.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

Question 2: What Variables Moderate the Relation

Between Language and Mathematics?

Types of language skills. As Table 3 shows, after controlling

for covariates (alphabetic language vs. nonalphabetic language,

publication type, SES, sample status) and other moderators (types

of mathematics skills, language measurement type, second-

language status, and age), comprehensive language skills were

more strongly related to mathematics than were phonological

awareness and RAN; vocabulary and oral comprehension were

more strongly related to mathematics than was RAN; no signifi-

cant differences were found in other comparisons.

For the relation between language and numerical knowledge

after controlling for covariates and other moderators, only types

of language skills emerged as a significant moderator, such that

comprehensive language skills showed a stronger relation to

numerical knowledge than did phonological awareness, RAN,

and vocabulary (see Table 4); for the relation between language

and calculations after controlling for covariates and other mod-

erators, comprehensive language skills showed a stronger rela-

tion to calculations than did phonological awareness (see Table

5); for the relation between language and word problems after

controlling for covariates and other moderators, vocabulary,

oral comprehension, and comprehensive language skills all

showed stronger relations to word problems than did RAN (see

Table 6).

Mathematics types. As Table 3 shows, after controlling for

covariates and other moderators, word problems showed stronger

relations with language than did numerical knowledge, calcula-

tions, fractions, and algebra; comprehensive mathematics skills

were more strongly related to language than were numerical

knowledge, calculations, and algebra; no significant differences

were found in other comparisons.

Age. As Table 3 shows, after controlling for covariates and

other moderators, age did not significantly moderate the relation

between language and mathematics. However, for the relation

between language and calculations, after controlling for covariates

and other moderators, the relation between language and calcula-

tions decreased with age.

We also a series of moderation analysis to examine whether age

moderated the relations between phonological awareness/RAN/

oral comprehension and numerical knowledge/calculations/word

problems, with/without controlling for working memory and in-

telligence. The results showed that after controlling for covariates

and other moderators, without controlling for working memory

and intelligence, only age significantly moderated the relations

between phonological awareness and numerical knowledge/calcu-

lations such that these relations decreased with age. After control-

ling for working memory and intelligence, age did not emerge as

a significant moderator. Due to insufficient data points (less than

10), we did not examine whether age moderated the relations

between phonological awareness/RAN/oral comprehension and

other mathematics skills.

Language measurement type. As Table 2 shows, the aver-

age correlation between mathematics and receptive language

was r⫽.44, 95% CI [.41, .47]; the average correlation between

mathematics and expressive language was r⫽.39, 95% CI [.36,

.41], and the average correlation between mathematics and

receptive-expressive language was r⫽.50, 95% CI [.43, .57].

As Table 3 shows, after controlling for covariates and other

moderators, there were no significant differences among recep-

tive language, expressive language, and receptive-expressive

language.

Second-language learning status. As Table 2 shows, the

average correlation between language and mathematics among

second-language learners was r⫽.34, 95% CI [.28, .39]; the

average correlation between language and mathematics among

native language speakers was r⫽.43, 95% CI [.41, .45], and the

average correlation between language and mathematics among

samples mixed with second-language learners and native speakers

was r⫽.40, 95% CI [.35, .43]. As Table 3 shows, after controlling

for covariates and other moderators, the relation between language

and mathematics was stronger among native language speakers

and among samples mixed with second-language learners and

native language speakers than among second-language learners.

There was no difference between native language speakers and

Table 2

Correlations Between Language and Mathematics

Categories of covariates

and moderators

Language and mathematics

kr95% CI of r␶

Main average correlation 2066 .42 [.40, .44] .04

Publication type

1. Peer-reviewed 1650 .41 [.39, .43] .05

2. Other types 416 .46 [.41, .51] .03

Sample status

1. Typically developing 1381 .44 [.42, .46] .03

2. Atypically developing 685 .36 [.33, .40] .05

SES

1. Below middle class 482 .41 [.37, .44] .04

2. Middle class or above 515 .43 [.39, .47] .05

3. General/unspecified 1069 .42 [.39, .45] .03

Language type

1. Alphabetic 1985 .43 [.40, .44] .04

2. Nonalphabetic 81 .40 [.35, .45] .03

Language measurement type

1. Receptive 391 .44 [.41, .47] .02

2. Expressive 1513 .39 [.36, .41] .05

3. Receptive ⫹Expressive 110 .50 [.43, .57] .06

Second-language learning status

1. Native language speakers 1713 .43 [.41, .45] .04

2. Second-language learners 96 .34 [.28, .39] .02

3. Mixed sample 257 .40 [.35, .43] .03

Types of language skills

1. Phonological processing 835 .35 [.31, .38] .04

1a. Phonological awareness 476 .35 [.31, .39] .05

1b. Rapid automatized naming 359 .31 [.25, .35] .03

2. Vocabulary 830 .42 [.41, .45] .03

3. Oral comprehension 262 .43 [.39, .47] .04

4. Comprehensive language 139 .51 [.44, .57] .09

Types of mathematics skills

1. Numerical knowledge 790 .35 [.33, .39] .05

2. Calculations 608 .35 [.33, .38] .01

3. Word problems 309 .48 [.45, .51] .01

4. Fractions 13 .29 [.14, .43] .02

5. Geometry 10 .39 [.22, .53] .03

6. Algebra 32 .32 [.15, .36] .02

7. Comprehensive mathematics 304 .49 [.45, .52] .02

Note.k⫽number of effect sizes; CI ⫽confidence interval; SES ⫽

socioeconomic status; ␶

⫽between-study sampling variance.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

10 PENG ET AL.

Table 3

Moderation Analysis on the Relation Between Language and Mathematics

Measure Beta SE t 95% CI pvalue

Publication type

Peer-Reviewed versus Other Types ⴚ.06 .03 ⴚ2.08 [ⴚ.12, ⴚ.003] .04

Sample status

Typically Developing versus Atypically Developing .08 .02 3.18 [.03, .13] .002

SES

Low SES versus General/Unspecified ⫺.02 .03 ⫺.68 [⫺.07, .03] .49

Middle SES versus General/Unspecified .002 .03 .11 [⫺.05, .06] .92

Middle SES versus Low SES .02 .03 .69 [⫺.04, .08] .49

Language type

Alphabetic versus Nonalphabetic .04 .03 1.18 [⫺.02, .09] .24

Language measurement type

Receptive versus Expressive .01 .02 .45 [⫺.04 .06] .65

Receptive versus Receptive ⫹Expressive ⫺.05 .05 ⫺.92 [⫺.14, .05] .36

Expressive versus Receptive ⫹Expressive ⫺.06 .05 ⫺1.19 [⫺.15, .04] .24

Age ⫺.003 .002 ⫺1.50 [⫺.01, .001] .13

Second-language learning status

Second-Language Learners versus Mixed ⴚ.15 .05 ⴚ2.96 [ⴚ.26, ⴚ.05] .003

Native Language Speakers versus Second-Language Learners .17 .05 3.29 [.06, .26] .001

Native Language Speaker versus Mixed .01 .03 .31 [⫺.04, .06] .76

Types of language skills

Phonological Awareness versus Rapid Automatized Naming .04 .04 .98 [⫺.04, .11] .33

Phonological Awareness versus Vocabulary ⫺.06 .03 ⫺1.92 [⫺.11, .001] .06

Phonological Awareness versus Oral Comprehension ⫺.06 .03 ⫺1.80 [⫺.12, .005] .07

Phonological Awareness versus Comprehensive Language ⴚ.16 .05 ⴚ2.91 [ⴚ.26, ⴚ.05] .004

Rapid Automatized Naming versus Vocabulary ⴚ.09 .04 ⴚ2.55 [ⴚ.16, ⴚ.02] .01

Rapid Automatized Naming versus Oral Comprehension ⴚ.09 .04 ⴚ2.50 [ⴚ.17, ⴚ.02] .01

Rapid Automatized Naming versus Comprehensive Language ⴚ.19 .06 ⴚ3.44 [ⴚ30, ⴚ.08] .001

Vocabulary versus Oral Comprehension .00 .03 ⫺.12 [⫺.05, .05] .91

Vocabulary versus Comprehensive Language ⫺.10 .05 ⫺2.04 [⫺.20, ⫺.003] .04

Oral Comprehension versus Comprehensive Language ⫺.10 .05 ⫺1.94 [⫺.20, .002] .05

Types of mathematics skills

Calculations versus Numerical Knowledge ⫺.02 .03 ⫺.74 [⫺.07, .03] .46

Word Problems versus Numerical Knowledge .13 .03 4.76 [.08, .18] <.001

Fractions versus Numerical Knowledge ⫺.03 .06 ⫺.55 [⫺.16, .09] .58

Geometry versus Numerical Knowledge .002 .09 .02 [⫺.17, .18] .98

Algebra versus Numerical Knowledge ⫺.14 .06 ⫺2.29 [⫺.26, ⫺.02] .02

Comprehensive Mathematics versus Numerical Knowledge .11 .03 3.57 [.05, .17] <.001

Word Problems versus Calculations .15 .03 5.89 [.10, .20] <.001

Fractions versus Calculations ⫺.02 .06 ⫺.26 [⫺.13, .10] .80

Geometry versus Calculations .02 .09 .24 [⫺.15, .19] .81

Algebra versus Calculations ⫺.12 .06 ⫺2.08 [⫺.24, ⫺.007] .04

Comprehensive Mathematics versus Calculations .13 .03 4.49 [.07, .19] <.001

Fractions versus Word Problems ⴚ.16 .06 ⴚ2.65 [ⴚ.28, ⴚ.04] .01

Geometry versus Word Problems ⫺.13 .09 ⫺1.44 [⫺.30, .05] .15

Algebra versus Word Problems ⴚ.27 .06 ⴚ4.44 [ⴚ.39, ⴚ.15] <.001

Comprehensive Mathematics versus Word Problems ⫺.02 .03 ⫺.60 [⫺.08, .04] .55

Geometry versus Fractions .04 .10 .35 [⫺.17, .24] .73

Algebra versus Fractions ⫺.10 .08 ⫺1.26 [⫺.26, .06] .21

Comprehensive Mathematics versus Fractions .15 .06 2.26 [.02, .27] .03

Algebra versus Geometry ⫺.14 .08 ⫺1.75 [⫺.31, .02] .08

Comprehensive Mathematics versus Geometry .11 .09 1.22 [⫺.07, .28] .22

Comprehensive Mathematics versus Algebra .25 .06 4.29 [.14, .37] <.001

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval; SES ⫽socioeconomic status. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus

nonalphabetic, nonalphabetic is the reference group in the dummy coding of language type). Bolded number means significant after applying Benjamini-

Hochberg procedure. There are 2,006 correlations and 331 independent samples. Between-study sampling variance (␶

) is .02.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

mixed samples with second-language learners and native language

speakers.

Question 3: What Is the Role of Working Memory

and Intelligence in the Relation Between Language

and Mathematics?

Controlling for working memory. There were 101 studies,

with 111 independent samples and 2,111 correlations between

language and mathematics partialing out working memory. The

results showed that based on these studies, the correlation between

language and mathematics was r⫽.37, 95% CI [.35, .41], the

correlation between language and working memory was r⫽.29,

95% CI [.26, .32], and the correlation between working memory

and mathematics was r⫽.32, 95% CI [.30, .35]. After partialing

out working memory, the correlation between language and math-

ematics was r⫽.31, 95% CI [.28, .34]. After partialing out

working memory and controlling for types of working memory

tasks (controlling for the medium effects), the correlation between

language and mathematics was r⫽.34, 95% CI [.29, .37]. Taken

together, working memory explained about 8%⬃16% of the vari-

ance in the relation between language and mathematics.

Numerical knowledge. There were 47 studies, with 49 inde-

pendent samples and 837 correlations between language and nu-

merical knowledge partialing out working memory. The results

showed that based on these studies, the correlation between lan-

guage and numerical knowledge was r⫽.32, 95% CI [.28, .35],

the correlation between language and working memory was r⫽

.27, 95% CI [.24, .30], and the correlation between working

memory and numerical knowledge was r⫽.28, 95% CI [.25, .31].

After partialing out working memory, the correlation between

language and numerical knowledge was r⫽.26, 95% CI [.24, .30].

After partialing out working memory and controlling for types of

working memory tasks (controlling for the medium effects), the

correlation between language and numerical knowledge was r⫽

.28, 95% CI [.25, .33]. Taken together, working memory explained

about 13%⬃19% of the variance in the relation between language

and numerical knowledge.

Calculations. There were 64 studies, with 71 independent

samples and 706 correlations between language and calculations

partialing out working memory. The results showed that based on

these studies, the correlation between language and calculations

was r⫽.33, 95% CI [.29, .36], the correlation between language

and working memory was r⫽.29, 95% CI [.25, .32], and the

correlation between working memory and calculations was r⫽

.30, 95% CI [.27, .33]. After partialing out working memory, the

correlation between language and calculations was r⫽.26, 95%

Table 4

Moderation Analysis on the Relation Between Language and Numerical Knowledge

Measure Beta SE t 95% CI pvalue

Publication type

Peer-reviewed versus Other Types ⫺.06 .06 ⫺.97 [⫺.18, .06] .34

Sample status

Typically Developing versus Atypically Developing .10 .04 2.53 [.02, .18] .01

SES

Low SES versus General/Unspecified .03 .04 .73 [⫺.05, .11] .47

Middle SES versus General/Unspecified ⫺.04 .04 ⫺1.05 [⫺.13, .04] .30

Middle SES versus Low SES ⫺.07 .05 ⫺1.60 [⫺.16, .02] .11

Language type

Alphabetic versus Nonalphabetic .07 .04 1.47 [⫺.02, .15] .15

Language measurement type

Receptive versus Expressive .06 .04 1.59 [⫺.02, .14] .12

Receptive versus Receptive ⫹Expressive .19 .13 1.43 [⫺.07, .45] .16

Expressive versus Receptive ⫹Expressive .13 .13 .95 [⫺.14, .39] .35

Age 0.00 .01 ⫺.03 [⫺.02, .02] .98

Second-language learning status

Second-Language Learners versus Mixed ⫺.14 .11 ⫺1.22 [⫺.37, .09] .22

Native Language Speakers versus Second-Language Learners .17 .11 1.49 [⫺.06, .39] .14

Native Language Speaker versus Mixed .03 .04 .67 [⫺.05, .11] .50

Types of language skills

Rapid Automatized Naming versus Phonological Awareness ⫺.05 .04 ⫺1.33 [⫺.13, .03] .19

Vocabulary versus Phonological Awareness .003 .04 .09 [⫺.07, .08] .93

Oral Comprehension versus Phonological Awareness .05 .05 .96 [⫺.05, .16] .34

Comprehensive Language versus Phonological Awareness .23 .11 2.02 [.01, .46] .046

Vocabulary versus Rapid Automatized Naming .06 .04 1.41 [⫺.02, .14] .16

Oral Comprehension versus Rapid Automatized Naming .11 .06 1.85 [⫺.01, .22] .07

Comprehensive Language versus Rapid Automatized Naming .29 .11 2.55 [.06, .51] .01

Oral Comprehension versus Vocabulary .05 .05 .95 [⫺.05, .15] .34

Comprehensive Language versus Vocabulary .23 .11 2.10 [.01, .45] .04

Comprehensive Language versus Oral Comprehension .18 .12 1.56 [⫺.05, .41] .12

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). Bolded number means significant after applying Benjamini-Hochberg procedure. There are

781 correlations and 113 independent samples. Between-study sampling variance (␶

) is .03.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

12 PENG ET AL.

CI [.23, .29]. After partialing out working memory and controlling

for materials of working memory (controlling for the medium

effects), the correlation between language and calculations was

r⫽.31, 95% CI [.26, .35]. Taken together, working memory

explained about 6%⬃21% of the variance in the relation between

language and calculations.

Word problems. There were 44 studies, with 46 independent

samples and 225 correlations between language and word prob-

lems partialing out working memory. Results showed that based on

these studies, the correlation between language and word problems

was r⫽.45, 95% CI [.42, .49], the correlation between language

and working memory was r⫽.33, 95% CI [.28, .36], and the

correlation between working memory and word problems was r⫽

.38, 95% CI [.35, .41]. After partialing out working memory, the

correlation between language and word problems was r⫽.38,

95% CI [.35, .41]. After partialing out working memory and

controlling for types of working memory tasks (controlling for the

medium effects), the correlation between language and word prob-

lems was r⫽.43, 95% CI [.37, .49]. Taken together, working

memory explained about 4%⬃16% of the variance in the relation

between language and word problems.

Fractions. There were eight studies, with eight independent

samples and 40 correlations between language and fractions par-

tialing out working memory. The results showed that based on

these studies, the correlation between language and fractions was

r⫽.31, 95% CI [.23, .38], the correlation between language and

working memory was r⫽.23, 95% CI [.15, .30], and the corre-

lation between working memory and fractions was r⫽.24, 95%

CI [.17, .31]. After partialing out working memory, the correlation

between language and fractions was r⫽.26, 95% CI [.20, .35].

After partialing out working memory and controlling for types of

working memory tasks (controlling for the medium effects), the

correlation between language and fractions was r⫽.31, 95% CI

[.19, .42]. Taken together, working memory explained about

0%⬃16% of the variance in the relation between language and

fractions.

Geometry. There were four studies, with five independent

samples and 67 correlations between language and geometry par-

tialing out working memory. The results showed that based on

these studies, the correlation between language and geometry was

r⫽.37, 95% CI [.13, .57], the correlation between language and

working memory was r⫽.28, 95% CI [.13, .42], and the corre-

lation between working memory and geometry was r⫽.35, 95%

CI [.18, .51]. After partialing out working memory, the correlation

between language and geometry was r⫽.29, 95% CI [.03, .51].

Table 5

Moderation Analysis on the Relation Between Language and Calculations

Measure Beta SE t 95% CI pvalue

Publication type

Peer-reviewed versus Other Types ⫺.06 .03 ⫺1.69 [⫺.12, .01] .09

Sample status

Typically Developing versus Atypically Developing .05 .03 1.86 [⫺.003, .11] .07

SES

Low SES versus General/Unspecified ⫺.06 .03 ⫺1.97 [⫺.12, 0] .05

Middle SES versus General/Unspecified .03 .05 .53 [⫺.08, .13] .59

Middle SES versus low SES .09 .05 1.64 [⫺.02, .19] .10

Language type

Alphabetic versus Nonalphabetic ⫺.06 .06 ⫺1.15 [⫺.17, .05] .25

Language Measurement Type

Receptive versus Expressive .03 .04 .88 [⫺.04, .10] .38

Receptive versus Receptive ⫹Expressive ⫺.02 .07 ⫺.30 [⫺.16, .12] .77

Expressive versus Receptive ⫹Expressive ⫺.05 .06 ⫺.83 [⫺.18, .07] .41

Age ⴚ.004 .002 ⴚ2.59 [ⴚ.01, ⴚ.001] .01

Second-Language Learning Status

Second-Language Learners versus Mixed .01 .04 .24 [⫺.08, .10] .81

Native Language Speakers versus Second-Language Learners .01 .04 .19 [⫺.07, .08] .85

Native Language Speaker versus Mixed .02 .03 .53 [⫺.05, .09] .60

Types of language skills

Rapid Automatized Naming versus Phonological Awareness .08 .04 1.82 [⫺.01, .17] .07

Vocabulary versus Phonological Awareness .08 .04 1.78 [⫺.01, .16] .08

Oral Comprehension versus Phonological Awareness .07 .04 1.73 [⫺.01, .16] .09

Comprehensive Language versus Phonological Awareness .15 .06 2.30 [.02, .28] .02

Vocabulary versus Rapid Automatized Naming ⫺.003 .04 ⫺.06 [⫺.09, .09] .96

Oral Comprehension versus Rapid Automatized Naming ⫺.01 .04 ⫺.20 [⫺.09, .07] .84

Comprehensive Language versus Rapid Automatized Naming .07 .06 1.07 [⫺.06, .19] .29

Oral Comprehension versus Vocabulary ⫺.01 .03 ⫺.20 [⫺.06, .05] .84

Comprehensive Language versus Vocabulary .07 .06 1.24 [⫺.04, .18] .22

Comprehensive Language versus Oral Comprehension .08 .06 1.37 [⫺.03, .19] .17

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). Bolded number means significant after applying Benjamini-Hochberg procedure. There are

596 correlations and 160 independent samples. Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

After partialing out working memory and controlling for types of

working memory tasks (controlling for the medium effects), the

correlation between language and geometry was r⫽.31, 95% CI

[⫺.14, .65]. Taken together, working memory explained all the

variance in the relation between language and geometry.

Algebra. There were three studies, with independent samples

and 53 correlations between language and algebra partialing out

working memory. Results showed that based on these studies, the

correlation between language and algebra was r⫽.40, 95% CI

[.29, .49], the correlation between language and working memory

was r⫽.28, 95% CI [.09, .45], and the correlation between

working memory and algebra was r⫽.34, 95% CI [.21, .45]. After

partialing out working memory, the correlation between language

and algebra was r⫽.34, 95% CI [.16, .49]. After partialing out

working memory and controlling for types of working memory

tasks (controlling for the medium effects), the correlation between

language and algebra was r⫽.39, 95% CI [.28, .47]. Taken

together, working memory explained 3%⬃15% of the variance in

the relation between language and algebra.

Controlling for intelligence. There were 128 studies, with

141 independent samples and 1,550 correlations between language

and mathematics partialing out intelligence. Results showed that

based on these studies, the correlation between language and

mathematics was r⫽.39, 95% CI [.36, .42], the correlation

between language and intelligence was r⫽.35, 95% CI [.32, .37],

and the correlation between intelligence and mathematics was r⫽

.36, 95% CI [.34, .39]. After partialing out intelligence, the cor-

relation between language and mathematics was r⫽.30, 95% CI

[.27, .32]. After partialing out intelligence and controlling for types

of intelligence tasks (controlling for the medium effects), the

correlation between language and mathematics was r⫽.31, 95%

CI [.28, .33]. Taken together, intelligence explained about

21%⬃23% of the variance in the relation between language and

mathematics.

Numerical knowledge. There were 46 studies, with 49 inde-

pendent samples and 432 correlations between language and nu-

merical knowledge partialing out intelligence. The results showed

that based on these studies, the correlation between language and

numerical knowledge was r⫽.35, 95% CI [.30, .38], the corre-

lation between language and intelligence was r⫽.35, 95% CI

[.29, 40], and the correlation between intelligence and numerical

knowledge was r⫽.32, 95% CI [.28, .36]. After partialing out

intelligence, the correlation between language and numerical

knowledge was r⫽.25, 95% CI [.23, .29]. After partialing out

intelligence controlling for types of intelligence tasks (controlling

for the medium effects), the correlation between language and

Table 6

Moderation Analysis on the Relation Between Language and Word Problems

Measure Beta SE t 95% CI pvalue

Publication type

Peer-reviewed versus Other Types ⫺.05 .05 ⫺1.03 [⫺.15, .05] .30

Sample status

Typically Developing versus Atypically Developing .04 .04 .96 [⫺.04, .12] .34

SES

Low SES versus General/Unspecified .01 .04 .26 [⫺.07, .09] .79

Middle SES versus General/Unspecified .04 .05 .75 [⫺.06, .13] .45

Middle SES versus Low SES .02 .05 .48 [⫺.08, .12] .63

Language type

Alphabetic versus Nonalphabetic .16 .08 2.12 [.01, .31] .04

Language measurement type

Receptive versus Expressive .05 .05 1.21 [⫺.03, .14] .23

Receptive versus Receptive ⫹Expressive .01 .07 .20 [⫺.13, .15] .84

Expressive versus Receptive ⫹Expressive ⫺.04 .07 ⫺.57 [⫺.18, .10] .57

Age ⫺.002 .002 ⫺.63 [⫺.01, .003] .53

Second-language learning status

Second-Language Learners versus Mixed ⫺.19 .11 ⫺1.79 [⫺.41, .02] .08

Native Language Speakers versus Second-Language Learners .24 .10 2.31 [.03, .45] .02

Native Language Speaker versus Mixed .05 .04 1.17 [⫺.03, .13] .25

Types of language skills

Rapid Automatized Naming versus Phonological Awareness ⴚ.21 .06 ⴚ3.67 [ⴚ.32, ⴚ.10] <.001

Vocabulary versus Phonological Awareness .07 .06 1.18 [⫺.05, .18] .24

Oral Comprehension versus Phonological Awareness .06 .06 .98 [⫺.06, .17] .33

Comprehensive Language versus Phonological Awareness .08 .08 .96 [⫺.08, .24] .34

Vocabulary versus Rapid Automatized Naming .27 .05 5.89 [.18, .37] <.001

Oral Comprehension versus Rapid Automatized Naming .27 .05 5.42 [.17, .36] <.001

Comprehensive Language versus Rapid Automatized Naming .29 .07 4.20 [.15, .42] <.001

Oral Comprehension versus Vocabulary ⫺.01 .04 ⫺.24 [⫺.08, .06] .81

Comprehensive Language versus Vocabulary .01 .07 .17 [⫺.13, .15] .87

Comprehensive Language versus Oral Comprehension .02 .07 .30 [⫺.11, .15] .77

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). Bolded number means significant after applying Benjamini-Hochberg procedure. There are

302 correlations and 112 independent samples. Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

14 PENG ET AL.

numerical knowledge was r⫽.26, 95% CI [.23, .30]. Taken

together, intelligence explained about 26%⬃29% of the variance

in the relation between language and numerical knowledge.

Calculations. There were 82 studies, with 94 independent

samples and 615 correlations between language and calculations

partialing out intelligence. Results showed that based on these

studies, the correlation between language and calculations was r⫽

.35, 95% CI [.31, .39], the correlation between language and

intelligence was r⫽.34, 95% CI [.31, .37], and the correlation

between intelligence and calculations was r⫽.35, 95% CI [.31,

.38]. After partialing out intelligence, the correlation between

language and calculations was r⫽.26, 95% CI [.24, .29]. After

partialing out intelligence and controlling for types of intelligence

tasks (controlling for the medium effects), the correlation between

language and calculations was r⫽.27, 95% CI [.24, .30]. Taken

together, intelligence explained about 23%⬃26% of the variance

in the relation between language and calculations.

Word problems. There were 49 studies, with 53 independent

samples and 305 correlations between language and word prob-

lems partialing out intelligence. The results showed that based on

these studies, the correlation between language and word problems

was r⫽.45, 95% CI [.41, .49], the correlation between language

and intelligence was r⫽.36, 95% CI [.31, .41], and the correlation

between intelligence and word problems was r⫽.41, 95% CI [.37,

.45]. After partialing out intelligence, the correlation between

language and word problems was r⫽.35, 95% CI [.32, .40]. After

partialing out intelligence controlling for types of intelligence

tasks (controlling for the medium effects), the correlation between

language and word problems was r⫽.36, 95% CI [.33, .40].

Taken together, intelligence explained about 20%⬃22% of the

variance in the relation between language and word problems.

Fractions. There were nine studies, with nine independent

samples and 33 correlations between language and fractions par-

tialing out intelligence. The results showed that based on these

studies, the correlation between language and fractions was r⫽

.36, 95% CI [.28, .43], the correlation between language and

intelligence was r⫽.38, 95% CI [.28, .47], and the correlation

between intelligence and fractions was r⫽.39, 95% CI [.30, .47].

After partialing out intelligence, the correlation between language

and fractions was r⫽.25, 95% CI [.18, .30]. After partialing out

intelligence and controlling for types of intelligence tasks (con-

trolling for the medium effects), the correlation between language

and fractions was r⫽.25, 95% CI [.18, .31]. Taken together,

intelligence explained about 29% of the variance in the relation

between language and fractions.

Geometry. There were six studies, with seven independent

samples and 16 correlations between language and geometry par-

tialing out intelligence. Results showed that based on these studies,

the correlation between language and geometry was r⫽.34, 95%

CI [.15, .49], the correlation between language and intelligence

was r⫽.35, 95% CI [.18, .51], and the correlation between

intelligence and geometry was r⫽.31, 95% CI [.23, .39]. After

partialing out intelligence, the correlation between language and

geometry was r⫽.25, 95% CI [.10, .38]. Because we acquired

only nonverbal intelligence for the relation between language and

geometry, we did not run the partial correlation controlling for

types of intelligence tasks. Taken together, intelligence explained

about 26% of the variance in the relation between language and

geometry.

Algebra. There were six studies, with six independent sam-

ples and 13 correlations between language and algebra partialing

out intelligence. The results showed that based on these studies,

the correlation between language and algebra was r⫽.24, 95% CI

[.07, .39], the correlation between language and intelligence was

r⫽.32, 95% CI [.20, .43], and the correlation between intelligence

and algebra was r⫽.34, 95% CI [.25, .41]. After partialing out

intelligence, the correlation between language and algebra was r⫽

.15, 95% CI [⫺.03, .32]. Because we acquired only nonverbal

intelligence for the relation between language and algebra, we did

not run the partial correlation controlling for types of intelligence

tasks. Taken together, intelligence explained 38% of the relation

between language and algebra based on the data we acquired.

Controlling for intelligence and working memory. There

were 59 studies, with 66 independent samples and 1,469 correla-

tions between language and mathematics partialing out intelli-

gence and working memory. Results based on this pool of studies

showed that the correlation between language and mathematics

was r⫽.37, 95% CI [.34, .41]. After partialing out intelligence

and working memory, the correlation between language and math-

ematics was r⫽.17, 95% CI [.15, .20]. After partialing out

intelligence and working memory and controlling for types of

intelligence and working memory tasks (controlling for the me-

dium effects), the correlation between language and mathematics

was r⫽.22, 95% CI [.17, .26]. Taken together, intelligence and

working memory explained about 41%⬃54% of the variance in

the relation between language and mathematics.

Numerical knowledge. There were 22 studies, with 23 inde-

pendent samples and 517 correlations between language and nu-

merical knowledge partialing out intelligence and working mem-

ory. Results based on this pool of studies showed that the

correlation between language and numerical knowledge was r⫽

.30, 95% CI [.24, .35]. After partialing out intelligence and work-

ing memory, the correlation between language and numerical

knowledge was r⫽.22, 95% CI [.19, .25]. After partialing out

intelligence and working memory and controlling for types of

intelligence and working memory tasks (controlling for the me-

dium effects), the correlation between language and numerical

knowledge was r⫽.27, 95% CI [.22, .33]. Taken together,

intelligence and working memory explained about 10%⬃30% of

the variance in the relation between language and numerical

knowledge.

Calculations. There were 41 studies, with 47 independent

samples and 571 correlations between language and calculations

partialing out intelligence and working memory. Results based on

this pool of studies showed that the correlation between language

and calculations was r⫽.33, 95% CI [.27, .37]. After partialing

out intelligence and working memory, the correlation between

language and calculations was r⫽.19, 95% CI [.16, .22]. After

partialing out intelligence and working memory and controlling for

types of intelligence and working memory tasks (controlling for

the medium effects), the correlation between language and calcu-

lations was r⫽.22, 95% CI [.16, .27]. Taken together, intelligence

and working memory explained about 33%⬃42% of the variance

in the relation between language and calculations.

Word problems. There were 27 studies, with 29 independent

samples and 231 correlations between language and word prob-

lems partialing out intelligence and working memory. Results

based on this pool of studies showed that the correlation between

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

language and word problems was r⫽.46, 95% CI [.41, .51]. After

partialing out intelligence and working memory, the correlation

between language and word problems was r⫽.15, 95% CI [.12,

.18]. After partialing out intelligence and working memory and

controlling for types of intelligence and working memory tasks

(controlling for the medium effects), the correlation between lan-

guage and word problems was r⫽.24, 95% CI [.18, .29]. Taken

together, intelligence and working memory explained about

48%⬃67% of the variance in the relation between language and

word problems.

Fractions. There were five studies, with five independent

samples and 21 correlations between language and fractions

partialing out intelligence and working memory. Results based

on the pool of studies showed that the correlation between

language and fractions was r⫽.32, 95% CI [.21, .43]. After

partialing out intelligence and working memory, the correlation

between language and fractions was r⫽.18, 95% CI [.12, .23].

Because we did not have sufficient effect sizes for nonverbal

intelligence, we did not run the partial correlation analysis

controlling for types of intelligence and working memory tasks.

Taken together, intelligence and working memory explained

about 50% of the variance in the relation between language and

fractions.

Geometry. There were three studies, with three indepen-

dent samples and 19 correlations between language and geom-

etry partialing out intelligence and working memory. Results

based on this pool of studies showed that the correlation be-

tween language and geometry was r⫽.32, 95% CI [⫺.31, .75].

Because the relation between language and geometry based on

this pool of studies was not significant, we did not run the

partial correlation analysis controlling for intelligence and

working memory.

Algebra. There were two studies, with two independent

samples and five correlations between language and algebra

partialing out intelligence and working memory. Results based

on this pool of studies showed that the correlation between

language and algebra was r⫽.40, 95% CI [⫺.39, .84]. Because

the relation between language and algebra based on this pool of

studies was not significant, we did not run the partial correla-

tion analysis controlling for intelligence and working memory.

Moderation analyses based on partial correlations. Next,

we ran moderation analyses for partial relations between lan-

guage and mathematics controlling for intelligence and working

memory (see Table 7). After controlling for covariates, we did

not find any significant moderators. With respect to the relation

between language and numerical knowledge controlling for

intelligence and working memory (see Table 8), after control-

ling for covariates, only types of language skills emerged as a

significant moderator such that RAN showed a stronger relation

to numerical knowledge than did comprehensive language

skills, p⬍.01. With respect to the relation between language

and calculations controlling for intelligence and working mem-

ory (see Table 9), after controlling for covariates, we did not

find any significant moderators. With respect to the relation

between language and word problems controlling for intelli-

gence and working memory (see Table 10), after controlling for

covariates, we did not find any significant moderators. Because

we did not have sufficient studies (n⬍5), we did not run

moderation analyses for the partial correlations between lan-

guage and fractions/geometry/algebra.

Question 4: What Is the Longitudinal Relation

Between Language and Mathematics?

Last, we examined whether language and mathematics were

significantly correlated from a longitudinal perspective. We first

investigated whether language predicted later mathematics perfor-

mance partialing out initial mathematics performance. There were

61 studies, with 63 independent samples and 884 correlations, with

the majority of studies focusing on children before age 14 (around

3⬃14 years old) and the majority of prediction time intervals

spanning within 2 years. Results showed that language signifi-

cantly predicted later mathematics performance partialing out ini-

tial mathematics performance, r⫽.20, 95% CI [.17, .23]. We then

ran moderation analyses to investigate the predictive power of

different types of language skills for later mathematics perfor-

mance and whether time interval (the length of time between

Times 1 and 2) affected the relation. Results showed that after

controlling for covariates, types of mathematics skills at Times 1

and 2, types of language measures, second-language status, age,

and time interval (the length of time between Times 1 and 2), we

did not find types of language skills as a significant moderator,

ps⬎.05.

Next, we investigated whether mathematics performance at

Time 1 predicted later language partialing out initial language

performance. There were 26 studies, with 27 independent samples

and 178 correlations, with the majority of studies focusing on

children before age 14 (around 3⬃14 years old) and the majority

of prediction time intervals spanning within 2 years. Results

showed that mathematics performance at Time 1 significantly

predicted later language performance partialing out initial lan-

guage performance, r⫽.22, 95% CI [.17, .27]. We then ran

moderation analyses to investigate the predictive power of differ-

ent types of mathematics for later language skills and whether time

intervals affected the relation. The results showed that after con-

trolling for covariates, types of language skills at Times 1 and 2,

types of language measures at Times 1 and 2, second-language

status, age, and time interval, we did not find the type of mathe-

matics skills as a significant moderator, ps⬎.05.

Summary of Results

Taken together, these results indicate that the relation between

language and mathematics was significant and moderate and was

influenced by types of language skills, types of mathematics skills,

second-language learning status, and age. Specifically, after con-

trolling covariates and including all moderators simultaneously in

the metaregression models, we found the following:

1. Comprehensive language skills showed the strongest re-

lations to mathematics in general, numerical knowledge,

calculations, and word problems, whereas phonological

processing including phonological awareness and RAN

showed the weakest relations with mathematics in gen-

eral, numerical knowledge, calculations, and word prob-

lems. After partialing out both working memory and

intelligence, only RAN seemed to show the strongest

relation to numerical knowledge.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

16 PENG ET AL.

2. The relations between language and mathematics perfor-

mance in general were stronger among native language

speakers than among second-language learners. After

partialing out working memory and intelligence, there

were no differences between native language speakers

and second-language learners on the relation between

language and mathematics.

3. Advanced and more comprehensive mathematics skills,

such as solving word problems showed stronger relations

Table 7

Moderation Analysis on the Relation Between Language and Mathematics Controlling for Working Memory and Reasoning

Measure Beta SE t 95% CI pvalue

Publication type

Peer-Reviewed versus Other Types .11 .07 1.49 [⫺.03, .26] .14

Sample status

Typically Developing versus Atypically Developing .01 .03 .38 [⫺.05, .08] .70

SES

Low SES versus General/Unspecified ⫺.07 .04 ⫺1.81 [⫺.15, .01] .08

Middle SES versus General/Unspecified .04 .05 ⫺.73 [⫺.14, .07] .47

Middle SES versus low SES .03 .05 .64 [⫺.07, .13] .53

Language type

Alphabetic versus Nonalphabetic — — — — —

Language measurement type

Receptive versus Expressive .004 .04 .11 [⫺.07, .08] .91

Receptive versus Receptive ⫹Expressive .05 .06 .71 [⫺.08, .18] .48

Expressive versus Receptive ⫹Expressive .04 .05 .83 [⫺.06, .14] .41

Age ⫺.0002 .001 ⫺.22 [⫺.002, .001] .83

Second-language learning status

Second-Language Learners versus Mixed .003 .04 .08 [⫺.07, .08] .94

Native Language Speakers versus Second-Language Learners ⫺.06 .05 ⫺1.33 [⫺.15, .03] .19

Native Language Speaker versus Mixed ⫺.06 .04 ⫺1.56 [⫺.13, .02] .13

Types of language skills

Rapid Automatized Naming versus Phonological Awareness ⫺.02 .05 ⫺.44 [⫺.12, .08] .79

Vocabulary versus Phonological Awareness .02 .04 .47 [⫺.06, .10] .64

Oral Comprehension versus Phonological Awareness ⫺.002 .04 ⫺.05 [⫺.07, .07] .98

Comprehensive Language versus Phonological Awareness .08 .05 2.00 [⫺.0004, .16] .05

Vocabulary versus Rapid Automatized Naming .04 .05 .78 [⫺.06, .14] .43

Oral Comprehension versus Rapid Automatized Naming .02 .05 .42 [⫺.08, .12] .68

Comprehensive Language versus Rapid Automatized Naming .10 .05 2.08 [.003, .20] .04

Oral Comprehension versus Vocabulary ⫺.02 .03 ⫺.75 [⫺.07, .03] .45

Comprehensive Language versus Vocabulary .06 .04 1.71 [⫺.01, .13] .09

Comprehensive Language versus Oral Comprehension .08 .04 2.19 [.01, .15] .03

Types of mathematics skills

Calculations versus Numerical Knowledge ⫺.02 .03 ⫺.54 [⫺.08, .04] .59

Word Problems versus Numerical Knowledge ⫺.05 .03 ⫺1.53 [⫺.12, .02] .13

Fractions versus Numerical Knowledge ⫺.03 .04 ⫺.95 [⫺.11, .04] .35

Geometry versus Numerical Knowledge .02 .04 .44 [⫺.07, .11] .66

Algebra versus Numerical Knowledge ⫺.03 .04 ⫺.77 [⫺.10, .05] .45

Comprehensive Mathematics versus Numerical Knowledge ⫺.001 .06 ⫺.01 [⫺.12, .12] .99

Word problems versus Calculations ⫺.04 .03 ⫺1.21 [⫺.10, .02] .23

Fractions versus Calculations ⫺.02 .03 ⫺.51 [⫺.09, .05] .61

Geometry versus Calculations .04 .05 .72 [⫺.06, .14] .48

Algebra versus Calculations ⫺.01 .04 ⫺.32 [⫺.09, .07] .75

Comprehensive Mathematics versus Calculations .02 .06 .25 [⫺.11, .14] .81

Fractions versus Word Problems .02 .04 .47 [⫺.06, .10] .64

Geometry versus Word Problems .07 .05 1.37 [⫺.03, .18] .18

Algebra versus Word Problems .02 .04 .57 [⫺.06, .11] .57

Comprehensive Mathematics versus Word Problems .05 .06 .80 [⫺.08, .18] .43

Geometry versus Fractions .05 .06 .87 [⫺.07, .18] .39

Algebra versus Fractions .01 .05 .11 [⫺.09, .10] .91

Comprehensive Mathematics versus Fractions .03 .07 .49 [⫺.10, .17] .63

Algebra versus Geometry ⫺.05 .06 ⫺.86 [⫺.16, .06] .39

Comprehensive Mathematics versus Geometry ⫺.02 .07 ⫺.29 [⫺.16, .12] .77

Comprehensive Mathematics versus Algebra .03 .07 .39 [⫺.11, .17] .70

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). — ⫽no data for analysis. There are 1,457 correlations and 66 independent samples.

Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

with language than did relatively foundational mathemat-

ics skills, such as numerical knowledge and calculations.

However, the types of mathematics skills did not affect

the relation between language and mathematics after

partialing out working memory and intelligence.

4. Age moderated the relations between language in general/

phonological awareness/RAN and numerical knowledge/

calculations such that these relations decreased with age.

However, these age effects were not detected when work-

ing memory and intelligence were partialed out.

5. Working memory alone explained 8%⬃16% of the vari-

ance in the relation between language and mathematics in

general and 0%⬃21% of the variance in the relation

between language and different types of mathematics

skills; intelligence alone explained 21%–23% of the vari-

ance in the relation between language and mathematics in

general and 20%⬃38% of the variance in the relation

between language and different types of mathematics;

working memory and intelligence together (in one

model) can explain 49%⬃54% of the variance in the

relation between language and mathematics in general

and 27%⬃67% of the variance in the relation between

language and different types of mathematics.

6. Language significantly predicted later mathematics when

controlling for initial mathematics. Mathematics perfor-

mance significantly predicted later language when con-

trolling for initial language.

Discussion

In the present meta-analysis, we found that language was mod-

erately related to mathematics. More importantly, our moderation

and partial correlation analyses provided direct and indirect evi-

dence on the role of the medium and the thinking functions of

language in the relation between language and mathematics, re-

spectively. In the following sections, we discuss these findings in

detail.

The Medium Function of Language in Mathematics

Types of language/mathematics skills and development.

Based on the medium function hypothesis of language and the

accumulative nature of mathematics learning, we hypothesized

Table 8

Moderation Analysis on the Relation Between Language and Numerical Knowledge Controlling for Working Memory and Reasoning

Measure Beta SE t 95% CI pvalue

Publication type

Peer-reviewed versus Other Types .29 .17 1.71 [⫺.09, .68] .12

Sample status

Typically Developing versus Atypically Developing .03 .06 .58 [⫺.09, .16] .58

SES

Low SES versus General/Unspecified ⫺.05 .04 ⫺1.11 [⫺.14, .05] .29

Middle SES versus General/Unspecified .06 .08 .81 [⫺.11, .23] .44

Middle SES versus low SES .11 .08 1.32 [⫺.07, .29] .22

Language type

Alphabetic versus Nonalphabetic — — — — —

Language measurement type

Receptive versus Expressive .003 .06 .06 [⫺.13, .13] .95

Receptive versus Receptive ⫹Expressive .05 .11 .48 [⫺.19, .29] .64

Expressive versus Receptive ⫹Expressive .05 .07 .73 [⫺.10, .20] .49

Age ⫺.01 .02 ⫺.42 [⫺.05, .03] .68

Second-language learning status

Second-Language Learners versus Mixed — — — — —

Native Language Speakers versus Second-Language Learners — — — — —

Native Language Speaker versus Mixed ⫺.12 .11 ⫺1.14 [⫺.36, .12] .28

Types of language skills

Rapid Automatized Naming versus Phonological Awareness .10 .05 1.83 [⫺.02, .22] .10

Vocabulary versus Phonological Awareness ⫺.05 .07 ⫺.73 [⫺.20, .10] .48

Oral Comprehension versus Phonological Awareness ⫺.05 .09 ⫺.55 [⫺.24, .15] .60

Comprehensive Language versus Phonological Awareness ⫺.10 .07 ⫺1.38 [⫺.26, .06] .20

Vocabulary versus Rapid Automatized Naming ⫺.15 .06 ⫺2.34 [⫺.29, ⫺.01] .04

Oral Comprehension versus Rapid Automatized Naming ⫺.14 .08 ⫺1.80 [⫺.32, .03] .10

Comprehensive Language versus Rapid Automatized Naming ⴚ.20 .04 ⴚ4.64 [ⴚ.29, ⴚ.10] .001

Oral Comprehension versus Vocabulary .002 .06 .04 [⫺.12, .13] .97

Comprehensive Language versus Vocabulary ⫺.05 .07 ⫺.76 [⫺.20, .10] .46

Comprehensive Language versus Oral Comprehension ⫺.05 .08 ⫺.63 [⫺.24, .13] .54

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). — ⫽no data for analysis. Bolded number means significant after applying Benjamini-

Hochberg procedure. There are 517 correlations and 23 independent samples. Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

18 PENG ET AL.

that different types of language skills might be differentially re-

lated to different types of mathematics skills. Foundational lan-

guage skills (e.g., phonological processing) might be important

mediums for foundational mathematics skills (e.g., numerical

knowledge and calculations), and the importance of language

retrieval (e.g., RAN) for these foundational mathematics skills

would also increase with age. In contrast, more semantically

oriented language skills (e.g., vocabulary and oral comprehension)

are more important mediums for word-problem solving (Fuchs et

al., 2015, 2018). We indeed found different types of mathematics

related to phonological processing, vocabulary, and oral compre-

hension, although comprehensive language skills (tapping two or

more skills out of phonological processing [phonological aware-

ness and RAN], vocabulary, and oral comprehension) showed the

strongest relations to most mathematics tasks. Compared with

RAN, vocabulary and oral comprehension showed stronger rela-

tions with word problems. However, we also found that working

memory and intelligence explained more variance (48%⬃67%) in

the relation between language and word problems than in the

relation between language and foundational mathematics skills

(numerical knowledge and calculations, 27%⬃42%). These find-

ings suggest that the stronger relation between vocabulary/oral

comprehension and word problems may reflect the important

medium function of semantically oriented language skills for word

problems, but can also partly reflect that these semantically ori-

ented language skills bear a bigger thinking function for word

problems. That is, word problems draw heavily on making infer-

ences in the use of vocabulary and oral comprehension about the

relations among quantities beyond simply using vocabulary and

oral comprehension to decode text.

We did not find phonological processing to show stronger

relations to numerical knowledge/calculations in comparison with

vocabulary/oral comprehension. The relation between phonologi-

cal processing and numerical knowledge/calculations also did not

increase with age. Actually, we found that age exerted a negative

impact on the relations between phonological awareness/RAN and

numerical knowledge/calculations. This might be because both

RAN and numerical knowledge/calculations have less variance

among older students. However, after partialing out intelligence

and working memory, we did not find that age affected these

relations, and RAN seemed to show the strongest relation with

numerical knowledge. These findings suggest that the thinking

function of language could potentially mask the importance of

foundational language skills as important mediums for founda-

tional mathematics skills. That is, when cognitive processes are

controlled for, performing numerical tasks indeed relies more

Table 9

Moderation Analysis on the Relation Between Language and Calculations Controlling for Working Memory and Reasoning

Measure Beta SE t 95% CI pvalue

Publication type

Peer-Reviewed versus Other Types .18 .10 1.85 [⫺.02, .37] .07

Sample status

Typically Developing versus Atypically Developing .01 .04 .24 [⫺.06, .08] .81

SES

Low SES versus General/Unspecified ⫺.09 .05 ⫺1.92 [⫺.19, .005] .06

Middle SES versus General/Unspecified ⫺.07 .06 ⫺1.15 [⫺.20, .05] .26

Middle SES versus Low SES .02 .05 .44 [⫺.07, .12] .66

Language type

Alphabetic versus Nonalphabetic — — — — —

Language measurement type

Receptive versus Expressive ⫺.01 .05 ⫺.12 [⫺.11, .10] .91

Receptive versus Receptive ⫹Expressive .07 .08 .85 [⫺.09, .22] .40

Expressive versus Receptive ⫹Expressive .07 .04 1.99 [⫺.002, .15] .06

Age .002 .007 .31 [⫺.01, .02] .76

Second-language learning status

Second-Language Learners versus Mixed .0003 .06 .01 [⫺.12, .12] .99

Native Language Speakers versus Second-Language Learners ⫺.03 .06 ⫺.50 [⫺.15, .09] .62

Native Language Speaker versus Mixed ⫺.03 .04 ⫺.79 [⫺.10, .05] .43

Types of language skills

Rapid Automatized Naming versus Phonological Awareness ⫺.01 .05 ⫺.12 [⫺.11, .10] .91

Vocabulary versus Phonological Awareness .06 .05 1.07 [⫺.05, .17] .29

Oral Comprehension versus Phonological Awareness .03 .05 .64 [⫺.07, .14] .53

Comprehensive Language versus Phonological Awareness .06 .05 1.33 [⫺.03, .16] .19

Vocabulary versus Rapid Automatized Naming .06 .05 1.22 [⫺.04, .17] .23

Oral Comprehension versus Rapid Automatized Naming .04 .05 .78 [⫺.06, .14] .44

Comprehensive Language versus Rapid Automatized Naming .07 .04 1.55 [⫺.02, .16] .13

Oral Comprehension versus Vocabulary ⫺.03 .03 ⫺.77 [⫺.09, .04] .45

Comprehensive Language versus Vocabulary .01 .04 .14 [⫺.07, .08] .89

Comprehensive Language versus Oral Comprehension .03 .04 .86 [⫺.04, .10] .40

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than 2 categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in Alphabetic versus Nonalphabetic, Nonalphabetic

is the reference group in the dummy coding of language type). — ⫽no data for analysis. There are 571 correlations and 47 independent samples.

Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

heavily on the retrieval of mathematics facts based on language

compared with other mathematics skills. This finding is also in

line with Koponen et al.’s (2017) finding that RAN is a strong

predictor of the relation between language and calculations. Al-

though we did not find the salient retrieval role of language in

calculations as Koponen et al. (2017) did (partly due to the fact that

those researchers placed a great emphasis on relatively simple

calculations such as fact retrieval tasks and calculation fluency

tasks), their findings, together with ours, suggest that the retrieval

mechanism underlying RAN makes RAN an important variable in

explaining the variance of numerical knowledge and calculations.

The importance of using language as a medium to retrieve

mathematics knowledge for foundational mathematics also re-

ceives support from intervention and cross-cultural comparison

studies. Specifically, several intervention studies with both typi-

cally and atypically developing children have highlighted that the

involvement of language in numerical knowledge and calculations

may be most effective when language is used as a medium to

facilitate the consolidation and the retrieval of mathematics facts

(Geary, 1994). For example, Morgan et al. (2015) found that for

first graders with mathematics difficulties, instruction focused on

discussion/explanation for early numeracy and calculations was

not as effective as teacher-directed activities that focused on ex-

plicit and direct number knowledge instruction and practice. Rittle-

Johnson (2006) found that using language for self-explanation in

calculations did not produce more sophisticated procedures or

understanding, but tended to place more cognitive load on per-

forming calculation tasks, which sometimes led to incorrect pro-

cedures. Moreover, research on cross-cultural comparisons re-

vealed that Chinese children and adults often outperformed their

English-speaking counterparts in solving calculation problems

(LeFevre & Liu, 1997). The advantage in calculations among

Chinese individuals, especially in early development, has partly

been attributed to mathematics instruction in China, which puts a

strong emphasis on memorizing mathematics facts (e.g., rote mem-

ory of a multiplication table) and relies heavily on the retrieval of

mathematics facts in performing calculations (Geary, Bow-

Thomas, Liu, & Siegler, 1996; Liu, Ding, Xu, & Wang, 2017).

Second-language learning status. Research on mathematics

learning among second-language learners often emphasizes the

medium effects of the second language on acquiring mathematics-

specific terminology and expressions as well as on students’ com-

munication quality in mathematics classrooms (Moschkovich,

2002; Pimm, 1987; Schleppegrell, 2007). Thus, we hypothesized

that the relation between language and mathematics might be

stronger among second-language learners. However, our findings

Table 10

Moderation Analysis on the Relation Between Language and Word Problems Controlling for Working Memory and Reasoning

Measure Beta SE t 95% CI pvalue

Publication type

Peer-reviewed versus Other Types .06 .07 .79 [⫺.09, .21] .44

Sample status

Typically Developing versus Atypically Developing .02 .04 .46 [⫺.07, .10] .65

SES

Low SES versus General/Unspecified .004 .04 .08 [⫺.09, .10] .94

Middle SES versus General/Unspecified ⫺.01 .07 ⫺.21 [⫺.15, .13] .84

Middle SES versus Low SES ⫺.02 .05 ⫺.35 [⫺.12, .09] .73

Language type

Alphabetic versus Nonalphabetic — — — — —

Language measurement type

Receptive versus Expressive .05 .04 1.34 [⫺.03, .14] .20

Receptive versus Receptive ⫹Expressive ⫺.03 .05 ⫺.52 [⫺.13, .08] .61

Expressive versus Receptive ⫹Expressive ⫺.08 .06 ⫺1.26 [⫺.21, .05] .23

Age ⫺.001 .001 ⫺1.46 [⫺.002, .0004] .16

Second-language learning status

Second-Language Learners versus Mixed — — — — —

Native Language Speakers versus Second-Language Learners — — — — —

Native Language Speaker versus Mixed ⫺.03 .03 ⫺1.00 [⫺.10, .04] .33

Types of language skills

Rapid Automatized Naming versus Phonological Awareness ⫺.002 .05 ⫺.04 [⫺.12, .11] .97

Vocabulary versus Phonological Awareness ⫺.01 .07 ⫺.10 [⫺.15, .14] .93

Oral Comprehension versus Phonological Awareness ⫺.02 .06 ⫺.34 [⫺.15, .11] .74

Comprehensive Language versus Phonological Awareness .02 .06 .34 [⫺.11, .16] .74

Vocabulary versus Rapid Automatized Naming ⫺.004 .05 ⫺.09 [⫺.11, .10] .93

Oral Comprehension versus Rapid Automatized Naming ⫺.02 .04 ⫺.47 [⫺.10, .07] .65

Comprehensive Language versus Rapid Automatized Naming .02 .05 .51 [⫺.07, .12] .61

Oral Comprehension versus Vocabulary ⫺.01 .03 ⫺.51 [⫺.07, .04] .62

Comprehensive Language versus Vocabulary .03 .03 .98 [⫺.03, .09] .34

Comprehensive Language versus Oral Comprehension .04 .03 1.43 [⫺.02, .10] .17

Note. All covariates and moderators were entered in one model. Several models were run for thorough subgroup comparisons among moderators with

more than two categories. For the convenience of presentation, subgroup comparisons within categorical moderators are all listed in the model. CI ⫽

confidence interval. The second group in each group comparison variable is the reference group (e.g., in alphabetic versus nonalphabetic, nonalphabetic

is the reference group in the dummy coding of language type). — ⫽no data for analysis. There are 219 correlations and 29 independent samples.

Between-study sampling variance (␶

) is .01.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

20 PENG ET AL.

indicated that the relation between language and mathematics was

weaker among second-language learners than among native lan-

guage speakers. When partialing out working memory and intel-

ligence, we did not find a significant difference in the relation

between language and mathematics between native language

speakers and second-language learners. These findings, taken to-

gether, suggest that language may play an equally important me-

dium role in mathematics performance for both native language

speakers and second-language learners, but that the thinking func-

tion of language for mathematics may be more obvious for native

language speakers than for second-language learners.

One plausible explanation is that inadequate proficiency in the

second language among second-language learners may create a

bottleneck in their use of the second language to think in mathe-

matics tasks. This is also in line with some research that suggests

that teaching mathematics to second-language learners in their first

language can make it easier for them to engage in mathematical

reasoning (e.g., de Araujo et al., 2018; Martin & Fuchs, 2019).

Another explanation is that it may be more cognitively efficient for

second-language learners to rely on their first language to perform

mathematics. That is, using only the first language may reduce the

cognitive switching cost between the first language and the second

language during mathematics performance. This cognitive switch-

ing cost may be especially important for solving difficult mathe-

matics tasks, and using the first language can save more cognitive

resources for mathematics cognition (Clarkson, 2007; Rubinstein-

Ávila, Sox, Kaplan, & McGraw, 2015).

Partial correlations. One important piece of indirect evi-

dence on the medium function of language in mathematics comes

from the partial correlation analysis. We found that working mem-

ory and intelligence can each independently explain up to 25% of

the variance in the relation between language and mathematics,

and when combined together can explain up to about 50% of the

variance in the relation between language and mathematics. These

findings suggest that core cognition, although important as re-

flected in large variances (we discuss the importance of the think-

ing function of language in mathematics later), cannot explain all

variance in the relation between language and mathematics, sup-

porting the medium function of language in mathematics.

The Thinking Function of Language in Mathematics

Partial correlations. We begin by discussing partial correla-

tions in the context of the thinking function hypothesis, because

the findings from the partial correlations between language and

mathematics, controlling for working memory, intelligence, or

both, provided the most direct evidence for the thinking function of

language for mathematics. Specifically, working memory alone

explained 8%⬃16% of the variance in the relation between lan-

guage and mathematics in general, and 0%⬃21% of the variance

in the relations between language and different types of mathe-

matics skills. Interestingly, working memory did not seem to

explain more variance in the relations between language and

relatively complex mathematics skills (e.g., word problems, frac-

tions, and algebra) than in those between language and relatively

simple mathematics skills (e.g., numerical knowledge and calcu-

lations). This finding is line with the previous meta-analysis on the

relation between mathematics and working memory suggesting

that working memory was related to both advanced and founda-

tional mathematics skills to a similar degree, even when control-

ling for age (Peng et al., 2016).

Intelligence alone explained 21%⬃23% of the variance in the

relation between language and mathematics in general and

20%⬃38% of the variance in the relations between language and

different types of mathematics. Thus, in contrast to working mem-

ory, intelligence seemed to be more important in the relation

between language and mathematics. This may be partly because

intelligence tasks often tap working memory (Ackerman et al.,

2005), and intelligence exerts greater influence on language and

mathematics than working memory does (Peng et al., 2016; Peng

et al., 2018). Similar to working memory, intelligence did not seem

to explain more variance in the relations involving relatively

complex mathematics skills (e.g., word problems, fractions, and

algebra) than in those involving relatively simple mathematics

skills (e.g., numerical knowledge and calculations).

However, when both working memory and intelligence were

combined in a model, they explained 49%⬃54% of the variance in

the relation between language and mathematics in general and

27%⬃67% of the variance in the relations between language and

different types of mathematics. These findings, taken together,

support the hypothesis that working memory and intelligence are

the core cognitive components reflecting the thinking function of

language for mathematics. However, working memory and intel-

ligence did not explain all variance in the relation between lan-

guage and mathematics. Thus, language is important in and of

itself, potentially as a medium as discussed above, for mathemat-

ics. For example, research has suggested that, controlling for

cognition, language skills such as general vocabulary, mathematics

vocabulary, and language comprehension are demonstrated as

important parts of many important mathematics skills such as

calculation (e.g., Peng & Lin, 2019), solving word problems (e.g.,

Fuchs et al., 2018), and solving problems with fractions (Jordan et

al., 2013).

Types of language/mathematics skills and development.

We found that relatively complex language skills (e.g., compre-

hensive language and oral comprehension) showed the strongest

relations with mathematics performance in general, numerical

knowledge, calculations, and word problems, whereas relatively

simple language skills (e.g., phonological awareness and RAN)

showed the weakest relations with mathematics in general, numer-

ical knowledge, calculations, and word problems. Relatively com-

plex mathematic skills (e.g., solving word problems, comprehen-

sive mathematics skills) showed stronger relations with language

than did other types of mathematics skills. Working memory and

intelligence together seemed to explain more variance in the rela-

tions involving relatively more complex mathematics skills (e.g.,

solving word problems and fractions; e.g., about 48%⬃67%) than

in the relations involving relatively simple mathematics skills (e.g.,

numerical knowledge and calculations) and language (e.g., about

27%⬃42%). In addition, the relations between phonological

awareness/RAN and numerical knowledge/calculations decreased

with age, but age did not affect the relations between relatively

complex language skills (e.g., oral comprehension) and relatively

complex mathematics skills (e.g., word problems).

These findings, taken together, are in line with the thinking func-

tion hypothesis of language and the accumulative nature of mathe-

matics learning. That is, more complex mathematics skills may in-

volve more working memory, intelligence, and more complex and

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

semantically oriented language skills (e.g., language comprehension)

than do relatively simple mathematics skills. The thinking function of

language is relatively stable for these complex language and mathe-

matics skills across development, but the importance of the thinking

function of language decreases for relatively simple mathematics

skills across development, partly due to the increasing role of math-

ematics knowledge retrieval in performing simple mathematics tasks

(e.g., Geary et al., 2017; Lee & Bull, 2016).

Language measurement. Based on the thinking function hy-

pothesis of language, expressive language tasks would show stronger

relations to mathematics than would receptive language tasks. How-

ever, our findings indicate that expressive and receptive language

show comparable relations to mathematics, which is also in line with

previous research showing that expressive language is not necessarily

more working memory demanding than receptive language when

controlling for age and sample status (Adams & Gathercole, 1995;

Peng et al., 2018). This finding may suggest that the expressive/

receptive format of language should be considered a characteristic of

the medium function of language. Measuring language in either an

expressive format or a receptive format would not alter the degrees of

cognitive involvement in those measures. That said, our finding is

based on unselected samples. An expressive language measure may

be more cognitively demanding than a receptive language measure for

individuals with disabilities (e.g., language impairment or cognitive

deficits).

Mutualism. Based on the theory of mutualism, high-level cog-

nition (i.e., working memory and intelligence) and academic skills

mutually influence each other during development (Kievit et al.,

2017; McArdle et al., 2000; Peng et al., 2019; Peng et al., 2018;

Rindermann et al., 2010; Van Der Maas et al., 2006). This is because

working memory and intelligence are invested in the learning of

academic skills, and the learning of academic skills that involve

working memory and intelligence may serve as a “long-term inter-

vention” for those cognitive skills (e.g., Peng et al., 2019; Van Der

Maas et al., 2006). Our synthesis of the findings from longitudinal

studies suggests that language and mathematics significantly pre-

dicted each other, even when initial performance was controlled for.

This finding indirectly supports mutualism and provides further evi-

dence on the importance of the thinking function of language for

mathematics from a developmental perspective.

Limitations

We note several limitations in interpreting our findings. First, other

functions of language may play an indirect but still non-negligible role

in the relation between language and mathematics. For example, an

increasing number of studies of children with emotional and behav-

ioral disorders emphasize the social-emotional function of language

for behavioral management and academic performance. Often, we use

language to make meaning of sensations from our body and world in

a given context so that we can better regulate our emotions and

behaviors (Lindquist, MacCormack, & Shablack, 2015). Further, we

need language in order to navigate complex educational and social

systems, systems that often involve dyadic linguistic interactions

(Chow, 2018; Chow & Ekholm, 2019). Research on children with

emotional and behavioral disorders has shown that these children

often demonstrate language deficits, which may be one major reason

for their behavioral problems (Chow & Wehby, 2019; Hollo, Wehby,

& Oliver, 2014). Moreover, interventions that focus on language or

communication skills for children with language delays can signifi-

cantly reduce behavioral problems (Curtis, Kaiser, Estabrook, & Rob-

erts, 2019). Because emotional regulation and behavior management

are foundational for academic performance at school (Hinshaw, 1992;

Kremer, Flower, Huang, & Vaughn, 2016) as well as essential for

high-quality language-learning interactions (Chow & Ekholm, 2019),

the relation between language and mathematics may be partly ex-

plained by the social-emotional function of language (language ¡

emotion/behavior ¡mathematics learning/performance).

Second, in this study we considered only working memory and

intelligence as reflecting the thinking function of language, because

they are important for both language and mathematics (Ackerman et

al., 2005; Daneman & Merikle, 1996; Gathercole & Baddeley, 1990;

Peng et al., 2019). That said, other cognitive skills such as executive

functions and processing speed are also important for language and

mathematics (Bull & Johnston, 1997; Bull & Lee, 2014; Miller, Kail,

Leonard, & Tomblin, 2001; Weiland & Yoshikawa, 2013). Working

memory and intelligence overlap largely with (arguably contain)

executive functions (e.g., Baddeley, 1992; Rey-Mermet, Gade, Souza,

von Bastian, & Oberauer, 2019) and processing speed (e.g., process-

ing speed may share overlapping variance with RAN in predicting

mathematics ability; Georgiou, Tziraki, Manolitsis, & Fella, 2013),

yet including executive functions and processing speed (or other

important cognitive skills) may increase the importance of the think-

ing function of language for mathematics.

Third, to increase the generalizability of our findings, we included

heterogeneous samples (i.e., typically and nontypically developing

individuals). Although we controlled for sample types in our analyses,

we could not conduct further analyses within the atypical sample. This

is because the atypically developing group was quite heterogeneous,

including different developmental or acquired disorders such as learn-

ing disabilities, Alzheimer’s disease, hearing impairment, brain inju-

ries, and the like, and the sample sizes for those subgroups were very

small. Future studies should further examine whether different disor-

ders differentially influence the relations between language and math-

ematics. On a related note, there is research on patients with aphasia

(we did not have any aphasia sample in this study) in which some of

the patients could still perform nonlinguistic intelligence tasks and

mathematics tasks that involved relatively simple numerical knowl-

edge and calculations (Fedorenko & Varley, 2016). These findings

suggest that mathematics facts/knowledge in long-term memory may

not necessarily be stored or processed in a language format and thus

that the medium/thinking function of language may not explain all of

the retrieval and reasoning processes during mathematics tasks. Fu-

ture studies should investigate this issue further.

Fourth, we defined the types of language skills as phonological

processing (phonological awareness and RAN), vocabulary, and oral

comprehension. This categorization of language skills, although com-

monly used in studying the relations between language and academic

skills and emphasized in language assessment and instruction at

school (Chow & Wehby, 2018; Fuchs et al., 2015; LeFevre et al.,

2010; Peng & Lin, 2019; Purpura & Napoli, 2015), may not fully

capture the effects of more nuanced skills from the perspective of

linguistics (e.g., grammar on both the word and sentence level; mor-

phological skills tapping vocabulary measured in an oral comprehen-

sion format). Relatedly, we are also aware of the research/debate on

the dimensionality/construct of language, which suggests that differ-

ent language skills may reflect different constructs depending on

development. For example, some suggests receptive language, ex-

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

22 PENG ET AL.

pressive language, vocabulary, oral comprehension, and grammar

may be best captured as one construct across development (Bornstein

et al., 2014; Lervåg et al., 2018), while some suggests grammar,

vocabulary, and discourse may become gradually distinct with devel-

opment (Language and Reading Research Consortium, 2015). Thus,

future studies on the relation between language and mathematics

should consider the dimensionality of language and the interaction

between the dimensionality of language and development.

Last but not least, because of our small sample size, we were unable

to run analyses for some categories of moderators, and some of the

moderation analyses we conducted may have been underpowered. For

example, we did not have a sufficient number of studies to run

moderation analyses on the relation between language and geometry,

algebra, or fractions or moderation analyses on whether age moder-

ates the relations between phonological awareness/RAN/oral compre-

hension and fractions/geometry/algebra with/without controlling for

working memory and intelligence. We had only a small number of

effect sizes for the moderation analyses on the longitudinal studies,

and the results of those moderation analyses may be more exploratory

in nature and warrant further investigation.

Implications for Theory

With these limitations in mind, this is the first meta-analysis that

systematically investigated the relation between language and math-

ematics and the mechanisms underlying this relation. The findings

have important implications for our understanding of theories of

language and mathematics cognition. First, although the medium and

the thinking functions of language have long been discussed and

debated in the theory of language/cognition (Bruner, 1966; Car-

ruthers, 2002; Fetzer & Tiedemann, 2018; Vygotsky, 1986), little

research has disentangled the contributions of these functions to

academic performance. The present meta-analysis provides direct and

indirect empirical evidence to show that language bears both medium

and thinking functions in its relation to mathematics.

Second, the importance of these two functions of language varies

for different types of mathematics and across development. The

medium function of language is consistently important for all types of

mathematics, especially for the foundational mathematics skills (nu-

merical knowledge and simple calculations) that rely heavily on the

retrieval of mathematics knowledge based on language with devel-

opment. The thinking function of language is important for all types

of mathematics but is particularly important for advanced mathemat-

ics that heavily involves high-level cognition. However, the impor-

tance of the thinking function of language for foundational mathe-

matics seems to reduce over development, as individuals become

more efficient in retrieving mathematics knowledge through lan-

guage. Thus, the medium and the thinking functions of language may

interact with each other in learning/performing mathematics. That is,

the fluent use of language as a medium in mathematics performance,

especially for foundational mathematics skills, can possibly free up

cognitive resources for the use of the thinking function of language in

learning/performing advanced mathematics skills. This interaction

effect between the medium and the thinking functions of language

may become more important for mathematics with the accumulation

of mathematics knowledge.

Third, our findings further supplement the mutualism theory of

cognition. Previous research has suggested that core cognition (e.g.,

working memory and intelligence) and academic skills mutually

influence each other’s development. Our findings suggest that such

mutualistic effects between cognition and academic skills (e.g., math-

ematics) may be partly driven by the use of language in performing/

learning academic skills.

Considering all these findings, we tentatively propose a develop-

mental function hypothesis of language for mathematics (see Figure

2). Based on this hypothesis, children use language as a medium to

communicate, represent, and retrieve mathematics knowledge and

also as a thinking tool to facilitate working memory and reasoning

processes during mathematics performance and learning. The me-

dium function of language may become more important for funda-

mental mathematics skills with development, which further strength-

ens the role of the thinking function of language in advanced

mathematics. Such use of language may bolster the reciprocal effects

between cognition and mathematics during development.

Implications for Practice

Our findings also have implications for mathematics instruction.

First, mathematics instruction may need to place different emphases

on the medium and the thinking functions of language for different

types of mathematics skills during development. For foundational

mathematics skills, although language should be used to help children

gain conceptual knowledge, it is critical for children to use language

primarily as a medium (e.g., for retrieval) in foundational tasks after

they grasp conceptual knowledge. This is also in line with recent

research showing that early mathematics classroom instruction em-

phasizing discussion (the thinking function of language) is not as

effective as explicit instruction and practice, especially for children

with mathematics difficulties who lack foundational numerical

knowledge (Morgan et al., 2015). For advanced mathematics skills,

language should be used as an important tool to understand concep-

tual knowledge first before procedural knowledge/practice. This sug-

gestion is especially important for children with mathematics diffi-

culties and cognitive weaknesses, and it is supported by recent

findings that children with mathematics difficulties and very weak

working memory learn fractions better with conceptual activities

(using language to think) than with fluency activities (using language

as a medium; Fuchs et al., 2014).

On a related note, despite researchers advocating against the use of

ineffective “keyword” strategies, such strategies are commonly used

in teaching word-problem solving. Keyword strategies rely on iden-

tifying certain key words related to a specific mathematical operation

(e.g., total,sum,altogether,in all denote addition; Xin, Jitendra, &

Deatline-Buchman, 2005). Such a strategy focuses narrowly on the

meaning of vocabulary (the medium function of language) rather than

engaging students in high levels of understanding, thinking, and

reasoning (the thinking function of language). Given our finding that

word problems draw heavily on the thinking function, the instruc-

tional focus should be on facilitating students’ reasoning and infer-

ence making in solving word problems. For example, word-problem

solving strategies, such as schema-based instruction, in which stu-

dents build a schema for an underlying structure of a word problem,

and cognitive strategy instruction, in which students engage in meta-

cognitive processes of solving word problems, have been found to be

effective (e.g., Montague, 1992; Pennequin, Sorel, Nanty, & Fontaine,

2010; Powell & Fuchs, 2018; Xin et al., 2005).

Second, language proficiency at school entry varies enormously

(e.g., Norbury et al., 2016), and some children need extensive lan-

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

guage support (Castles, Rastle, & Nation, 2018). Indeed, language

intervention has gained increasing attention for children with mathe-

matics difficulties. Research has demonstrated that oral comprehen-

sion is malleable and can be taught to improve mathematics. For

example, Fuchs, Geary, Fuchs, Compton, and Hamlett (2016) found

that embedding supported self-explaining in a fractions intervention

significantly improved children’s accuracy and quality of explana-

tions for comparing fractions, in comparison with the same fractions

intervention but without a language component. This effect of expla-

nation is especially obvious for those with relatively low working

memory at the beginning of the intervention. In another study, Fuchs

et al. (2020) found that teaching children mathematics vocabulary and

integrating mathematics vocabulary instruction with text comprehen-

sion instruction for word problems can help at-risk children better

understand the word-problem schema and improve their word-

problem solving accuracy in comparison with instruction focused

solely on calculations. Likewise, Purpura, Napoli, Wehrspann, and

Gold (2017) have demonstrated that dialogic intervention focused on

quantitative and spatial mathematical language can improve pre-

schoolers’ mathematical language as well as early numeracy skills.

Third, it may be important for second-language learners to learn

mathematics in their second language. On the one hand, trying to

fluently use the second language in mathematics classrooms is nec-

essary for second-language learners to better engage in mathematics

classroom instruction and discussion (de Araujo et al., 2018). On the

other hand, learning numerical facts in a second language can form a

stronger representation of the numerical facts in the second language

than in the first language (Spelke & Tsivkin, 2001). These findings,

together with our finding that the second language constantly serves

as an important medium for mathematics performance among second-

language learners, suggest that for second-language learners, it is

important to master mathematics skills in their second language,

especially for the foundational skills at the beginning of formal

mathematics education. Because the medium function of language

may also facilitate the thinking function of language for mathematics

during development, second-language learners may gradually become

more efficient in using the second language as a thinking tool in

mathematical contexts. Using the second language to learn mathe-

matics with appropriate support may be more beneficial for second-

language learners in the long run.

Last, we have based our proposed developmental function hypoth-

esis of language for mathematics and the above-mentioned implica-

tions for practice on the correlational data from our meta-analysis.

Future experimental/intervention studies should further investigate

Figure 2. Developmental function hypothesis of language for mathematics. A solid arrow means the impact is

relatively stable with development. A dotted arrow with a “⫹” means the impact increases with development.

A dotted arrow with a “⫺” means the impact decreases with development. See the online article for the color

version of this figure.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

24 PENG ET AL.

whether training foundational language skills (e.g., phonological pro-

cessing) can increase foundational mathematics performance, whether

training higher order language skills (e.g., vocabulary and language

comprehension) can transfer to foundational mathematics as well as

advanced mathematics skills, and whether the language training ef-

fects on mathematics, if any, vary with students’ language skills,

mathematics knowledge, and cognitive abilities.

Conclusion

In summary, in this meta-analysis, we have investigated the relation

(and mechanism of this relation) between language and mathematics.

Our main findings provide some new and updated information as

follows: (a) language is significantly and moderately associated with

mathematics, and this relation is stronger for relatively complex

language and mathematics skills; (b) working memory and intelli-

gence can each explain up to 25% of the variance in the relation

between language and mathematics, and, when combined, they can

explain over 50% of the variance in this relation; (c) the retrieval of

language plays an especially important role in numerical knowledge

even when controlling for working memory and intelligence; (d) the

medium function of language for mathematics is equally important for

both native language speakers and second-language learners, but the

thinking function of language for mathematics is more important

among first-language speakers; (e) language and mathematics predict

each other in their development, suggesting a reciprocal relation

between the two.

References

References marked with an asterisk indicate studies included in the

meta-analysis.

ⴱ

Abrahamson, C. A. (1994). Reading disabilities and the third R: The

relationship between reading and arithmetic performance in reading

disabled children (Doctoral dissertation). Springfield, MA: American

International College.

ⴱ

Abreu-Lima, I. M., Leal, T. B., Cadima, J., & Gamelas, A. M. (2013).

Predicting child outcomes from preschool quality in Portugal. European

Journal of Psychology of Education, 28, 399–420. http://dx.doi.org/10

.1007/s10212-012-0120-y

Acheson, D. J., & MacDonald, M. C. (2009). Verbal working memory and

language production: Common approaches to the serial ordering of

verbal information. Psychological Bulletin, 135, 50–68. http://dx.doi

.org/10.1037/a0014411

Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005). Working memory

and intelligence: The same or different constructs? Psychological Bul-

letin, 131, 30–60. http://dx.doi.org/10.1037/0033-2909.131.1.30

ⴱ

Ackerman, P. T., Holloway, C. A., Youngdahl, P. L., & Dykman, R. A.

(2001). The double-deficit theory of reading disability does not fit all.

Learning Disabilities Research & Practice, 16, 152–160. http://dx.doi

.org/10.1111/0938-8982.00016

Ackerman, P. L., & Lohman, D. F. (2003). Education and g. In H. Nyborg

(Ed.), The scientific study of general intelligence (pp. 275–292). http://

dx.doi.org/10.1016/B978-008043793-4/50052-0

Adams, A. M., & Gathercole, S. E. (1995). Phonological working memory

and speech production in preschool children. Journal of Speech and

Hearing Research, 38, 403–414. http://dx.doi.org/10.1044/jshr.3802

.403

Ahmed, Y., Francis, D. J., York, M., Fletcher, J. M., Barnes, M., & Kulesz,

P. (2016). Validation of the direct and inferential mediation (DIME)

model of reading comprehension in grades 7 through 12. Contemporary

Educational Psychology, 44, 68–82. http://dx.doi.org/10.1016/j

.cedpsych.2016.02.002

ⴱ

Alloway, T. P., Gathercole, S. E., Adams, A. M., Willis, C., Eaglen, R.,

& Lamont, E. (2005). Working memory and phonological awareness as

predictors of progress towards early learning goals at school entry.

British Journal of Developmental Psychology, 23, 417–426. http://dx

.doi.org/10.1348/026151005X26804

ⴱ

Andersson, U. (2007). The contribution of working memory to children’s

mathematical word problem solving. Applied Cognitive Psychology, 21,

1201–1216.

ⴱ

Andersson, U., & Lyxell, B. (2007). Working memory deficit in children

with mathematical difficulties: A general or specific deficit? Journal of

Experimental Child Psychology, 96, 197–228. http://dx.doi.org/10.1016/

j.jecp.2006.10.001

ⴱ

Anvari, S. H., Trainor, L. J., Woodside, J., & Levy, B. A. (2002).

Relations among musical skills, phonological processing, and early

reading ability in preschool children. Journal of Experimental Child

Psychology, 83, 111–130. http://dx.doi.org/10.1016/S0022-0965(02)

00124-8

ⴱ

Aram, D. M., & Ekelman, B. L. (1988). Scholastic aptitude and achieve-

ment among children with unilateral brain lesions. Neuropsychologia,

26, 903–916. http://dx.doi.org/10.1016/0028-3932(88)90058-9

ⴱ

Ardila, A., Galeano, L. M., & Rosselli, M. (1998). Toward a model of

neuropsychological activity. Neuropsychology Review, 8, 171–190.

http://dx.doi.org/10.1023/A:1021618218943

ⴱ

Argulewicz, E. N., Bingenheimer, L. T., & Anderson, C. C. (1983).

Concurrent validity of the PPVT-R for Anglo-American and Mexican-

American students. Journal of Psychoeducational Assessment, 1, 163–

167. http://dx.doi.org/10.1177/073428298300100207

ⴱ

Arndt, D., Sahr, K., Opfermann, M., Leutner, D., & Fritz, A. (2013). Core

knowledge and working memory as prerequisites of early school arith-

metic. South African Journal of Childhood Education, 3, 1–20. http://

dx.doi.org/10.4102/sajce.v3i1.29

ⴱ

Arnold, D. H., Kupersmidt, J. B., Voegler-Lee, M. E., & Marshall, N.

(2012). The association between preschool children’s social functioning

and their emergent academic skills. Early Childhood Research Quar-

terly, 27, 376–386. http://dx.doi.org/10.1016/j.ecresq.2011.12.009

ⴱ

Arvedson, P. J. (1999). Numerical cognition in preschool children who

have specific language impairment (Doctoral dissertation). University of

California, Los Angeles, CA.

ⴱ

Austin, A. M. B., Blevins-Knabe, B., & Lokteff, M. (2013). Early math-

ematics and phonological awareness in two child care settings. Early

Child Development and Care, 183, 1197–1214. http://dx.doi.org/10

.1080/03004430.2012.716832

Baddeley, A. (1986). Working memory, reading and dyslexia. Advances in

Psychology, 34, 141–152. http://dx.doi.org/10.1016/s0166-4115(08)

61202-9

Baddeley, A. (1992). Working memory. Science, 255, 556–559. http://dx

.doi.org/10.1126/science.1736359

Baddeley, A. (2000). The episodic buffer: a new component of working

memory? Trends in Cognitive Sciences, 4, 417–423. http://dx.doi.org/

10.1016/S1364-6613(00)01538-2

ⴱ

Baddeley, A., Gardner, J. M., & Grantham-McGregor, S. (1995). Cross-

cultural cognition: Developing tests for developing countries. Applied

Cognitive Psychology, 9, S173–S195. http://dx.doi.org/10.1002/acp

.2350090711

Baddeley, A., Gathercole, S., & Papagno, C. (1998). The phonological loop

as a language learning device. Psychological Review, 105, 158–173.

http://dx.doi.org/10.1037/0033-295X.105.1.158

ⴱ

Barnes, M. A., Raghubar, K. P., English, L., Williams, J. M., Taylor, H.,

& Landry, S. (2014). Longitudinal mediators of achievement in mathe-

matics and reading in typical and atypical development. Journal of

Experimental Child Psychology, 119, 1–16. http://dx.doi.org/10.1016/j

.jecp.2013.09.006

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

ⴱ

Barnes, M. A., Stubbs, A., Raghubar, K. P., Agostino, A., Taylor, H.,

Landry, S.,...Smith-Chant, B. (2011). Mathematical skills in 3- and

5-year-olds with spina bifida and their typically developing peers: A

longitudinal approach. Journal of the International Neuropsychological

Society, 17, 431–444. http://dx.doi.org/10.1017/S1355617711000233

Barre, N., Morgan, A., Doyle, L. W., & Anderson, P. J. (2011). Language

abilities in children who were very preterm and/or very low birth weight:

A meta-analysis. The Journal of Pediatrics, 158, 766–774.e1. http://dx

.doi.org/10.1016/j.jpeds.2010.10.032

ⴱ

Bat-Haee, M. A., Mehryar, A. H., & Sabharwal, V. (1972). The correla-

tion between Piaget’s conservation of quantity tasks and three measures

of intelligence in a select group of children in Iran. The Journal of

Psychology, 80, 197–201. http://dx.doi.org/10.1080/00223980.1972

.9924796

ⴱ

Beck, F. W., Black, F. L., & Doles, J. (1985). The concurrent validity of

the Peabody Picture Vocabulary Test-revised relative to the comprehen-

sive tests of basic skills. Educational and Psychological Measurement,

45, 705–710. http://dx.doi.org/10.1177/001316448504500333

ⴱ

Becker, D. R., Miao, A., Duncan, R., & McClelland, M. M. (2014).

Behavioral self-regulation and executive function both predict visuomo-

tor skills and early academic achievement. Early Childhood Research

Quarterly, 29, 411–424. http://dx.doi.org/10.1016/j.ecresq.2014.04.014

ⴱ

Bell, N. L., Rucker, M., Finch, A. J., Jr., & Alexander, J. (2002).

Concurrent validity of the Slosson full-range intelligence test: Compar-

ison with the Wechsler intelligence scale for children–third ed. and the

Woodcock Johnson tests of achievement–revised. Psychology in the

Schools, 39, 31–38. http://dx.doi.org/10.1002/pits.10002

ⴱ

Billings, L. R. (2015). The Peabody picture vocabulary test-revised: Adult

alternate from reliability and comparisons with the Wechsler Adult

Intelligence Scale-revised and Wide Range Achievement Test-revised

(Doctoral dissertation). The University of San Francisco, San Francisco,

CA.

ⴱ

Bjork, I. M., & Bowyer-Crane, C. (2013). Cognitive skills used to solve

mathematical word problems and numerical operations: A study of 6-to

7-year-old children. European Journal of Psychology of Education, 28,

1345–1360. http://dx.doi.org/10.1007/s10212-012-0169-7

Blair, C., Gamson, D., Thorne, S., & Baker, D. (2005). Rising mean IQ:

Cognitive demand of mathematics education for young children, popu-

lation exposure to formal schooling, and the neurobiology of the pre-

frontal cortex. Intelligence, 33, 93–106. http://dx.doi.org/10.1016/j.intell

.2004.07.008

ⴱ

Bloland, R. N. (1998). A comparison of the relative effectiveness of a

measure of Piagetian cognitive development and a set of conventional

prognostic measures in the prediction of the future success of ninth- and

tenth-grade students in algebra (Doctoral dissertation). University of

Southern California, Los Angeles, CA.

ⴱ

Blums, A., Belsky, J., Grimm, K., & Chen, Z. (2017). Building links

between early socioeconomic status, cognitive ability, and math and

science achievement. Journal of Cognition and Development, 18, 16–

40. http://dx.doi.org/10.1080/15248372.2016.1228652

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2005).

Comprehensive meta-analysis (Version 2). Englewood, NJ: Biostat.

Bornstein, M. H., Hahn, C. S., Putnick, D. L., & Suwalsky, J. T. (2014).

Stability of core language skill from early childhood to adolescence: A

latent variable approach. Child Development, 85, 1346–1356. http://dx

.doi.org/10.1111/cdev.12192

ⴱ

Bowey, J. A. (1995). Socioeconomic status differences in preschool

phonological sensitivity and first-grade reading achievement. Journal of

Educational Psychology, 87, 476–487. http://dx.doi.org/10.1037/0022-

0663.87.3.476

ⴱ

Bracken, B. A., Prasse, D. P., & Breen, M. J. (1984). Concurrent validity

of the Woodcock-Johnson Psycho-Educational Battery with regular and

learning-disabled students. Journal of School Psychology, 22, 185–192.

http://dx.doi.org/10.1016/0022-4405(84)90038-4

ⴱ

Breen, M. I. (1983). A correlational analysis between the PPVT-R and

Woodcock-Johnson achievement cluster scores for nonreferred regular

education and learning disabled students. Psychology in the Schools, 20,

295–297. http://dx.doi.org/10.1002/1520-6807(198307)20:3⬍295::

AID-PITS2310200307⬎3.0.CO;2-7

ⴱ

Brock, H. (1982). Factor structure of intellectual and achievement mea-

sures for learning disabled children. Psychology in the Schools, 19,

297–304. http://dx.doi.org/10.1002/1520-6807(198207)19:3⬍297::

AID-PITS2310190306⬎3.0.CO;2-R

ⴱ

Brown, H. S. (1950). Differential prediction by the ACE. The Journal of

Educational Research, 44, 116–121. http://dx.doi.org/10.1080/

00220671.1950.10881846

Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Cambridge,

MA: Harvard University Press.

Bull, R., & Johnston, R. S. (1997). Children’s arithmetical difficulties:

Contributions from processing speed, item identification, and short-term

memory. Journal of Experimental Child Psychology, 65, 1–24. http://dx

.doi.org/10.1006/jecp.1996.2358

Bull, R., & Lee, K. (2014). Executive functioning and mathematics

achievement. Child Development Perspectives, 8, 36–41. http://dx.doi

.org/10.1111/cdep.12059

ⴱ

Bulotsky-Shearer, R. J., Bell, E. R., Carter, T. M., & Dietrich, S. L.

(2014). Peer play interactions and learning for low-income preschool

children: The moderating role of classroom quality. Early Education and

Development, 25, 815–840. http://dx.doi.org/10.1080/10409289.2014

.864214

ⴱ

Burchinal, M., Field, S., López, M. L., Howes, C., & Pianta, R. (2012).

Instruction in Spanish in pre-kindergarten classrooms and child out-

comes for English language learners. Early Childhood Research Quar-

terly, 27, 188–197. http://dx.doi.org/10.1016/j.ecresq.2011.11.003

ⴱ

Burchinal, M., Vernon-Feagans, L., Vitiello, V., & Greenberg, M. (2014).

Thresholds in the association between child care quality and child

outcomes in rural preschool children. Early Childhood Research Quar-

terly, 29, 41–51. http://dx.doi.org/10.1016/j.ecresq.2013.09.004

ⴱ

Bustamante, A. S., White, L. J., & Greenfield, D. B. (2017). Approaches

to learning and school readiness in Head Start: Applications to preschool

science. Learning and Individual Differences, 56, 112–118. http://dx.doi

.org/10.1016/j.lindif.2016.10.012

ⴱ

Cadima, J., Leal, T., & Burchinal, M. (2010). The quality of teacher-

student interactions: Associations with first graders’ academic and be-

havioral outcomes. Journal of School Psychology, 48, 457–482. http://

dx.doi.org/10.1016/j.jsp.2010.09.001

ⴱ

Cai, D., Li, Q. W., & Deng, C. P. (2013). Cognitive processing charac-

teristics of 6th to 8th grade Chinese students with mathematics learning

disability: Relationships among working memory, PASS processes, and

processing speed. Learning and Individual Differences, 27, 120–127.

http://dx.doi.org/10.1016/j.lindif.2013.07.008

Cain, K., Oakhill, J., & Lemmon, K. (2004). Individual differences in the

inference of word meanings from context: The influence of reading

comprehension, vocabulary knowledge, and memory capacity. Journal

of Educational Psychology, 96, 671–681. http://dx.doi.org/10.1037/

0022-0663.96.4.671

ⴱ

Callens, M., Tops, W., Stevens, M., & Brysbaert, M. (2014). An explor-

atory factor analysis of the cognitive functioning of first-year bachelor

students with dyslexia. Annals of Dyslexia, 64, 91–119. http://dx.doi.org/

10.1007/s11881-013-0088-6

ⴱ

Cantrell, J. A. (1992). A comparison of cognitive ability measures in the

prediction of achievement in a referred population of college students

(Doctoral dissertation). The Ohio State University, Columbus, Ohio.

Carey, S. (2009). The origin of concepts. New York, NY: Oxford Univer-

sity Press. http://dx.doi.org/10.1093/acprof:oso/9780195367638.001

.0001

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

26 PENG ET AL.

Carruthers, P. (2002). The cognitive functions of language. Behavioral and

Brain Sciences, 25, 657–674. http://dx.doi.org/10.1017/S0140525

X02000122

ⴱ

Carvajal, H., Kixmiller, J., Knapp, M., Vitt, J., & Weaver, K. A. (1991).

The use of the PPST and intelligence tests in teacher education pro-

grams. Bulletin of the Psychonomic Society, 29, 192–194. http://dx.doi

.org/10.3758/BF03342675

ⴱ

Casey, B. M., Pezaris, E., Fineman, B., Pollock, A., Demers, L., &

Dearing, E. (2015). A longitudinal analysis of early spatial skills com-

pared to arithmetic and verbal skills as predictors of fifth-grade girls’

math reasoning. Learning and Individual Differences, 40, 90–100.

http://dx.doi.org/10.1016/j.lindif.2015.03.028

Castles, A., Rastle, K., & Nation, K. (2018). Ending the reading wars:

Reading acquisition from novice to expert. Psychological Science in the

Public Interest, 19, 5–51. http://dx.doi.org/10.1177/1529100618772271

ⴱ

Cathcart, W. G. (1974). The correlation of selected nonmathematical

measures with mathematics achievement. Journal for Research in Math-

ematics Education, 5, 47–56. http://dx.doi.org/10.2307/748721

Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A

critical experiment. Journal of Educational Psychology, 54, 1–22. http://

dx.doi.org/10.1037/h0046743

Catts, H. W., Adlof, S. M., & Ellis Weismer, S. (2006). Language deficits

in poor comprehenders: A case for the simple view of reading. Journal

of Speech, Language, and Hearing Research, 49, 278–293. http://dx.doi

.org/10.1044/1092-4388(2006/023)

ⴱ

Cavanaugh, A. L. (1992). Computers, self-efficacy, and primary children

(Doctoral dissertation). The University of Connecticut, Mansfield, CN.

Chandler, P., & Sweller, J. (1991). Cognitive load theory and the format of

instruction. Cognition and Instruction, 8, 293–332. http://dx.doi.org/10

.1207/s1532690xci0804_2

ⴱ

Chansa-Kabali, T. (2017). Home literacy activities: Accounting for dif-

ferences in early grade literacy outcomes in low-income families in

Zambia. South African Journal of Childhood Education, 7, 1–9. http://

dx.doi.org/10.4102/sajce.v7i1.523

ⴱ

Cheng, D., Yan, X., Gao, Z., Xu, K., & Chen, Q. (2017). attention

contributes to arithmetic Deficits in new-Onset childhood absence epi-

lepsy. Frontiers in Psychiatry, 8, 166. http://dx.doi.org/10.3389/fpsyt

.2017.00166

Chow, J. C. (2018). Comorbid language and behavior problems: Develop-

ment, frameworks, and intervention. School Psychology Quarterly, 33,

356–360. http://dx.doi.org/10.1037/spq0000270

Chow, J. C., & Ekholm, E. (2018). Do published studies yield larger effect

sizes than unpublished studies in education and special education? A

meta-review. Educational Psychology Review, 30, 727–744.

Chow, J. C., & Ekholm, E. (2019). Language domains differentially predict

mathematics performance in young children. Early Childhood Research

Quarterly, 46, 179–186. http://dx.doi.org/10.1016/j.ecresq.2018.02.011

Chow, J. C., & Jacobs, M. (2016). The role of language in fraction

performance: A synthesis of literature. Learning and Individual Differ-

ences, 47, 252–257. http://dx.doi.org/10.1016/j.lindif.2015.12.017

Chow, J. C., & Wehby, J. H. (2018). Associations between language and

problem behavior: A systematic review and correlational meta-analysis.

Educational Psychology Review, 30, 61–82. http://dx.doi.org/10.1007/

s10648-016-9385-z

Chow, J. C., & Wehby, J. H. (2019). Effects of symbolic and nonsymbolic

equal-sign intervention in second-grade classrooms. The Elementary

School Journal, 119, 677–702. http://dx.doi.org/10.1086/703086

ⴱ

Christian, K., Morrison, F. J., & Bryant, F. B. (1998). Predicting kinder-

garten academic skills: Interactions among child care, maternal educa-

tion, and family literacy environments. Early Childhood Research Quar-

terly, 13, 501–521. http://dx.doi.org/10.1016/S0885-2006(99)80054-4

ⴱ

Chung, K. K., Liu, H., McBride, C., Wong, A. M. Y., & Lo, J. C. (2017).

How socioeconomic status, executive functioning and verbal interac-

tions contribute to early academic achievement in Chinese children.

Educational Psychology, 37, 402–420. http://dx.doi.org/10.1080/

01443410.2016.1179264

ⴱ

Cirino, P. T. (2011). The interrelationships of mathematical precursors in

kindergarten. Journal of Experimental Child Psychology, 108, 713–733.

http://dx.doi.org/10.1016/j.jecp.2010.11.004

ⴱ

Cirino, P. T., Child, A. E., & Macdonald, K. (2018). Longitudinal pre-

dictors of the overlap between reading and math skills. Contemporary

Educational Psychology, 54, 99–111. http://dx.doi.org/10.1016/j

.cedpsych.2018.06.002

ⴱ

Cirino, P. T., Tolar, T. D., Fuchs, L. S., & Huston-Warren, E. (2016).

Cognitive and numerosity predictors of mathematical skills in middle

school. Journal of Experimental Child Psychology, 145, 95–119. http://

dx.doi.org/10.1016/j.jecp.2015.12.010

ⴱ

Clark, C. A., Sheffield, T. D., Wiebe, S. A., & Espy, K. A. (2013).

Longitudinal associations between executive control and developing

mathematical competence in preschool boys and girls. Child Develop-

ment, 84, 662–677. http://dx.doi.org/10.1111/j.1467-8624.2012.01854.x

ⴱ

Clarke, B., Shanley, L., Kosty, D., Baker, S. K., Cary, M. S., Fien, H., &

Smolkowski, K. (2018). Investigating the incremental validity of cog-

nitive variables in early mathematics screening. School Psychology

Quarterly, 33, 264–271. http://dx.doi.org/10.1037/spq0000214

Clarkson, P. C. (2007). Australian Vietnamese students learning mathe-

matics: High ability bilinguals and their use of their languages. Educa-

tional Studies in Mathematics, 64, 191–215. http://dx.doi.org/10.1007/

s10649-006-4696-5

ⴱ

Coates, D. L., & Lewis, M. (1984). Early mother-infant interaction and

infant cognitive status as predictors of school performance and cognitive

behavior in six-year-olds. Child Development, 55, 1219–1230. http://dx

.doi.org/10.2307/1129991

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple

regression/correlation analysis for the behavioral sciences. New York,

NY: Routledge. http://dx.doi.org/10.4324/9780203774441

ⴱ

Coladarci, T., & McIntire, G. (1988). Gender, urbanicity, and ability!

Reading, 50, 24–72.

ⴱ

Collins, M. A., & Laski, E. V. (2019). Digging deeper: Shared deep

structures of early literacy and mathematics involve symbolic mapping

and relational reasoning. Early Childhood Research Quarterly, 46, 201–

212. http://dx.doi.org/10.1016/j.ecresq.2018.02.008

Common Core State Standards Initiative. (2010). National Governors

Association, Washington, DC.

ⴱ

Cornu, V., Schiltz, C., Martin, R., & Hornung, C. (2018). Visuo-spatial

abilities are key for young children’s verbal number skills. Journal of

Experimental Child Psychology, 166, 604–620. http://dx.doi.org/10

.1016/j.jecp.2017.09.006

ⴱ

Cowan, R., Donlan, C., Shepherd, D. L., Cole-Fletcher, R., Saxton, M., &

Hurry, J. (2011). Basic calculation proficiency and mathematics achieve-

ment in elementary school children. Journal of Educational Psychology,

103, 786–803. http://dx.doi.org/10.1037/a0024556

ⴱ

Cowan, R., & Powell, D. (2014). The contributions of domain-general and

numerical factors to third-grade arithmetic skills and mathematical

learning disability. Journal of Educational Psychology, 106, 214–229.

http://dx.doi.org/10.1037/a0034097

ⴱ

Critten, V., Campbell, E., Farran, E., & Messer, D. (2018). Visual per-

ception, visual-spatial cognition and mathematics: Associations and

predictions in children with cerebral palsy. Research in Developmental

Disabilities, 80, 180–191. http://dx.doi.org/10.1016/j.ridd.2018.06.007

Cross, A. M., Joanisse, M. F., & Archibald, L. M. D. (2019). Mathematical

abilities in children with developmental language disorder. Language,

Speech, and Hearing Services in Schools, 50, 150–163. http://dx.doi

.org/10.1044/2018_LSHSS-18-0041

Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role

of understanding in solving word problems. Cognitive Psychology, 20,

405–438. http://dx.doi.org/10.1016/0010-0285(88)90011-4

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

ⴱ

Cupples, L., Ching, T. Y., Crowe, K., Day, J., & Seeto, M. (2014).

Predictors of early reading skill in 5-year-old children with hearing loss

who use spoken language. Reading Research Quarterly, 49, 85–104.

http://dx.doi.org/10.1002/rrq.60

Currie, N. K., & Cain, K. (2015). Children’s inference generation: The role

of vocabulary and working memory. Journal of Experimental Child

Psychology, 137, 57–75. http://dx.doi.org/10.1016/j.jecp.2015.03.005

ⴱ

Curtis, K. (1992). An investigation of the predictive utility of the Satz

Battery for the early identification of learning disabilities (Master dis-

sertation). University of Toronto, Toronto, Ontario, Canada.

Curtis, P. R., Kaiser, A. P., Estabrook, R., & Roberts, M. Y. (2019). The

longitudinal effects of early language intervention on children’s problem

behaviors. Child Development, 90, 576–592. http://dx.doi.org/10.1111/

cdev.12942

Daneman, M., & Carpenter, P. A. (1980). Individual differences in working

memory and reading. Journal of Verbal Learning and Verbal Behavior,

19, 450–466. http://dx.doi.org/10.1016/S0022-5371(80)90312-6

Daneman, M., & Merikle, P. M. (1996). Working memory and language

comprehension: A meta-analysis. Psychonomic Bulletin & Review, 3,

422–433. http://dx.doi.org/10.3758/BF03214546

ⴱ

Davis, D. J. N. (1995). The relationship between reading and attitudes

and mathematical verbal problem-solving ability of introductory alge-

bra college students (Doctoral dissertation). University of Houston,

Houston, Texas.

ⴱ

Day, S. L. (2012). Examining the relations between self-regulation and

academic achievement in third grade students (Doctoral dissertation).

Florida State University, Tallahassee, FL.

de Araujo, Z., Roberts, S. A., Willey, C., & Zahner, W. (2018). English

learners in K–12 mathematics education: A review of the literature.

Review of Educational Research, 88, 879–919. http://dx.doi.org/10

.3102/0034654318798093

Deary, I. J., Strand, S., Smith, P., & Fernandes, C. (2007). Intelligence and

educational achievement. Intelligence, 35, 13–21. http://dx.doi.org/10

.1016/j.intell.2006.02.001

ⴱ

de Bilde, J., Boonen, T., Speybroeck, S., De Fraine, B., Van Damme, J.,

& Goos, M. (2015). Experiential education in kindergarten: Associations

with school adjustment and the moderating role of initial achievement.

The Elementary School Journal, 116, 173–197. http://dx.doi.org/10

.1086/683802

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.

http://dx.doi.org/10.1016/0010-0277(92)90049-N

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional

model of number processing. Mathematical Cognition, 1, 83–120.

ⴱ

Deloche, G., Hannequin, D., Carlomagno, S., Agniel, A., Dordain, M., &

Pasquier, F. (1995). Calculation and number processing in mild Alzhei-

mer’s disease. Journal of Clinical and Experimental Neuropsychology,

17, 634–639. http://dx.doi.org/10.1080/01688639508405151

ⴱ

Demetriou, A., Merrell, C., & Tymms, P. (2017). Mapping and predicting

literacy and reasoning skills from early to later primary school. Learning

and Individual Differences, 54, 217–225. http://dx.doi.org/10.1016/j

.lindif.2017.01.023

ⴱ

De Smedt, B., & Boets, B. (2010). Phonological processing and arithmetic

fact retrieval: Evidence from developmental dyslexia. Neuropsycholo-

gia, 48, 3973–3981. http://dx.doi.org/10.1016/j.neuropsychologia.2010

.10.018

ⴱ

De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is

phonological processing related to individual differences in children’s

arithmetic skills? Developmental Science, 13, 508–520. http://dx.doi

.org/10.1111/j.1467-7687.2009.00897.x

ⴱ

Dinehart, L., & Manfra, L. (2013). Associations between low-income

children’s fine motor skills in preschool and academic performance in

second grade. Early Education and Development, 24, 138–161. http://

dx.doi.org/10.1080/10409289.2011.636729

ⴱ

Donker, M., Kroesbergen, E., Slot, E., Van Viersen, S., & De Bree, E.

(2016). Alphanumeric and non-alphanumeric Rapid Automatized Nam-

ing in children with reading and/or spelling difficulties and mathematical

difficulties. Learning and Individual Differences, 47, 80–87. http://dx

.doi.org/10.1016/j.lindif.2015.12.011

Donlan, C., Cowan, R., Newton, E. J., & Lloyd, D. (2007). The role of

language in mathematical development: Evidence from children with

specific language impairments. Cognition, 103, 23–33. http://dx.doi.org/

10.1016/j.cognition.2006.02.007

ⴱ

Downer, J. T., & Pianta, R. C. (2006). Academic and cognitive function-

ing in first grade: Associations with earlier home and child care predic-

tors and with concurrent home and classroom experiences. School Psy-

chology Review, 35, 11–31.

ⴱ

Duncan, R. J., McClelland, M. M., & Acock, A. C. (2017). Relations

between executive function, behavioral regulation, and achievement:

Moderation by family income. Journal of Applied Developmental Psy-

chology, 49, 21–30. http://dx.doi.org/10.1016/j.appdev.2017.01.004

ⴱ

Dunn, D. W., Johnson, C. S., Perkins, S. M., Fastenau, P. S., Byars, A. W.,

deGrauw, T. J., & Austin, J. K. (2010). Academic problems in children

with seizures: Relationships with neuropsychological functioning and

family variables during the 3 years after onset. Epilepsy & Behavior, 19,

455–461. http://dx.doi.org/10.1016/j.yebeh.2010.08.023

ⴱ

Dupere, V., Leventhal, T., Crosnoe, R., & Dion, E. (2010). Understanding

the positive role of neighborhood socioeconomic advantage in achieve-

ment: The contribution of the home, child care, and school environ-

ments. Developmental Psychology, 46, 1227–1244. http://dx.doi.org/10

.1037/a0020211

ⴱ

Durand, M., Hulme, C., Larkin, R., & Snowling, M. (2005). The cognitive

foundations of reading and arithmetic skills in 7- to 10-year-olds. Jour-

nal of Experimental Child Psychology, 91, 113–136. http://dx.doi.org/

10.1016/j.jecp.2005.01.003

Egger, M., Davey Smith, G., Schneider, M., & Minder, C. (1997). Bias in

meta-analysis detected by a simple, graphical test. British Medical

Journal, 315, 629–634. http://dx.doi.org/10.1136/bmj.315.7109.629

ⴱ

Einarsdóttir, J. T., Björnsdóttir, A., & Símonardóttir, I. (2016). The

predictive value of preschool language assessments on academic

achievement: A 10-year longitudinal study of Icelandic children. Amer-

ican Journal of Speech-Language Pathology, 25, 67–79. http://dx.doi

.org/10.1044/2015_AJSLP-14-0184

Elbro, C. (1996). Early linguistic abilities and reading development: A

review and a hypothesis. Reading and Writing, 8, 453–485. http://dx

.doi.org/10.1007/BF00577023

Ellis Weismer, S., Evans, J., & Hesketh, L. J. (1999). An examination of

verbal working memory capacity in children with specific language

impairment. Journal of Speech, Language, and Hearing Research, 42,

1249–1260. http://dx.doi.org/10.1044/jslhr.4205.1249

Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory.

Psychological Review, 102, 211–245. http://dx.doi.org/10.1037/0033-

295X.102.2.211

ⴱ

Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A.,

& Senn, T. E. (2004). The contribution of executive functions to emer-

gent mathematic skills in preschool children. Developmental Neuropsy-

chology, 26, 465–486. http://dx.doi.org/10.1207/s15326942dn2601_6

Evans, J. S. B., & Stanovich, K. E. (2013). Dual-process theories of higher

cognition: Advancing the debate. Perspectives on Psychological Sci-

ence, 8, 223–241. http://dx.doi.org/10.1177/1745691612460685

ⴱ

Faux, D. K. (1985). The relationship of spatial and memory factors to

reading and arithmetic learning disabilities in children (Doctoral disser-

tation). McMaster University, Hamilton, Ontario, Canada.

ⴱ

Fazio, B. B. (1999). Arithmetic calculation, short-term memory, and

language performance in children with specific language impairment: A

5-year follow-up. Journal of Speech, Language, and Hearing Research,

42, 420–431. http://dx.doi.org/10.1044/jslhr.4202.420

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

28 PENG ET AL.

Fedorenko, E. (2014). The role of domain-general cognitive control in

language comprehension. Frontiers in Psychology, 5, 335. http://dx.doi

.org/10.3389/fpsyg.2014.00335

Fedorenko, E., & Varley, R. (2016). Language and thought are not the

same thing: Evidence from neuroimaging and neurological patients.

Annals of the New York Academy of Sciences, 1369, 132–153. http://dx

.doi.org/10.1111/nyas.13046

ⴱ

Ferrari, M., & Palladino, P. (2012). A longitudinal study of English as

foreign language learning: L1 predictors in Italian students. Applied

Cognitive Psychology, 26, 616–625. http://dx.doi.org/10.1002/acp.2839

Fetzer, M., & Tiedemann, K. (2018). The interplay of language and objects

in the process of abstracting. In J. Moschkovich, D. Wagner, A. Bose, J.

Rodrigues, & M. Schütte (Eds.), Language and communication in math-

ematics education, international perspectives (pp. 91–103). Dordrecht,

the Netherlands: Springer. http://dx.doi.org/10.1007/978-3-319-75055-

2_8

ⴱ

Fitzpatrick, C., McKinnon, R. D., Blair, C. B., & Willoughby, M. T.

(2014). Do preschool executive function skills explain the school read-

iness gap between advantaged and disadvantaged children? Learning

and Instruction, 30, 25–31. http://dx.doi.org/10.1016/j.learninstruc.2013

.11.003

ⴱ

Foley, T. E. (2003). Community college students’ understanding of frac-

tions: An investigation of the cognitive and metacognitive characteristics

of students verbalizations while problem solving (Doctoral dissertation).

University of Connecticut, Mansfield, CT.

ⴱ

Foreman-Murray, L., & Fuchs, L. S. (2019). Quality of explanation as an

indicator of fraction magnitude understanding. Journal of Learning Disabil-

ities, 52, 181–191. http://dx.doi.org/10.1177/0022219418775120

ⴱ

Forsyth, S. R., & Powell, S. R. (2017). Differences in the mathematics-

vocabulary knowledge of fifth-grade students with and without learning

difficulties. Learning Disabilities Research & Practice, 32, 231–245.

http://dx.doi.org/10.1111/ldrp.12144

ⴱ

Foster, M. E., Anthony, J. L., Clements, D. H., & Sarama, J. H. (2015).

Processes in the development of mathematics in kindergarten children

from Title 1 schools. Journal of Experimental Child Psychology, 140,

56–73. http://dx.doi.org/10.1016/j.jecp.2015.07.004

Francis, D. J., Kulesz, P. A., & Benoit, J. S. (2018). Extending the simple

view of reading to account for variation within readers and across texts:

The complete view of reading (CVRi). Remedial and Special Education,

39, 274–288. http://dx.doi.org/10.1177/0741932518772904

ⴱ

Freeman, H. (2018). Developmental predictors of early numeracy out-

comes (Master dissertation). University of the Sciences in Philadelphia,

Philadelphia, PA.

Friso-Van Den Bos, I., Van Der Ven, S. H., Kroesbergen, E. H., & Van

Luit, J. E. (2013). Working memory and mathematics in primary school

children: A meta-analysis. Educational Research Review, 10, 29–44.

http://dx.doi.org/10.1016/j.edurev.2013.05.003

ⴱ

Frost, B. P. (1968). Anxiety and educational achievement. The British

Journal of Educational Psychology, 38, 293–301. http://dx.doi.org/10

.1111/j.2044-8279.1968.tb02022.x

ⴱ

Fuchs, L. S., Compton, D. L., Fuchs, D., Hollenbeck, K. N., Craddock,

C. F., & Hamlett, C. L. (2008). Dynamic assessment of algebraic

learning in predicting third graders’ development of mathematical prob-

lem solving. Journal of Educational Psychology, 100, 829–850. http://

dx.doi.org/10.1037/a0012657

ⴱ

Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., &

Hamlett, C. L. (2005). The prevention, identification, and cognitive

determinants of math difficulty. Journal of Educational Psychology, 97,

493–513. http://dx.doi.org/10.1037/0022-0663.97.3.493

ⴱ

Fuchs, L. S., Compton, D. L., Fuchs, D., Powell, S. R., Schumacher, R. F.,

Hamlett, C. L.,...Vukovic, R. K. (2012). Contributions of domain-

general cognitive resources and different forms of arithmetic develop-

ment to pre-algebraic knowledge. Developmental Psychology, 48, 1315–

1326. http://dx.doi.org/10.1037/a0027475

ⴱ

Fuchs, L. S., Fuchs, D., Compton, D. L., Hamlett, C. L., & Wang, A. Y.

(2015). Is word-problem solving a form of text comprehension? Scien-

tific Studies of Reading, 19, 204–223. http://dx.doi.org/10.1080/

10888438.2015.1005745

ⴱ

Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M.,

Capizzi, A. M.,...Fletcher, J. M. (2006). The cognitive correlates of

third-grade skill in arithmetic, algorithmic computation, and arithmetic

word problems. Journal of Educational Psychology, 98, 29–43. http://

dx.doi.org/10.1037/0022-0663.98.1.29

Fuchs, L. S., Seethaler, P. M., Sterba, S. K., Craddock, C., Fuchs, D.,

Compton, D. L.,...Changas, P. (2020). Closing the word-problem

achievement gap in first grade: Schema-based word-problem interven-

tion with embedded language comprehension instruction. Journal of

Educational Psychology. Advance online publication. http://dx.doi.org/

10.1037/edu0000467

ⴱ

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Lambert, W., Stuebing, K., &

Fletcher, J. M. (2008). Problem solving and computational skill: Are

they shared or distinct aspects of mathematical cognition? Journal of

Educational Psychology, 100, 30–47. http://dx.doi.org/10.1037/0022-

0663.100.1.30

Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., & Hamlett, C. L.

(2016). Pathways to third-grade calculation versus word-reading com-

petence: Are they more alike or different? Child Development, 87,

558–567. http://dx.doi.org/10.1111/cdev.12474

ⴱ

Fuchs, L. S., Gilbert, J. K., Fuchs, D., Seethaler, P. M., & Martin, B. N.

(2018). Text comprehension and oral language as predictors of word-

problem solving: Insights into word-problem solving as a form of text

comprehension. Scientific Studies of Reading, 22, 152–166. http://dx.doi

.org/10.1080/10888438.2017.1398259

ⴱ

Fuchs, L. S., Gilbert, J. K., Powell, S. R., Cirino, P. T., Fuchs, D., Hamlett,

C.L.,...Tolar, T. D. (2016). The role of cognitive processes,

foundational math skill, and calculation accuracy and fluency in word-

problem solving versus prealgebraic knowledge. Developmental Psy-

chology, 52, 2085–2098. http://dx.doi.org/10.1037/dev0000227

ⴱ

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L.,

Cirino, P. T.,...Changas, P. (2013). Improving at-risk learners’

understanding of fractions. Journal of Educational Psychology, 105,

683–700. http://dx.doi.org/10.1037/a0032446

Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J.,

Malone, A.,...Changas, P. (2014). Does working memory moderate the

effects of fraction intervention? An aptitude–treatment interaction. Jour-

nal of Educational Psychology, 106, 499–514. http://dx.doi.org/10

.1037/a0034341

ⴱ

Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics

ability in preschoolers from low-income homes: Contributions of inhib-

itory control. Developmental Science, 16, 136–148. http://dx.doi.org/10

.1111/desc.12013

ⴱ

Fuhs, M. W., Nesbitt, K. T., Farran, D. C., & Dong, N. (2014). Longitu-

dinal associations between executive functioning and academic skills

across content areas. Developmental Psychology, 50, 1698–1709. http://

dx.doi.org/10.1037/a0036633

ⴱ

Fuller, R., Nopoulos, P., Arndt, S., O’Leary, D., Ho, B. C., & Andreasen,

N. C. (2002). Longitudinal assessment of premorbid cognitive function-

ing in patients with schizophrenia through examination of standardized

scholastic test performance. The American Journal of Psychiatry, 159,

1183–1189. http://dx.doi.org/10.1176/appi.ajp.159.7.1183

Fyfe, E. R., Matz, L. E., Hunt, K. M., & Alibali, M. W. (2019). Mathe-

matical thinking in children with developmental language disorder: The

roles of pattern skills and verbal working memory. Journal of Commu-

nication Disorders, 77, 17–30. http://dx.doi.org/10.1016/j.jcomdis.2018

.11.001

ⴱ

Gardner-Neblett, N., DeCoster, J., & Hamre, B. K. (2014). Linking

preschool language and sustained attention with adolescent achievement

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

through classroom self-reliance. Journal of Applied Developmental Psy-

chology, 35, 457–467. http://dx.doi.org/10.1016/j.appdev.2014.09.003

ⴱ

Garrett, H. E. (1930). A study of the CAVD intelligence examination. The

Journal of Educational Research, 21, 103–108. http://dx.doi.org/10

.1080/00220671.1930.10880021

ⴱ

Gathercole, S. E., Alloway, T. P., Willis, C., & Adams, A. M. (2006).

Working memory in children with reading disabilities. Journal of Ex-

perimental Child Psychology, 93, 265–281. http://dx.doi.org/10.1016/j

.jecp.2005.08.003

Gathercole, S. E., & Baddeley, A. D. (1990). Phonological memory deficits

in language disordered children: Is there a causal connection? Journal of

Memory and Language, 29, 336–360. http://dx.doi.org/10.1016/0749-

596X(90)90004-J

Gathercole, S. E., & Baddeley, A. D. (1993). Phonological working mem-

ory: A critical building block for reading development and vocabulary

acquisition? European Journal of Psychology of Education, 8, 259–272.

http://dx.doi.org/10.1007/BF03174081

ⴱ

Gathercole, S. E., Tiffany, C., Briscoe, J., & Thorn, A. (2005). Develop-

mental consequences of poor phonological short-term memory function

in childhood: A longitudinal study. Journal of Child Psychology and

Psychiatry, 46, 598–611. http://dx.doi.org/10.1111/j.1469-7610.2004

.00379.x

Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsycho-

logical, and genetic components. Psychological Bulletin, 114, 345–362.

http://dx.doi.org/10.1037/0033-2909.114.2.345

Geary, D. C. (1994). Children’s mathematical development: Research and

practical applications (1st ed.). Washington, DC: American Psycholog-

ical Association. http://dx.doi.org/10.1037/10163-000

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of

Learning Disabilities, 37, 4–15. http://dx.doi.org/10.1177/002221940

40370010201

ⴱ

Geary, D. C. (2011). Cognitive predictors of achievement growth in

mathematics: A 5-year longitudinal study. Developmental Psychology,

47, 1539–1552. http://dx.doi.org/10.1037/a0025510

Geary, D. C., Bow-Thomas, C. C., Liu, F., & Siegler, R. S. (1996).

Development of arithmetical competencies in Chinese and American

children: Influence of age, language, and schooling. Child Development,

67, 2022–2044. http://dx.doi.org/10.2307/1131607

Geary, D. C., Nicholas, A., Li, Y., & Sun, J. (2017). Developmental change

in the influence of domain-general abilities and domain-specific knowl-

edge on mathematics achievement: An eight-year longitudinal study.

Journal of Educational Psychology, 109, 680–693. http://dx.doi.org/10

.1037/edu0000159

Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the

convergence of componential and psychometric models. Intelligence,

16, 47–80. http://dx.doi.org/10.1016/0160-2896(92)90025-M

ⴱ

Georgiou, G. K., Tziraki, N., Manolitsis, G., & Fella, A. (2013). Is rapid

automatized naming related to reading and mathematics for the same

reason(s)? A follow-up study from kindergarten to Grade 1. Journal of

Experimental Child Psychology, 115, 481–496. http://dx.doi.org/10

.1016/j.jecp.2013.01.004

Georgiou, G. K., Wei, W., Inoue, T., & Deng, C. (in press). Are the

Relations of RAN with Reading and Mathematics Accuracy and Flu-

ency. Journal of Educational Psychology.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo,

J. (2009). Mathematics instruction for students with learning disabilities:

A meta-analysis of instructional components. Review of Educational

Research, 79, 1202–1242. http://dx.doi.org/10.3102/0034654309334431

ⴱ

Ghaleb, M. S. (1992). Performance and solution strategies of Arabic-

speaking second-graders in simple addition and subtraction word prob-

lems and relations of performance to their degree of bilingualism

(Doctoral dissertation). University of Wisconsin-Madison, Madison, WI.

ⴱ

Gilligan, K. A., Flouri, E., & Farran, E. K. (2017). The contribution of

spatial ability to mathematics achievement in middle childhood. Journal

of Experimental Child Psychology, 163, 107–125. http://dx.doi.org/10

.1016/j.jecp.2017.04.016

Gleason, J. B., & Ratner, N. B. (2005). The development of language. 6th.

Boston: Allyn and Bacon.

ⴱ

Gold, D. P., Andres, D., Etezadi, J., Arbuckle, T., Schwartzman, A., &

Chaikelson, J. (1995). Structural equation model of intellectual change

and continuity and predictors of intelligence in older men. Psychology

and Aging, 10, 294–303. http://dx.doi.org/10.1037/0882-7974.10.2.294

ⴱ

Goldman, R. D., Hudson, D., & Daharsh, B. J. (1973). Self-estimated task

persistence as a nonlinear predictor of college success. Journal of

Educational Psychology, 65, 216–221. http://dx.doi.org/10.1037/

h0034989

ⴱ

Goodwin, J. W., III. (2017). Arithmetical computation and associated

neuropsychological capabilities in children, adolescents, and young

adults with nonsyndromic orofacial clefts (Doctoral dissertation). The

University of Iowa, Iowa City, IA.

ⴱ

Gray, S. A., & Reeve, R. A. (2016). Number-specific and general cogni-

tive markers of preschoolers’ math ability profiles. Journal of Experi-

mental Child Psychology, 147, 1–21. http://dx.doi.org/10.1016/j.jecp

.2016.02.004

ⴱ

Green, C. T., Bunge, S. A., Briones Chiongbian, V., Barrow, M., & Ferrer,

E. (2017). Fluid reasoning predicts future mathematical performance

among children and adolescents. Journal of Experimental Child Psy-

chology, 157, 125–143. http://dx.doi.org/10.1016/j.jecp.2016.12.005

ⴱ

Gremillion, M. L., & Martel, M. M. (2012). Semantic language as a

mechanism explaining the association between ADHD symptoms and

reading and mathematics underachievement. Journal of Abnormal Child

Psychology, 40, 1339–1349. http://dx.doi.org/10.1007/s10802-012-

9650-7

ⴱ

Griffin, E. A., & Morrison, F. J. (1997). The unique contribution of home

literacy environment to differences in early literacy skills. Early Child

Development and Care, 127, 233–243. http://dx.doi.org/10.1080/

0300443971270119

Griffiths, T. L., & Tenenbaum, J. B. (2009). Theory-based causal induc-

tion. Psychological Review, 116, 661–716. http://dx.doi.org/10.1037/

a0017201

ⴱ

Gubbels, J., Segers, E., & Verhoeven, L. (2018). How children’s intel-

lectual profiles relate to their cognitive, socio-emotional, and academic

functioning. High Ability Studies, 29, 149–168. http://dx.doi.org/10

.1080/13598139.2018.1507902

ⴱ

Guo, Y., Piasta, S. B., & Bowles, R. P. (2015). Exploring preschool

children’s science content knowledge. Early Education and Develop-

ment, 26, 125–146. http://dx.doi.org/10.1080/10409289.2015.968240

ⴱ

Guthmiller, M. L. (2010). Identifying factors predicting the math compu-

tation and math reasoning performance levels of Latino elementary

school students (Doctoral dissertation). The University of Utah, Salt

Lake City, Utah.

ⴱ

Häidkind, P., Kikas, E., Henno, H., & Peets, T. (2011). Controlled

drawing observation for assessing a child’s readiness for school and

predicting academic achievement at the end of the first grade. Scandi-

navian Journal of Educational Research, 55, 61–78. http://dx.doi.org/

10.1080/00313831.2011.539854

ⴱ

Han, K. S. (2003). Domain-specificity of creativity in young children:

How quantitative and qualitative data support it. The Journal of Creative

Behavior, 37, 117–142. http://dx.doi.org/10.1002/j.2162-6057.2003

.tb00829.x

ⴱ

Hansen, N. M. (2015). Development of fraction knowledge: A longitudinal

study from third through sixth grade (Doctoral dissertation). University

of Delaware, Newark, DE.

ⴱ

Harvey, H. A., & Miller, G. E. (2017). Executive function skills, early

mathematics, and vocabulary in head start preschool children. Early

Education and Development, 28, 290–307. http://dx.doi.org/10.1080/

10409289.2016.1218728

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

30 PENG ET AL.

ⴱ

Hauser-Cram, P., Durand, T. M., & Warfield, M. E. (2007). Early feelings

about school and later academic outcomes of children with special needs

living in poverty. Early Childhood Research Quarterly, 22, 161–172.

http://dx.doi.org/10.1016/j.ecresq.2007.02.001

ⴱ

Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017).

Enhancing children’s spatial and numerical skills through a dynamic

spatial approach to early geometry instruction: Effects of a 32-week

intervention. Cognition and Instruction, 35, 236–264. http://dx.doi.org/

10.1080/07370008.2017.1323902

ⴱ

Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001).

The relations between phonological processing abilities and emerging

individual differences in mathematical computation skills: A longitudi-

nal study from second to fifth grades. Journal of Experimental Child

Psychology, 79, 192–227. http://dx.doi.org/10.1006/jecp.2000.2586

Hedberg, E. C. (2014). ROBUMETA: Stata module to perform robust

variance estimation in meta-regression with dependent effect size esti-

mates. Statistical Software Components. Retrieved from https://ideas

.repec.org/c/boc/bocode/s457219.html

Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance

estimation in meta-regression with dependent effect size estimates. Re-

search Synthesis Methods, 1, 39–65. http://dx.doi.org/10.1002/jrsm.5

ⴱ

Heikkilä, R., Torppa, M., Aro, M., Närhi, V., & Ahonen, T. (2016).

Double-deficit hypothesis in a clinical sample: Extension beyond read-

ing. Journal of Learning Disabilities, 49, 546–560. http://dx.doi.org/10

.1177/0022219415572895

Henry, L. A., Messer, D. J., & Nash, G. (2012). Executive functioning in

children with specific language impairment. Journal of Child Psychol-

ogy and Psychiatry, and Allied Disciplines, 53, 37–45. http://dx.doi.org/

10.1111/j.1469-7610.2011.02430.x

ⴱ

Hershberger, K. A. (1997). The relationship between conceptually similar

subtests of the Wechsler Adult Intelligence Scale-Revised and the Career

Ability Placement Survey with a vocational rehabilitation sample (Doc-

toral dissertation). University of Cincinnati, Cincinnati, OH.)

ⴱ

Heyns, B., & Hilton, T. L. (1982). The cognitive tests for high school and

beyond: An assessment. Sociology of Education, 55, 89–102. http://dx

.doi.org/10.2307/2112290

ⴱ

Hill, M. A. (1981). Variables predicting student achievement on state

mandated competency tests: grant joint union high school district (Doc-

toral dissertation). The University of San Francisco, San Francisco, OH.

Hinshaw, S. P. (1992). Academic underachievement, attention deficits, and

aggression: Comorbidity and implications for intervention. Journal of

Consulting and Clinical Psychology, 60, 893–903. http://dx.doi.org/10

.1037/0022-006X.60.6.893

Hjetland, H. N., Lervåg, A., Lyster, S. A. H., Hagtvet, B. E., Hulme, C., &

Melby-Lervåg, M. (2019). Pathways to reading comprehension: A lon-

gitudinal study from 4 to 9 years of age. Journal of Educational

Psychology, 111, 751–763. http://dx.doi.org/10.1037/edu0000321

Hollo, A., Wehby, J. H., & Oliver, R. M. (2014). Unidentified language

deficits in children with emotional and behavioral disorders: A meta-

analysis. Exceptional Children, 80, 169–186. http://dx.doi.org/10.1177/

001440291408000203

Hoover, W., & Gough, P. (1990). The simple view of reading. Reading and

Writing, 2, 127–160. http://dx.doi.org/10.1007/BF00401799

ⴱ

Hornburg, C. B., Schmitt, S. A., & Purpura, D. J. (2018). Relations

between preschoolers’ mathematical language understanding and spe-

cific numeracy skills. Journal of Experimental Child Psychology, 176,

84–100. http://dx.doi.org/10.1016/j.jecp.2018.07.005

Horne, Z., Muradoglu, M., & Cimpian, A. (2019). Explanation as a

cognitive process. Trends in Cognitive Sciences, 23, 187–199. http://dx

.doi.org/10.1016/j.tics.2018.12.004

ⴱ

Hornung, C., Martin, R., & Fayol, M. (2017). General and specific

contributions of RAN to reading and arithmetic fluency in first graders:

A longitudinal latent variable approach. Frontiers in Psychology, 8,

1746. http://dx.doi.org/10.3389/fpsyg.2017.01746

ⴱ

Hornung, C., Schiltz, C., Brunner, M., & Martin, R. (2014). Predicting

first-grade mathematics achievement: The contributions of domain-

general cognitive abilities, nonverbal number sense, and early number

competence. Frontiers in Psychology, 5, 272. http://dx.doi.org/10.3389/

fpsyg.2014.00272

ⴱ

Hotulainen, R., Mononen, R., & Aunio, P. (2016). Thinking skills inter-

vention for low-achieving first graders. European Journal of Special

Needs Education, 31, 360–375. http://dx.doi.org/10.1080/08856257

.2016.1141541

ⴱ

Hoy, C. A. (1982). An investigation of certain components of division with

learning disabled and normal six-grade boys (Doctoral dissertation).

Northwestern University, Evanston, IL.

ⴱ

Hu, B. Y., Zhou, Y., Chen, L., Fan, X., & Winsler, A. (2017). Preschool

expenditures and Chinese children’s academic performance: The medi-

ating effect of teacher-child interaction quality. Early Childhood Re-

search Quarterly, 41, 37–49. http://dx.doi.org/10.1016/j.ecresq.2017.05

.002

Huang, B., Sivaganesan, S., Succop, P., & Goodman, E. (2004). Statistical

assessment of mediational effects for logistic mediational models. Sta-

tistics in Medicine, 23, 2713–2728. http://dx.doi.org/10.1002/sim.1847

ⴱ

Huang, Q., Zhang, X., Liu, Y., Yang, W., & Song, Z. (2017). The

contribution of parent-child numeracy activities to young Chinese chil-

dren’s mathematical ability. The British Journal of Educational Psychol-

ogy, 87, 328–344. http://dx.doi.org/10.1111/bjep.12152

ⴱ

Hur, E., Buettner, C. K., & Jeon, L. (2015). The association between

teachers’ child-centered beliefs and children’s academic achievement:

The indirect effect of children’s behavioral self-regulation. Child Youth

Care Forum, 44, 309–325. http://dx.doi.org/10.1007/s10566-014-

9283-9

ⴱ

Hutton, J. B., & Davenport, M. A. (1985). The WISC-R as a predictor of

Woodcock-Johnson achievement cluster scores for learning-disabled

students. Journal of Clinical Psychology, 41, 410–414. http://dx.doi

.org/10.1002/1097-4679(198505)41:3⬍410::AID-JCLP2270410318⬎3

.0.CO;2-K

ⴱ

Hyde, J. S., Geiringer, E. R., & Yen, W. M. (1975). On the empirical

relation between spatial ability and sex differences in other aspects of

cognitive performance. Multivariate Behavioral Research, 10, 289–309.

http://dx.doi.org/10.1207/s15327906mbr1003_3

Im-Bolter, N., Johnson, J., & Pascual-Leone, J. (2006). Processing limita-

tions in children with specific language impairment: The role of exec-

utive function. Child Development, 77, 1822–1841. http://dx.doi.org/10

.1111/j.1467-8624.2006.00976.x

Ingram, J., Andrews, N., & Pitt, A. (2016). Patterns of interaction that

encourage student explanations in mathematics lessons. Proceedings of

the British Society for Research into Learning Mathematics, 36, 37–41.

Ingram, J., Andrews, N., & Pitt, A. (2019). When students offer explana-

tions without the teacher explicitly asking them to. Educational Studies

in Mathematics, 101(1), 51–66. http://dx.doi.org/10.1007/s10649-018-

9873-9

ⴱ

Jap, B. A. J., Borleffs, E., & Maassen, B. A. M. (2017). Towards

identifying dyslexia in Standard Indonesian: The development of a

reading assessment battery. Reading and Writing, 30, 1729–1751. http://

dx.doi.org/10.1007/s11145-017-9748-y

ⴱ

Jensen, A. R., & Reynolds, C. R. (1983). Sex differences on the WISC-R.

Personality and Individual Differences, 4, 223–226. http://dx.doi.org/10

.1016/0191-8869(83)90029-6

ⴱ

Jerauld, J. (2014). Predicting early academic achievement: an investiga-

tion of the contribution of executive function (Doctoral dissertation). The

University of Arizona, Tucson, AZ.

ⴱ

Jerman, O. Y. (2007). Does growth in working memory predict growth in

crystallized intelligence in children with reading disabilities? (Doctoral

dissertation). University of California, Riverside, CA.

ⴱ

Jordan, J. A., Wylie, J., & Mulhern, G. (2015). Mathematics and reading

difficulty subtypes: Minor phonological influences on mathematics for

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

5–7-years-old. Frontiers in Psychology, 6, 221. http://dx.doi.org/10

.3389/fpsyg.2015.00221

ⴱ

Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., &

Micklos, D. (2013). Developmental predictors of fraction concepts and

procedures. Journal of Experimental Child Psychology, 116, 45–58.

http://dx.doi.org/10.1016/j.jecp.2013.02.001

Just, M. A., & Carpenter, P. A. (1992). A capacity theory of comprehen-

sion: Individual differences in working memory. Psychological Review,

99, 122–149. http://dx.doi.org/10.1037/0033-295X.99.1.122

Kane, M. J., Hambrick, D. Z., & Conway, A. R. A. (2005). Working

memory capacity and fluid intelligence are strongly related constructs:

Comment on Ackerman, Beier, and Boyle (2005). Psychological Bulle-

tin, 131, 66–71. http://dx.doi.org/10.1037/0033-2909.131.1.66

ⴱ

Kang, C. (1990). The nature and development of a cognitive screening

battery for academically gifted second and third grade students (Doc-

toral dissertation). University of Wisconsin-Madison, Wisconsin, WI.

Kaufmann, H., & Schmalstieg, D. (2003). Mathematics and geometry

education with collaborative augmented reality. Computers & Graphics,

27, 339–345. http://dx.doi.org/10.1016/S0097-8493(03)00028-1

Kazima, M. (2007). Malawian students’ meanings for probability vocab-

ulary. Educational Studies in Mathematics, 64, 169–189. http://dx.doi

.org/10.1007/s10649-006-9032-6

ⴱ

Kempert, S., Saalbach, H., & Hardy, I. (2011). Cognitive benefits and

costs of bilingualism in elementary school students: The case of math-

ematical word problems. Journal of Educational Psychology, 103, 547–

561. http://dx.doi.org/10.1037/a0023619

Kievit, R. A., Lindenberger, U., Goodyer, I. M., Jones, P. B., Fonagy, P.,

Bullmore, E. T.,...theNeuroscience in Psychiatry Network. (2017).

Mutualistic coupling between vocabulary and reasoning supports cog-

nitive development during late adolescence and early adulthood. Psy-

chological Science, 28, 1419–1431. http://dx.doi.org/10.1177/

0956797617710785

ⴱ

Kikas, E., & Jõgi, A. L. (2016). Assessment of learning strategies:

Self-report questionnaire or learning task. European Journal of Psychol-

ogy of Education, 31, 579–593. http://dx.doi.org/10.1007/s10212-015-

0276-3

ⴱ

Kikas, E., Soodla, P., & Mägi, K. (2018). Teacher judgments of student

reading and math skills: Associations with child-and classroom-related

factors. Scandinavian Journal of Educational Research, 62, 783–797.

http://dx.doi.org/10.1080/00313831.2017.1307271

ⴱ

Kim, Y. (1994). The relationship between the performance on Piagetian

tasks in kindergarten and arithmetic achievement in first-grade in Korea

(Doctoral dissertation). Arizona State University, Tempe, AZ.

ⴱ

King, C. M. (2009). Predictive validity of a kindergarten screening tool

(Doctoral dissertation). Fairleigh Dickinson University, Teaneck, NJ.

Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word

arithmetic problems. Psychological Review, 92, 109–129. http://dx.doi

.org/10.1037/0033-295X.92.1.109

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance

during instruction does not work: An analysis of the failure of construc-

tivist, discovery, problem-based, experiential, and inquiry-based teach-

ing. Educational Psychologist, 41, 75–86. http://dx.doi.org/10.1207/

s15326985ep4102_1

ⴱ

Kleczkowski, T. A. (1990). The interrelationships of emotional and

cognitive attributes among junior high students (Doctoral dissertation).

Northern Illinois University, DeKalb, IL.

Kleemans, T., Segers, E., & Verhoeven, L. (2011). Cognitive and linguistic

precursors to numeracy in kindergarten: Evidence from first and second

language learners. Learning and Individual Differences, 21, 555–561.

http://dx.doi.org/10.1016/j.lindif.2011.07.008

ⴱ

Kleemans, T., Segers, E., & Verhoeven, L. (2012). Naming speed as a

clinical marker in predicting basic calculation skills in children with

specific language impairment. Research in Developmental Disabilities,

33, 882–889. http://dx.doi.org/10.1016/j.ridd.2011.12.007

ⴱ

Kleemans, T., Segers, E., & Verhoeven, L. (2013). Relations between

home numeracy experiences and basic calculation skills of children with

and without specific language impairment. Early Childhood Research

Quarterly, 28, 415–423. http://dx.doi.org/10.1016/j.ecresq.2012.10.004

ⴱ

Kleemans, T., Segers, E., & Verhoeven, L. (2014). Cognitive and linguis-

tic predictors of basic arithmetic skills: Evidence from first-language and

second-language learners. International Journal of Disability Develop-

ment and Education, 61, 306–316. http://dx.doi.org/10.1080/1034912X

.2014.934017

ⴱ

Kleemans, T., Segers, E., & Verhoeven, L. (2018). Individual differences

in basic arithmetic skills in children with and without developmental

language disorder: Role of home numeracy experiences. Early Child-

hood Research Quarterly, 43, 62–72. http://dx.doi.org/10.1016/j.ecresq

.2018.01.005

Koponen, T., Georgiou, G., Salmi, P., Leskinen, M., & Aro, M. (2017). A

meta-analysis of the relation between RAN and mathematics. Journal of

Educational Psychology, 109, 977–992. http://dx.doi.org/10.1037/

edu0000182

ⴱ

Koponen, T., Mononen, R., Räsänen, P., & Ahonen, T. (2006). Basic

numeracy in children with specific language impairment: Heterogeneity

and connections to language. Journal of Speech, Language, and Hearing

Research, 49, 58–73. http://dx.doi.org/10.1044/1092-4388(2006/005)

ⴱ

Krajewski, K., & Schneider, W. (2009). Exploring the impact of phono-

logical awareness, visual-spatial working memory, and preschool

quantity-number competencies on mathematics achievement in elemen-

tary school: Findings from a 3-year longitudinal study. Journal of

Experimental Child Psychology, 103, 516–531. http://dx.doi.org/10

.1016/j.jecp.2009.03.009

Kremer, K. P., Flower, A., Huang, J., & Vaughn, M. G. (2016). Behavior

problems and children’s academic achievement: A test of growth-curve

models with gender and racial differences. Children and Youth Services

Review, 67, 95–104. http://dx.doi.org/10.1016/j.childyouth.2016.06.003

ⴱ

Kuusinen, J., & Leskinen, E. (1988). Latent structure analysis of longi-

tudinal data on relations between intellectual abilities and school

achievement. Multivariate Behavioral Research, 23, 103–118. http://dx

.doi.org/10.1207/s15327906mbr2301_6

ⴱ

Kvaraceus, W. C., & Lanigan, M. A. (1948). Pupil performance on the

Iowa every-pupil tests of basic skills administered at half-year intervals

in the junior high school. Educational and Psychological Measurement,

8, 91–99. http://dx.doi.org/10.1177/001316444800800109

ⴱ

Kyttälä, M., Aunio, P., Lepola, J., & Hautamäki, J. (2014). The role of the

working memory and language skills in the prediction of word problem

solving in 4-to 7-year-old children. Educational Psychology, 34, 674–

696. http://dx.doi.org/10.1080/01443410.2013.814192

ⴱ

Lago, R. M. (2007). Examining the psychometrics of number sense among

kindergarten students (Doctoral dissertation). Penn State University,

State College, PA.

Language and Reading Research Consortium. (2015). The dimensionality

of language ability in young children. Child Development, 86, 1948–

1965. http://dx.doi.org/10.1111/cdev.12450

ⴱ

Larocque, L. (1999). Preadolescent self-concept and self-concept/

academic achievement relations: Investigating multidimensional and

hierarchical structures within and across gender (Doctoral dissertation).

University of Ottawa, Ottawa, ON, Canada.

ⴱ

Leather, C. V., & Henry, L. A. (1994). Working memory span and

phonological awareness tasks as predictors of early reading ability.

Journal of Experimental Child Psychology, 58, 88–111. http://dx.doi

.org/10.1006/jecp.1994.1027

Lee, K., & Bull, R. (2016). Developmental changes in working memory,

updating, and math achievement. Journal of Educational Psychology,

108, 869–882. http://dx.doi.org/10.1037/edu0000090

ⴱ

LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J.,

Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics:

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

32 PENG ET AL.

Longitudinal predictors of performance. Child Development, 81, 1753–

1767. http://dx.doi.org/10.1111/j.1467-8624.2010.01508.x

LeFevre, J. A., & Liu, J. (1997). The role of experience in numerical skill:

Multiplication performance in adults from Canada and China. Mathe-

matical Cognition, 3, 31–62. http://dx.doi.org/10.1080/13546799

7387470

ⴱ

LeFevre, J. A., Skwarchuk, S. L., Smith-Chant, B. L., Fast, L., Kamawar,

D., & Bisanz, J. (2009). Home numeracy experiences and children’s

math performance in the early school years. Canadian Journal of Be-

havioural Science, 41, 55–66. http://dx.doi.org/10.1037/a0014532

ⴱ

Lepola, J., Niemi, P., Kuikka, M., & Hannula, M. M. (2005). Cognitive-

linguistic skills and motivation as longitudinal predictors of reading and

arithmetic achievement: A follow-up study from kindergarten to grade 2.

International Journal of Educational Research, 43, 250–271. http://dx

.doi.org/10.1016/j.ijer.2006.06.005

Lervåg, A., Hulme, C., & Melby-Lervåg, M. (2018). Unpicking the devel-

opmental relationship between oral language skills and reading compre-

hension: It’s simple, but complex. Child Development, 89, 1821–1838.

http://dx.doi.org/10.1111/cdev.12861

Levy, Y. (2011). IQ predicts word decoding skills in populations with

intellectual disabilities. Research in Developmental Disabilities, 32,

2267–2277. http://dx.doi.org/10.1016/j.ridd.2011.07.043

ⴱ

Li, K., Zhang, P., Hu, B. Y., Burchinal, M. R., Fan, X., & Qin, J. (2019).

Testing the ‘thresholds’ of preschool education quality on child out-

comes in China. Early Childhood Research Quarterly, 47, 445–456.

http://dx.doi.org/10.1016/j.ecresq.2018.08.003

ⴱ

Li, Y. H., & Tompkins, L. J. (2004). Examining the construct validity for

the multiple-content testing programs. International Journal of Testing,

4, 217–238. http://dx.doi.org/10.1207/s15327574ijt0403_2

ⴱ

Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Is approximate

number precision a stable predictor of math ability? Learning and

Individual Differences, 25, 126–133. http://dx.doi.org/10.1016/j.lindif

.2013.02.001

ⴱ

Libertus, M. E., Odic, D., Feigenson, L., & Halberda, J. (2016). The

precision of mapping between number words and the approximate

number system predicts children’s formal math abilities. Journal of

Experimental Child Psychology, 150, 207–226. http://dx.doi.org/10

.1016/j.jecp.2016.06.003

ⴱ

Lin, G. C. (2018). The roles of language and executive function on early

mathematics among emergent bilinguals (Doctoral dissertation). Univer-

sity of California, Irvine, CA.

ⴱ

Lindgren, S. D. (1978). Finger localization and the prediction of reading

disability. Cortex, 14, 87–101. http://dx.doi.org/10.1016/S0010-

9452(78)80011-2

Lindquist, K. A., MacCormack, J. K., & Shablack, H. (2015). The role of

language in emotion: Predictions from psychological constructionism.

Frontiers in Psychology, 6, 444. http://dx.doi.org/10.3389/fpsyg.2015

.00444

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Thousand

Oaks, CA: SAGE publications, Inc.

Liu, R. D., Ding, Y., Xu, L., & Wang, J. (2017). Involvement of working

memory in mental multiplication in Chinese elementary students. The

Journal of Educational Research, 110, 380–390. http://dx.doi.org/10

.1080/00220671.2015.1103689

ⴱ

Liu, Y., Lin, D., & Zhang, X. (2016). Morphological awareness longitu-

dinally predicts counting ability in Chinese kindergarteners. Learning

and Individual Differences, 47, 215–221. http://dx.doi.org/10.1016/j

.lindif.2016.01.007

ⴱ

Lockl, K., Ebert, S., & Weinert, S. (2017). Predicting school achievement

from early theory of mind: Differential effects on achievement tests and

teacher ratings. Learning and Individual Differences, 53, 93–102. http://

dx.doi.org/10.1016/j.lindif.2016.11.007

Lombrozo, T. (2006). The structure and function of explanations. Trends in

Cognitive Sciences, 10, 464–470. http://dx.doi.org/10.1016/j.tics.2006

.08.004

ⴱ

Long, I., Malone, S. A., Tolan, A., Burgoyne, K., Heron-Delaney, M.,

Witteveen, K., & Hulme, C. (2016). The cognitive foundations of early

arithmetic skills: It is counting and number judgment, but not finger

gnosis, that count. Journal of Experimental Child Psychology, 152,

327–334. http://dx.doi.org/10.1016/j.jecp.2016.08.005

ⴱ

Lopes-Silva, J. B., Moura, R., Júlio-Costa, A., Wood, G., Salles, J. F., &

Haase, V. G. (2016). What is specific and what is shared between

numbers and words? Frontiers in Psychology, 7, 22. http://dx.doi.org/

10.3389/fpsyg.2016.00022

ⴱ

Maclean, M. (1987). Rhymes, nursery rhymes, and reading in early

childhood. Merrill-Palmer Quarterly, 33, 255–281.

ⴱ

Magee, P., & Newcomer, P. (1978). The relationship between oral lan-

guage skills and academic achievement of learning disabled children.

Learning Disability Quarterly, 1, 63–67. http://dx.doi.org/10.2307/

1510965

ⴱ

Majumder, S. (2004). Factors in mathematical word problem solving: The

role of inhibition (Doctoral dissertation). York University, Toronto, ON,

Canada.

ⴱ

Malone, A. S., Loehr, A. M., & Fuchs, L. S. (2017). The role of domain-

general cognitive abilities and decimal labels in at-risk fourth-grade

students’ decimal magnitude understanding. Learning and Individual

Differences, 58, 90–96. http://dx.doi.org/10.1016/j.lindif.2017.05.007

ⴱ

Männamaa, M., Kikas, E., Peets, K., & Palu, A. (2012). Cognitive

correlates of math skills in third-grade students. Educational Psychol-

ogy, 32, 21–44. http://dx.doi.org/10.1080/01443410.2011.621713

Martin, B. N., & Fuchs, L. S. (2019). The mathematical performance of

at-risk first graders as a function of limited English proficiency status.

Learning Disability Quarterly, 42, 244–251. http://dx.doi.org/10.1177/

0731948719827489

ⴱ

Martin, R. B., Cirino, P. T., Sharp, C., & Barnes, M. (2014). Number and

counting skills in kindergarten as predictors of grade 1 mathematical

skills. Learning and Individual Differences, 34, 12–23. http://dx.doi.org/

10.1016/j.lindif.2014.05.006

Marton, K. (2008). Visuo-spatial processing and executive functions in

children with specific language impairment. International Journal of

Language & Communication Disorders, 43, 181–200. http://dx.doi.org/

10.1080/16066350701340719

Marton, K., & Schwartz, R. G. (2003). Working memory capacity and

language processes in children with specific language impairment. Jour-

nal of Speech, Language, and Hearing Research, 46, 1138–1153. http://

dx.doi.org/10.1044/1092-4388(2003/089)

Mata, A., Schubert, A. L., & Ferreira, M. B. (2014). The role of

language comprehension in reasoning: How “good-enough” repre-

sentations induce biases. Cognition, 133, 457–463. http://dx.doi.org/

10.1016/j.cognition.2014.07.011

ⴱ

Matthews, J. S., Ponitz, C. C., & Morrison, F. J. (2009). Early gender

differences in self-regulation and academic achievement. Journal of

Educational Psychology, 101, 689–704. http://dx.doi.org/10.1037/

a0014240

ⴱ

Mayo-Booker, T. E. (1995). Racial and global self-concept as they relate

to academic achievement in African Americans (Doctoral dissertation).

Fairleigh Dickinson University, Teaneck, NJ.

McArdle, J. J., Hamagami, F., Meredith, W., & Bradway, K. P. (2000).

Modeling the dynamic hypotheses of Gf–Gc theory using longitudinal

life-span data. Learning and Individual Differences, 12, 53–79. http://

dx.doi.org/10.1016/S1041-6080(00)00036-4

ⴱ

McClelland, M. M., Acock, A. C., Piccinin, A., Rhea, S. A., & Stallings,

M. C. (2013). Relations between preschool attention span-persistence

and age 25 educational outcomes. Early Childhood Research Quarterly,

28, 314–324. http://dx.doi.org/10.1016/j.ecresq.2012.07.008

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

ⴱ

McClelland, M. M., Cameron, C. E., Connor, C. M., Farris, C. L., Jewkes,

A. M., & Morrison, F. J. (2007). Links between behavioral regulation

and preschoolers’ literacy, vocabulary, and math skills. Developmental

Psychology, 43, 947–959. http://dx.doi.org/10.1037/0012-1649.43.4.947

ⴱ

McDevitt, T. M., Hess, R. D., Kashiwagi, K., Dickson, W. P., Miyake, N.,

& Azuma, H. (1987). Referential communication accuracy of mother-

child pairs and children’s later scholastic achievement: A follow-up

study. Merrill-Palmer Quarterly, 33, 171–186.

ⴱ

McEntire, M. E. (1981). Relationships between the language proficiency

of adolescents and their mathematics performance (Doctoral disserta-

tion). The University of Texas at Austin, Austin, TX.

ⴱ

McShane, D., & Plus, J. M. (1988). The relationship of intellectual and

psycholinguistic abilities to the achievement gains of American Indian

children. Canadian Journal of Native Education, 15, 66–86.

ⴱ

Mellard, D. F., Woods, K. L., & McJunkin, L. (2015). Literacy compo-

nents model for at-risk young adults enrolled in career and technical

education. Journal of Research in Reading, 38, 249–271. http://dx.doi

.org/10.1111/1467-9817.12014

Menon, V. (2016). Working memory in children’s math learning and its

disruption in dyscalculia. Current Opinion in Behavioral Sciences, 10,

125–132. http://dx.doi.org/10.1016/j.cobeha.2016.05.014

ⴱ

Merz, E. C., Zucker, T. A., Landry, S. H., Williams, J. M., Assel, M.,

Taylor, H. B.,...theSchool Readiness Research Consortium. (2015).

Parenting predictors of cognitive skills and emotion knowledge in so-

cioeconomically disadvantaged preschoolers. Journal of Experimental

Child Psychology, 132, 14–31. http://dx.doi.org/10.1016/j.jecp.2014.11

.010

ⴱ

Mestre, J. P. (1981). Predicting academic achievement among bilingual

Hispanic college technical students. Educational and Psychological

Measurement, 41, 1255–1264. http://dx.doi.org/10.1177/001316448

104100433

ⴱ

Meuwissen, A. S., & Carlson, S. M. (2018). The role of father parenting

in children’s school readiness: A longitudinal follow-up. Journal of

Family Psychology, 32, 588–598. http://dx.doi.org/10.1037/

fam0000418

ⴱ

Michael, R. (2003). Children’s cognitive skill development in Britain and

the United States. International Journal of Behavioral Development, 27,

396–408. http://dx.doi.org/10.1080/01650250344000000

ⴱ

Michalczyk, K., Krajewski, K., Pre␤ler, A. L., & Hasselhorn, M. (2013).

The relationships between quantity-number competencies, working

memory, and phonological awareness in 5- and 6-year-olds. British

Journal of Developmental Psychology, 31, 408–424. http://dx.doi.org/

10.1111/bjdp.12016

ⴱ

Miles, D. D. (1991). Algebra vocabulary: Domain-specific language as a

predictor of algebra skills (Doctoral dissertation). The University of

Connecticut, Mansfield, CN.

Miller, C. A., Kail, R., Leonard, L. B., & Tomblin, J. B. (2001). Speed of

processing in children with specific language impairment. Journal of

Speech, Language, and Hearing Research, 44, 416–433. http://dx.doi

.org/10.1044/1092-4388(2001/034)

ⴱ

Miller, K. F., Smith, C. M., Zhu, J., & Zhang, H. (1995). Preschool origins

of cross-national differences in mathematical competence: The role of

number-naming systems. Psychological Science, 6, 56–60. http://dx.doi

.org/10.1111/j.1467-9280.1995.tb00305.x

ⴱ

Miller, M. R., Müller, U., Giesbrecht, G. F., Carpendale, J. I., & Kerns,

K. A. (2013). The contribution of executive function and social under-

standing to preschoolers’ letter and math skills. Cognitive Development,

28, 331–349. http://dx.doi.org/10.1016/j.cogdev.2012.10.005

Miller-Cotto, D., & Byrnes, J. P. (2019). What’s the best way to charac-

terize the relationship between working memory and achievement?: An

initial examination of competing theories. Journal of Educational Psy-

chology. Advance online publication. http://dx.doi.org/10.1037/

edu0000395

Miyake, A., & Friedman, N. P. (2012). The nature and organization of

individual differences in executive functions: Four general conclusions.

Current Directions in Psychological Science, 21, 8–14. http://dx.doi

.org/10.1177/0963721411429458

Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A.,

& Wager, T. D. (2000). The unity and diversity of executive functions

and their contributions to complex “frontal lobe” tasks: A latent variable

analysis. Cognitive Psychology, 41, 49–100. http://dx.doi.org/10.1006/

cogp.1999.0734

ⴱ

Mokrova, I. L., O’Brien, M., Calkins, S. D., Leerkes, E. M., & Marco-

vitch, S. (2013). The role of persistence at preschool age in academic

skills at kindergarten. European Journal of Psychology of Education, 28,

1495–1503. http://dx.doi.org/10.1007/s10212-013-0177-2

ⴱ

Moll, K., Snowling, M. J., Göbel, S. M., & Hulme, C. (2015). Early

language and executive skills predict variations in number and arithme-

tic skills in children at family-risk of dyslexia and typically developing

controls. Learning and Instruction, 38, 53–62. http://dx.doi.org/10

.1016/j.learninstruc.2015.03.004

Montague, M. (1992). The effects of cognitive and metacognitive strategy

instruction on the mathematical problem solving of middle school stu-

dents with learning disabilities. Journal of Learning Disabilities, 25,

230–248. http://dx.doi.org/10.1177/002221949202500404

Montgomery, J. W., Magimairaj, B. M., & Finney, M. C. (2010). Working

memory and specific language impairment: An update on the relation

and perspectives on assessment and treatment. American Journal of

Speech-Language Pathology, 19, 78–94. http://dx.doi.org/10.1044/

1058-0360(2009/09-0028)

Montgomery, W. (2001). Creating culturally responsive, inclusive class-

rooms. Teaching Exceptional Children, 33, 4–9. http://dx.doi.org/10

.1177/004005990103300401

ⴱ

Morgan, J. E., Loo, S. K., & Lee, S. S. (2018). Neurocognitive functioning

mediates the prospective association of birth weight with youth ADHD

symptoms. Journal of Clinical Child and Adolescent Psychology, 47,

727–736. http://dx.doi.org/10.1080/15374416.2016.1183498

Morgan, P. L., Farkas, G., Hillemeier, M. M., Mattison, R., Maczuga, S.,

Li, H., & Cook, M. (2015). Minorities are disproportionately underrep-

resented in special education: Longitudinal evidence across five disabil-

ity conditions. Educational Researcher, 44, 278–292. http://dx.doi.org/

10.3102/0013189X15591157

Moschkovich, J. (2002). A situated and sociocultural perspective on bilin-

gual mathematics learners. Mathematical Thinking and Learning, 4,

189–212. http://dx.doi.org/10.1207/S15327833MTL04023_5

ⴱ

Mulder, H., Verhagen, J., Van der Ven, S. H. G., Slot, P. L., & Leseman,

P. P. M. (2017). Early executive function at age two predicts emergent

mathematics and literacy at age five. Frontiers in Psychology, 8, 1706.

http://dx.doi.org/10.3389/fpsyg.2017.01706

ⴱ

Mullins, J. E. (1999). A comparison of performance of students referred

for gifted evaluation on the WISC-III and Binet IV (Doctoral disserta-

tion). West Virginia University, Morgantown, WV.

ⴱ

Munford, P. R. (1978). A comparison of the WISC and WISC-R on black

child psychiatric outpatients. Journal of Clinical Psychology, 34, 938–

942. http://dx.doi.org/10.1002/1097-4679(197810)34:4⬍938::AID-

JCLP2270340423⬎3.0.CO;2-A

ⴱ

Naglieri, J. A., & Pfeiffer, S. I. (1981). Correlations among scores on

WISC-R and Woodcock-Johnson Achievement Tests for learning dis-

abled children. Psychological Reports, 49, 913–914. http://dx.doi.org/10

.2466/pr0.1981.49.3.913

ⴱ

Namkung, J. M., & Fuchs, L. S. (2016). Cognitive predictors of calcula-

tions and number line estimation with whole numbers and fractions

among at-risk students. Journal of Educational Psychology, 108, 214–

228. http://dx.doi.org/10.1037/edu0000055

National Council of Teachers of Mathematics. (2006). Curriculum focal

points for prekindergarten through grade 8 mathematics: A quest for

coherence. Reston, VA: Author.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

34 PENG ET AL.

National Reading Panel. (2000). Report of the National Reading Panel:

Teaching children to read: An evidence-based assessment of the scien-

tific research literature on reading and its implications for reading

instruction: Reports of the subgroups. Bethesda, MD: National Institute

of Child Health and Human Development, National Institutes of Health.

ⴱ

Navarro, J. I., Aguilar, M., Alcalde, C., Ruiz, G., Marchena, E., &

Menacho, I. (2011). Inhibitory processes, working memory, phonolog-

ical awareness, naming speed, and early arithmetic achievement. The

Spanish Journal of Psychology, 14, 580–588. http://dx.doi.org/10.5209/

rev_SJOP.2011.v14.n2.6

ⴱ

Navarro, M. G., Braham, E. J., & Libertus, M. E. (2018). Intergenerational

associations of the approximate number system in toddlers and their

parents. British Journal of Developmental Psychology, 36, 521–539.

http://dx.doi.org/10.1111/bjdp.12234

ⴱ

Nesbitt, K. T., Farran, D. C., & Fuhs, M. W. (2015). Executive function

skills and academic achievement gains in prekindergarten: Contributions

of learning-related behaviors. Developmental Psychology, 51, 865–878.

http://dx.doi.org/10.1037/dev0000021

ⴱ

Neuman, G. A., Bolin, A. U., & Briggs, T. E. (2000). Identifying general

factors of intelligence: A confirmatory factor analysis of the ball aptitude

battery. Educational and Psychological Measurement, 60, 697–712.

http://dx.doi.org/10.1177/00131640021970853

ⴱ

Newman, S. D. (2016). Does finger sense predict addition performance?

Cognitive Processing, 17, 139–146. http://dx.doi.org/10.1007/s10339-

016-0756-7

Newton, J. H., & McGrew, K. S. (2010). Introduction to the special issue:

Current research in Cattell–Horn–Carroll–based assessment. Psychol-

ogy in the Schools, 47, 621–634. http://dx.doi.org/10.1002/pits.20495

ⴱ

Niklas, F., & Schneider, W. (2013). Casting the die before the die is cast:

The importance of the home numeracy environment for preschool chil-

dren. European Journal of Psychology of Education, 29, 327–345.

http://dx.doi.org/10.1007/s10212-013-0201-6

Norbury, C. F., Gooch, D., Wray, C., Baird, G., Charman, T., Simonoff, E.,

. . . Pickles, A. (2016). The impact of nonverbal ability on prevalence

and clinical presentation of language disorder: Evidence from a popu-

lation study. Journal of Child Psychology and Psychiatry, and Allied

Disciplines, 57, 1247–1257. http://dx.doi.org/10.1111/jcpp.12573

ⴱ

Novak, P. A., Tsushima, W. T., & Tsushima, M. M. (1991). Predictive

validity of two short-forms of the WPPSI: A 3-year follow-up study.

Journal of Clinical Psychology, 47, 698–702. http://dx.doi.org/10.1002/

1097-4679(199109)47:5⬍698::AID-JCLP2270470511⬎3.0.CO;2-Q

O’Halloran, K. L. (2005). Mathematical discourse: Language, symbolism

and visual images. New York, NY: Continuum.

ⴱ

Olexa, L. W. (2001). Language ability scores at kindergarten entrance as

a predictor of later academic performance (Doctoral dissertation). Wal-

den University, Minneapolis, MN.

ⴱ

O’Neill, D. K., Pearce, M. J., & Pick, J. L. (2004). Preschool children’s

narratives and performance on the Peabody Individualized Achievement

Test–Revised: Evidence of a relation between early narrative and later

mathematical ability. First Language, 24, 149–183. http://dx.doi.org/10

.1177/0142723704043529

ⴱ

O’Shaughnessy, T. E. (1997). A comparison of two reading interventions

for children with or at-risk for reading disabilities (Doctoral disserta-

tion). University of California, Riverside, CA.

ⴱ

O’Shea, L. M. (2014). Predictive validity of reading and mathematics

curriculum-based measures on mathematics performance at third grade

(Doctoral dissertation). University of Oregon, Eugene, OR.

Östergren, R., & Träff, U. (2013). Early number knowledge and cognitive

ability affect early arithmetic ability. Journal of Experimental Child

Psychology, 115, 405–421. http://dx.doi.org/10.1016/j.jecp.2013.03.007

ⴱ

Pace, A., Alper, R., Burchinal, M. R., Golinkoff, R. M., & Hirsh-Pasek,

K. (2019). 2018). Measuring success: Within and cross-domain predic-

tors of academic and social trajectories in elementary school. Early

Childhood Research Quarterly, 46, 112–125. http://dx.doi.org/10.1016/

j.ecresq.2018.04.001

ⴱ

Pagani, L. S., Fitzpatrick, C., Archambault, I., & Janosz, M. (2010).

School readiness and later achievement: A French Canadian replication

and extension. Developmental Psychology, 46, 984–994. http://dx.doi

.org/10.1037/a0018881

ⴱ

Palmer, S. (2000). Development of phonological recoding and literacy

acquisition: A four-year cross-sequential study. British Journal of De-

velopmental Psychology, 18, 533–555. http://dx.doi.org/10.1348/

026151000165841

ⴱ

Panizo, M. I. (1991). English language proficiency as a moderator vari-

able in the prediction of academic achievement of Hispanic students

(Doctoral dissertation). University of Miami, Coral Gables, FL.

ⴱ

Parlato, V., Lopez, O., Panisset, M., Iavarone, A., Grafman, J., & Boller,

F. (1992). Mental calculation in mild Alzheimer’s-disease: A pilot-

study. International Journal of Geriatric Psychiatry, 7, 599–602. http://

dx.doi.org/10.1002/gps.930070810

ⴱ

Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and

domain-general precursors of mathematical achievement: A longitudinal

study from kindergarten to first grade. The British Journal of Educa-

tional Psychology, 82, 42–63. http://dx.doi.org/10.1111/j.2044-8279

.2011.02039.x

ⴱ

Passolunghi, M. C., Lanfranchi, S., Altoè, G., & Sollazzo, N. (2015).

Early numerical abilities and cognitive skills in kindergarten children.

Journal of Experimental Child Psychology, 135, 25–42. http://dx.doi

.org/10.1016/j.jecp.2015.02.001

ⴱ

Passolunghi, M. C., Vercelloni, B., & Schadee, H. (2007). The precursors

of mathematics learning: Working memory, phonological ability and

numerical competence. Cognitive Development, 22, 165–184. http://dx

.doi.org/10.1016/j.cogdev.2006.09.001

ⴱ

Pauly, H., Linkersdörfer, J., Lindberg, S., Woerner, W., Hasselhorn, M.,

& Lonnemann, J. (2011). Domain-specific rapid automatized naming

deficits in children at risk for learning disabilities. Journal of Neurolin-

guistics, 24, 602–610. http://dx.doi.org/10.1016/j.jneuroling.2011.02

.002

ⴱ

Pawk, M. L. (2003). A quantitative analysis of full-day kindergarten in

rural elementary schools: A measure of academic and social outcomes

for children at-risk in the arm strong school district (Doctoral disserta-

tion). Duquesne University, Pittsburgh, PA.

Peng, P., & Kievit, R. (2020). The development of academic achievement

and cognitive abilities: A bidirectional perspective. Child Development

Perspectives, 14, 15–20. http://dx.doi.org/10.1111/cdep.12352

Peng, P., & Lin, X. (2019). The relation between mathematics vocabulary

and mathematics performance among fourth graders. Learning and

Individual Differences, 69, 11–21. http://dx.doi.org/10.1016/j.lindif

.2018.11.006

Peng, P., Namkung, J., Barnes, M., & Sun, C. (2016). A meta-analysis of

mathematics and working memory: Moderating effects of working

memory domain, type of mathematics skill, and sample characteristics.

Journal of Educational Psychology, 108, 455–473. http://dx.doi.org/10

.1037/edu0000079

ⴱ

Peng, P., Namkung, J. M., Fuchs, D., Fuchs, L. S., Patton, S., Yen, L.,...

Hamlett, C. (2016). A longitudinal study on predictors of early calcula-

tion development among young children at risk for learning difficulties.

Journal of Experimental Child Psychology, 152, 221–241. http://dx.doi

.org/10.1016/j.jecp.2016.07.017

Peng, P., Wang, C., & Namkung, J. (2018). Understanding the cognition

related to mathematics difficulties: A meta-analysis on the cognitive

deficit profiles and the bottleneck theory. Review of Educational Re-

search, 88, 434–476. http://dx.doi.org/10.3102/0034654317753350

Peng, P., Wang, T., Wang, C., & Lin, X. (2019). A meta-analysis on the

relation between fluid intelligence and reading/mathematics: Effects of

tasks, age, and social economics status. Psychological Bulletin, 145,

189–236. http://dx.doi.org/10.1037/bul0000182

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

Pennequin, V., Sorel, O., Nanty, I., & Fontaine, R. (2010). Metacognition

and low achievement in mathematics: The effect of training in the use of

metacognitive skills to solve mathematical word problems. Thinking &

Reasoning, 16, 198–220. http://dx.doi.org/10.1080/13546783.2010

.509052

ⴱ

Phillips, C. J., & Marvelly, A. (1984). Basic educational skills of Asian

children at the end of infant schooling. Educational Research, 26,

36–45. http://dx.doi.org/10.1080/0013188840260107

Pimm, D. (1987). Speaking mathematically: Communication in mathemat-

ics classrooms. London, UK: Routledge & K. Paul. http://dx.doi.org/10

.4324/9781315278858

ⴱ

Pina, V., Fuentes, L. J., Castillo, A., & Diamantopoulou, S. (2014).

Disentangling the effects of working memory, language, parental edu-

cation, and non-verbal intelligence on children’s mathematical abilities.

Frontiers in Psychology, 5, 415. http://dx.doi.org/10.3389/fpsyg.2014

.00415

Pind, J., Gunnarsdóttir, E. K., & Jóhannesson, H. S. (2003). Raven’s

standard progressive matrices: New school age norms and a study of the

test’s validity. Personality and Individual Differences, 34, 375–386.

http://dx.doi.org/10.1016/S0191-8869(02)00058-2

ⴱ

Post, P. C. (1999). The usefulness of the Wechsler Intelligence Scales for

Children-Third Edition in the diagnosis of attentional disorders in a

special education population at the secondary level (Doctoral disserta-

tion). Adler School of Professional Psychology, Chicago, IL.

ⴱ

Powell, S. R., Cirino, P. T., & Malone, A. S. (2017). Child-level predic-

tors of responsiveness to evidence-based mathematics intervention. Ex-

ceptional Children, 83, 359–377. http://dx.doi.org/10.1177/

0014402917690728

ⴱ

Powell, S. R., Driver, M. K., Roberts, G., & Fall, A. (2017). An analysis

of the mathematics vocabulary knowledge of third- and fifth-grade

students: Connections to general vocabulary and mathematics computa-

tion. Learning and Individual Differences, 57, 22–32. http://dx.doi.org/

10.1016/j.lindif.2017.05.011

Powell, S. R., & Fuchs, L. S. (2018). Effective word-problem instruction:

Using schemas to facilitate mathematical reasoning. Teaching Excep-

tional Children, 51, 31–42. http://dx.doi.org/10.1177/004005991

8777250

ⴱ

Praet, M., Titeca, D., Ceulemans, A., & Desoete, A. (2013). Language in

the prediction of arithmetics in kindergarten and grade 1. Learning and

Individual Differences, 27, 90–96. http://dx.doi.org/10.1016/j.lindif

.2013.07.003

Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation

models: Quantitative strategies for communicating indirect effects. Psy-

chological Methods, 16, 93–115. http://dx.doi.org/10.1037/a0022658

ⴱ

Purpura, D. J., Hume, L. E., Sims, D. M., & Lonigan, C. J. (2011). Early

literacy and early numeracy: The value of including early literacy skills

in the prediction of numeracy development. Journal of Experimental

Child Psychology, 110, 647–658. http://dx.doi.org/10.1016/j.jecp.2011

.07.004

ⴱ

Purpura, D. J., & Logan, J. A. R. (2015). The nonlinear relations of the

approximate number system and mathematical language to early math-

ematics development. Developmental Psychology, 51, 1717–1724.

http://dx.doi.org/10.1037/dev0000055

ⴱ

Purpura, D. J., Logan, J. A. R., Hassinger-Das, B., & Napoli, A. R. (2017).

Why do early mathematics skills predict later reading? The role of

mathematical language. Developmental Psychology, 53, 1633–1642.

http://dx.doi.org/10.1037/dev0000375

ⴱ

Purpura, D. J., & Napoli, A. R. (2015). Early numeracy and literacy:

Untangling the relation between specific components. Mathematical

Thinking and Learning, 17, 197–218. http://dx.doi.org/10.1080/

10986065.2015.1016817

ⴱ

Purpura, D. J., Napoli, A. R., Wehrspann, E. A., & Gold, Z. S. (2017).

Causal connections between mathematical language and mathematical

knowledge: A dialogic reading intervention. Journal of Research on

Educational Effectiveness, 10, 116–137. http://dx.doi.org/10.1080/

19345747.2016.1204639

ⴱ

Purpura, D. J., & Reid, E. E. (2016). Mathematics and language: Individ-

ual and group differences in mathematical language skills in young

children. Early Childhood Research Quarterly, 36, 259–268. http://dx

.doi.org/10.1016/j.ecresq.2015.12.020

ⴱ

Purpura, D. J., Schmitt, S. A., & Ganley, C. M. (2017). Foundations of

mathematics and literacy: The role of executive functioning components.

Journal of Experimental Child Psychology, 153, 15–34. http://dx.doi

.org/10.1016/j.jecp.2016.08.010

Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory

and mathematics: A review of developmental, individual difference, and

cognitive approaches. Learning and Individual Differences, 20, 110–

122. http://dx.doi.org/10.1016/j.lindif.2009.10.005

ⴱ

Reid, G. A. (2000). Examining standardized and psychometric potential

assessment and acculturation of Jamaican immigrant children (Doctoral

dissertation). Howard University, Washington, DC.

ⴱ

Ren, L., Zhang, X., Yang, W., & Song, Z. (2018). Relations among

parenting, child behavioral regulation and early competencies: A study

on Chinese preschoolers. Journal of Child and Family Studies, 27,

639–652. http://dx.doi.org/10.1007/s10826-017-0898-y

Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationship

with visuo-spatial abilities and working memory. Educational Psychol-

ogy, 21, 387–399. http://dx.doi.org/10.1080/01443410120090786

Rey-Mermet, A., Gade, M., Souza, A. S., von Bastian, C. C., & Oberauer,

K. (2019). Is executive control related to working memory capacity and

fluid intelligence? Journal of Experimental Psychology: General,

148(8), 1335–1372. http://dx.doi.org/10.1037/xge0000593

ⴱ

Reynolds, C. R. (1983). Regression analyses of race and sex bias in seven

preschool tests. Journal of Psychoeducational Assessment, 1, 169–178.

http://dx.doi.org/10.1177/073428298300100208

ⴱ

Reynolds, E., Vernon-Feagans, L., Bratsch-Hines, M., & Baker, C. E.

(2019). Mothers’ and fathers’ language input from 6 to 36 months in

rural two-parent-families: Relations to children’s kindergarten achieve-

ment. Early Childhood Research Quarterly, 47, 385–395. http://dx.doi

.org/10.1016/j.ecresq.2018.09.002

ⴱ

Rhemtulla, M., & Tucker-Drob, E. M. (2011). Correlated longitudinal

changes across linguistic, achievement, and psychomotor domains in

early childhood: Evidence for a global dimension of development.

Developmental Science, 14, 1245–1254. http://dx.doi.org/10.1111/j

.1467-7687.2011.01071.x

Rindermann, H., Flores-Mendoza, C., & Mansur-Alves, M. (2010). Recip-

rocal effects between fluid and crystallized intelligence and their depen-

dence on parents’ socioeconomic status and education. Learning and

Individual Differences, 20, 544–548. http://dx.doi.org/10.1016/j.lindif

.2010.07.002

ⴱ

Rios, J. A. (2011). Psychometric evaluation of the listening sentence span

task: A working memory measure for English language learners (Doc-

toral dissertation). University of California, Riverside, CA.

ⴱ

Rispens, J. E., McBride-Chang, C., & Reitsma, P. (2008). Morphological

awareness and early and advanced word recognition and spelling in

Dutch. Reading and Writing, 21, 587–607. http://dx.doi.org/10.1007/

s11145-007-9077-7

Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation

and direct instruction. Child Development, 77, 1–15. http://dx.doi.org/

10.1111/j.1467-8624.2006.00852.x

ⴱ

Roberts, J. E., Burchinal, M. R., & Zeisel, S. A. (2002). Otitis media in

early childhood in relation to children’s school-age language and aca-

demic skills. Pediatrics, 110, 696–706. http://dx.doi.org/10.1542/peds

.110.4.696

ⴱ

Roditi, B. N. (1988). Automaticity, cognitive flexibility, and mathematics:

A longitudinal study of children with and without learning disabilities

(Doctoral dissertation). Tufts University Middlesex, MA.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

36 PENG ET AL.

ⴱ

Rohde, T. E., & Thompson, L. A. (2007). Predicting academic achieve-

ment with cognitive ability. Intelligence, 35, 83–92. http://dx.doi.org/10

.1016/j.intell.2006.05.004

ⴱ

Romano, E., Babchishin, L., Pagani, L. S., & Kohen, D. (2010). School

readiness and later achievement: Replication and extension using a

nationwide Canadian survey. Developmental Psychology, 46, 995–1007.

http://dx.doi.org/10.1037/a0018880

ⴱ

Rosselli, M., Ardila, A., Arvizu, L., Kretzmer, T., Standish, V., & Lieber-

mann, J. (1998). Arithmetical abilities in Alzheimer disease. The Inter-

national Journal of Neuroscience, 96, 141–148. http://dx.doi.org/10

.3109/00207459808986463

Rubinstein-Ávila, E., Sox, A. A., Kaplan, S., & McGraw, R. (2015).

Does biliteracy ⫹mathematical discourse ⫽binumerate develop-

ment? Language use in a middle school dual-language mathematics

classroom. Urban Education, 50, 899–937. http://dx.doi.org/10

.1177/0042085914536997

ⴱ

Ryan, J. J., Paolo, A. M., & Brungardt, T. M. (1990). Factor analysis of

the Wechsler Adult Intelligence Scale-revised for persons 75 years and

older. Professional Psychology, Research and Practice, 21, 177–181.

http://dx.doi.org/10.1037/0735-7028.21.3.177

ⴱ

Sarant, J. Z., Harris, D. C., & Bennet, L. A. (2015). Academic outcomes

for school-aged children with severe-profound hearing loss and early

unilateral and bilateral cochlear implants. Journal of Speech, Language,

and Hearing Research, 58, 1017–1032. http://dx.doi.org/10.1044/

2015_JSLHR-H-14-0075

Schleppegrell, M. J. (2007). The linguistic challenges of mathematics

teaching and learning: A research review. Reading & Writing Quarterly,

23, 139–159. http://dx.doi.org/10.1080/10573560601158461

ⴱ

Schmitt, S. A., McClelland, M. M., Tominey, S. L., & Acock, A. C.

(2015). Strengthening school readiness for head start children: Evalua-

tion of a self-regulation intervention. Early Childhood Research Quar-

terly, 30, 20–31. http://dx.doi.org/10.1016/j.ecresq.2014.08.001

ⴱ

Schult, J., & Sparfeldt, J. R. (2016). Do non-g factors of cognitive ability

tests align with specific academic achievements? A combined bifactor

modeling approach. Intelligence, 59, 96–102. http://dx.doi.org/10.1016/

j.intell.2016.08.004

ⴱ

Schwenck, C., Dummert, F., Endlich, D., & Schneider, W. (2015). Cog-

nitive functioning in children with learning problems. European Journal

of Psychology of Education, 30, 349–367. http://dx.doi.org/10.1007/

s10212-014-0242-5

ⴱ

Seethaler, P. M., & Fuchs, L. S. (2006). The cognitive correlates of

computational estimation skill among third-grade students. Learning

Disabilities Research & Practice, 21, 233–243. http://dx.doi.org/10

.1111/j.1540-5826.2006.00220.x

ⴱ

Seethaler, P. M., Fuchs, L. S., Fuchs, D., & Compton, D. L. (2012).

Predicting first graders’ development of calculation versus word-

problem performance: The role of dynamic assessment. Journal of

Educational Psychology, 104, 224–234. http://dx.doi.org/10.1037/

a0024968

ⴱ

Seethaler, P. M., Fuchs, L. S., Fuchs, D., & Compton, D. L. (2016). Does

the value of dynamic assessment in predicting end-of-first-grade math-

ematics performance differ as a function of English language profi-

ciency? The Elementary School Journal, 117, 171–191. http://dx.doi

.org/10.1086/688870

ⴱ

Seethaler, P. M., Fuchs, L. S., Star, J. R., & Bryant, J. (2011). The

cognitive predictors of computational skill with whole versus rational

numbers: An exploratory study. Learning and Individual Differences,

21, 536–542. http://dx.doi.org/10.1016/j.lindif.2011.05.002

ⴱ

Sektnan, M., McClelland, M. M., Acock, A., & Morrison, F. J. (2010).

Relations between early family risk, children’s behavioral regulation,

and academic achievement. Early Childhood Research Quarterly, 25,

464–479. http://dx.doi.org/10.1016/j.ecresq.2010.02.005

ⴱ

Sewell, R. D. (2008). Cognitive and behavioral correlates in mathemat-

ical ability subtypes (Doctoral dissertation). University of California,

Riverside, CA.

Sfard, A. (2008). Thinking as communicating: Human development, the

growth of discourses, and mathematizing. New York, NY: Cambridge

University Press. http://dx.doi.org/10.1017/CBO9780511499944

ⴱ

Shahaeian, A., Wang, C., Tucker-Drob, E., Geiger, V., Bus, A. G., &

Harrison, L. J. (2018). Early shared reading, socioeconomic status, and

children’s cognitive and school competencies: Six years of longitudinal

evidence. Scientific Studies of Reading, 22, 485–502. http://dx.doi.org/

10.1080/10888438.2018.1482901

ⴱ

Shankweiler, D., Crain, S., Katz, L., Fowler, A. E., Liberman, A. M.,

Brady, S. A.,...Shaywitz, B. A. (1995). Cognitive profiles of reading-

disabled children: Comparison of language skills in phonology, mor-

phology, and syntax. Psychological Science, 6, 149–156. http://dx.doi

.org/10.1111/j.1467-9280.1995.tb00324.x

ⴱ

Shaul, S., & Schwartz, M. (2014). The role of the executive functions in

school readiness among preschool-age children. Reading and Writing,

27, 749–768. http://dx.doi.org/10.1007/s11145-013-9470-3

ⴱ

Shaw, R. R. (2007). The relationship between pediatric HIV infection,

CD4 percentage, HAART, and WISC-III performance (Doctoral disser-

tation). Columbia University, New York City, NY.

ⴱ

Sholl, M. J., & Egeth, H. E. (1982). Cognitive correlates of map-reading

ability. Intelligence, 6, 215–230. http://dx.doi.org/10.1016/0160-

2896(82)90015-0

Sidney, P. G., Hattikudur, S., & Alibali, M. W. (2015). How do contrasting

cases and self-explanation promote learning? evidence from fraction

division. Learning and Instruction, 40, 29–38. http://dx.doi.org/10

.1016/j.learninstruc.2015.07.006

ⴱ

Simmons, F., Singleton, C., & Horne, J. (2008). Brief report-phonological

awareness and visual-spatial sketchpad functioning predict early arith-

metic attainment: Evidence from a longitudinal study. The European

Journal of Cognitive Psychology, 20, 711–722. http://dx.doi.org/10

.1080/09541440701614922

ⴱ

Simmons, F. R., Willis, C., & Adams, A. M. (2012). Different compo-

nents of working memory have different relationships with different

mathematical skills. Journal of Experimental Child Psychology, 111,

139–155. http://dx.doi.org/10.1016/j.jecp.2011.08.011

ⴱ

Singer, V., Strasser, K., & Cuadro, A. (2019). Direct and indirect paths

from linguistic skills to arithmetic school performance. Journal of Ed-

ucational Psychology, 111, 434–445. http://dx.doi.org/10.1037/

edu0000290

ⴱ

Skwarchuk, S. L., Sowinski, C., & LeFevre, J. A. (2014). Formal and

informal home learning activities in relation to children’s early nu-

meracy and literacy skills: The development of a home numeracy model.

Journal of Experimental Child Psychology, 121, 63–84. http://dx.doi

.org/10.1016/j.jecp.2013.11.006

ⴱ

Slate, J. R. (1995). Two investigations of the validity of the WISC-III.

Psychological Reports, 76, 299–306. http://dx.doi.org/10.2466/pr0.1995

.76.1.299

ⴱ

Slot, E. M., van Viersen, S., de Bree, E. H., & Kroesbergen, E. H. (2016).

Shared and unique risk factors underlying mathematical disability and

reading and spelling disability. Frontiers in Psychology, 7, 803. http://

dx.doi.org/10.3389/fpsyg.2016.00803

ⴱ

Smiley, D. F. (2002). Problem solving ability in elementary school age

children with hearing impairment (Doctoral dissertation). University of

Tennessee, Knoxville, TN.

ⴱ

Smith, T. C., Smith, B. L., & Dobbs, K. (1991). Relationship between the

Peabody Picture Vocabulary test-revised, wide range achievement test-

revised, and Weschler Intelligence Scale for children-revised. Journal of

School Psychology, 29, 53–56. http://dx.doi.org/10.1016/0022-

4405(91)90015-J

ⴱ

Son, S. C., Kwon, K., Jeon, H., & Hong, S. (2013). Head start classrooms

and children’s school readiness benefit from teachers’ qualifications and

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

ongoing training. Child and Youth Care Forum, 42, 525–553. http://dx

.doi.org/10.1007/s10566-013-9213-2

ⴱ

Sorhagen, N. S. (2013). Early teacher expectations disproportionately

affect poor children’s high school performance. Journal of Educational

Psychology, 105, 465–477. http://dx.doi.org/10.1037/a0031754

ⴱ

Soto-Calvo, E., Simmons, F. R., Willis, C., & Adams, A. M. (2015).

Identifying the cognitive predictors of early counting and calculation

skills: Evidence from a longitudinal study. Journal of Experimental

Child Psychology, 140, 16–37. http://dx.doi.org/10.1016/j.jecp.2015.06

.011

ⴱ

Sowinski, C., LeFevre, J. A., Skwarchuk, S. L., Kamawar, D., Bisanz, J.,

& Smith-Chant, B. (2015). Refining the quantitative pathway of the

Pathways to Mathematics model. Journal of Experimental Child Psy-

chology, 131, 73–93. http://dx.doi.org/10.1016/j.jecp.2014.11.004

Spelke, E. S. (2017). Core knowledge, language, and number. Language

Learning and Development, 13, 147–170. http://dx.doi.org/10.1080/

15475441.2016.1263572

Spelke, E. S., & Tsivkin, S. (2001). Language and number: A bilingual

training study. Cognition, 78, 45–88. http://dx.doi.org/10.1016/S0010-

0277(00)00108-6

ⴱ

Speybroeck, S., Kuppens, S., Van Damme, J., Van Petegem, P., Lamote,

C., Boonen, T., & de Bilde, J. (2012). The role of teachers’ expectations

in the association between children’s SES and performance in kinder-

garten: A moderated mediation analysis. PLoS ONE, 7, e34502. http://

dx.doi.org/10.1371/journal.pone.0034502

ⴱ

Srinivasan, R. (1991). A cross-cultural study of subtypes of learning

disabilities in multilingual children residing in Lidia (Doctoral disser-

tation). California School of Professional Psychology, Berkeley/

Alameda, CA.

Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student

capacity for mathematical thinking and reasoning: An analysis of math-

ematical tasks used in reform classrooms. American Educational Re-

search Journal, 33, 455–488. http://dx.doi.org/10.3102/00028312

033002455

ⴱ

Stevenson, H. W., & Newman, R. S. (1986). Long-term prediction of

achievement and attitudes in mathematics and reading. Child Develop-

ment, 57, 646–659. http://dx.doi.org/10.2307/1130343

ⴱ

Sun, J., Zhang, L., Chen, E., Lau, C., & Rao, N. (2018). Preschool

attendance and executive function mediate early academic achievement

gaps in East Asia and the Pacific. Early Education and Development, 29,

1039–1060. http://dx.doi.org/10.1080/10409289.2018.1498999

ⴱ

Super, D. E. (1940). The A. C. E. psychological examination and special

abilities. The Journal of Psychology, 10, 221–226. http://dx.doi.org/10

.1080/00223980.1940.9917688

ⴱ

Susperreguy Jorquera, M. I. (2013). “Math talk” in families of preschool-

aged children: Frequency and relations to children’s early math skills

across time (Doctoral dissertation). The University of Michigan, Ann

Arbor, MI.

ⴱ

Swanson, H. L. (2004). Working memory and phonological processing as

predictors of children’s mathematical problem solving at different ages.

Memory & Cognition, 32, 648–661. http://dx.doi.org/10.3758/

BF03195856

ⴱ

Swanson, H. L. (2006). Cognitive processes that underlie mathematical

precociousness in young children. Journal of Experimental Child Psy-

chology, 93, 239–264. http://dx.doi.org/10.1016/j.jecp.2005.09.006

ⴱ

Swanson, H. L. (2011). Working memory, attention, and mathematical

problem solving: A longitudinal study of elementary school children.

Journal of Educational Psychology, 103, 821–837. http://dx.doi.org/10

.1037/a0025114

ⴱ

Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship

between working memory and mathematical problem solving in children

at risk and not at risk for serious math difficulties. Journal of Educa-

tional Psychology, 96, 471–491. http://dx.doi.org/10.1037/0022-0663

.96.3.471

ⴱ

Swanson, H. L., & Fung, W. (2016). Working memory components and

problem-solving accuracy: Are there multiple pathways? Journal of

Educational Psychology, 108, 1153–1177. http://dx.doi.org/10.1037/

edu0000116

ⴱ

Swanson, H. L., Jerman, O., & Zheng, X. (2008). Growth in working

memory and mathematical problem solving in children at risk and not at

risk for serious math difficulties. Journal of Educational Psychology,

100, 343–379. http://dx.doi.org/10.1037/0022-0663.100.2.343

ⴱ

Swanson, H. L., Kong, J., & Petcu, S. (2018). Math difficulties and

working memory growth in English language learner children: Does

bilingual proficiency play a significant role? Language, Speech, and

Hearing Services in Schools, 49, 379–394. http://dx.doi.org/10.1044/

2018_LSHSS-17-0098

ⴱ

Swanson, H. L., & Sachse-Lee, C. (2001). Mathematical problem solving

and working memory in children with learning disabilities: Both exec-

utive and phonological processes are important. Journal of Experimental

Child Psychology, 79, 294–321. http://dx.doi.org/10.1006/jecp.2000

.2587

ⴱ

Swanson, L., & Kim, K. (2007). Working memory, short-term memory,

and naming speed as predictors of children’s mathematical performance.

Intelligence, 35, 151–168. http://dx.doi.org/10.1016/j.intell.2006.07.001

Sweller, J. (1994). Cognitive load theory, learning difficulty, and instruc-

tional design. Learning and Instruction, 4, 295–312. http://dx.doi.org/

10.1016/0959-4752(94)90003-5

Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014).

Cognitive components of a mathematical processing network in 9-year-

old children. Developmental Science, 17, 506–524. http://dx.doi.org/10

.1111/desc.12144

ⴱ

Tan, M., Mourgues, C., Bolden, D. S., & Grigorenko, E. L. (2013).

Making numbers come to life: Two scoring methods for creativity in

Aurora’s cartoon numbers. The Journal of Creative Behavior, 48, 25–

43. http://dx.doi.org/10.1002/jocb.39

ⴱ

Tang, W. (2007). Cognitive processes related to reading and arithmetic

(Doctoral dissertation). The University of British Columbia, Vancouver,

BC, Canada.

ⴱ

Tillinghast, B. S., Morrow, J. E., & Uhlig, G. E. (1984). Validity of the

PPVT—R using elementary school academic grades as criteria. Psychol-

ogy: A Journal of Human Behavior, 21, 43–47.

Tiu, R. D., Jr., Thompson, L. A., & Lewis, B. A. (2003). The role of IQ in

a component model of reading. Journal of Learning Disabilities, 36,

424–436. http://dx.doi.org/10.1177/00222194030360050401

ⴱ

Tolar, T. D., Fuchs, L., Cirino, P. T., Fuchs, D., Hamlett, C. L., &

Fletcher, J. M. (2012). Predicting development of mathematical word

problem solving across the intermediate grades. Journal of Educational

Psychology, 104, 1083–1093. http://dx.doi.org/10.1037/a0029020

ⴱ

Toll, S. W. M., & Van Luit, J. E. H. (2014). The developmental relation-

ship between language and low early numeracy skills throughout kin-

dergarten. Exceptional Children, 81, 64–78. http://dx.doi.org/10.1177/

0014402914532233

ⴱ

Träff, U., Desoete, A., & Passolunghi, M. C. (2017). Symbolic and

non-symbolic number processing in children with developmental dys-

lexia. Learning and Individual Differences, 56, 105–111. http://dx.doi

.org/10.1016/j.lindif.2016.10.010

ⴱ

Träff, U., & Passolunghi, M. C. (2015). Mathematical skills in children

with dyslexia. Learning and Individual Differences, 40, 108–114. http://

dx.doi.org/10.1016/j.lindif.2015.03.024

ⴱ

Träff, U., Skagerlund, K., Olsson, L., & Östergren, R. (2017). Pathways

to arithmetic fact retrieval and percentage calculation in adolescents. The

British Journal of Educational Psychology, 87, 647–663. http://dx.doi

.org/10.1111/bjep.12170

ⴱ

Tsushima, W. T. (1994). Short form of the WPPSI and WPPSI-R. Journal

of Clinical Psychology, 50, 877–880. http://dx.doi.org/10.1002/1097-

4679(199411)50:6⬍877::AID-JCLP2270500610⬎3.0.CO;2-R

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

38 PENG ET AL.

ⴱ

Tupa, D. J., O’Dougherty Wright, M., & Fristad, M. A. (1997). Confir-

matory factor analysis of the WISC-III with child psychiatric inpatients.

Psychological Assessment, 9, 302–306. http://dx.doi.org/10.1037/1040-

3590.9.3.302

ⴱ

University of Iowa. (2008). ITBS research guide. Retrieved from https://

itp.education.uiowa.edu/ia/documents/itbs-research-guide.pdf

ⴱ

van Bergen, E., de Jong, P. F., Maassen, B., & van der Leij, A. (2014).

The effect of parents’ literacy skills and children’s preliteracy skills on

the risk of dyslexia. Journal of Abnormal Child Psychology, 42, 1187–

1200. http://dx.doi.org/10.1007/s10802-014-9858-9

ⴱ

Vanbinst, K., Ansari, D., Ghesquière, P., & De Smedt, B. (2016). Sym-

bolic numerical magnitude processing is as important to arithmetic as

phonological awareness is to reading. PLoS ONE, 11, e0151045. http://

dx.doi.org/10.1371/journal.pone.0151045

van der Maas, H. L., Dolan, C. V., Grasman, R. P., Wicherts, J. M.,

Huizenga, H. M., & Raijmakers, M. E. (2006). A dynamical model of

general intelligence: The positive manifold of intelligence by mutualism.

Psychological Review, 113, 842–861. http://dx.doi.org/10.1037/0033-

295X.113.4.842

ⴱ

Van Rooijen, M., Verhoeven, L., & Steenbergen, B. (2016). Working

memory and fine motor skills predict early numeracy performance of

children with cerebral palsy. Child Neuropsychology, 22, 735–747.

http://dx.doi.org/10.1080/09297049.2015.1046426

ⴱ

Verdine, B. N., Irwin, C. M., Golinkoff, R. M., & Hirsh-Pasek, K. (2014).

Contributions of executive function and spatial skills to preschool math-

ematics achievement. Journal of Experimental Child Psychology, 126,

37–51. http://dx.doi.org/10.1016/j.jecp.2014.02.012

ⴱ

von Suchodoletz, A., & Gunzenhauser, C. (2013). Behavior regulation

and early math and vocabulary knowledge in German preschool chil-

dren. Early Education and Development, 24, 310–331. http://dx.doi.org/

10.1080/10409289.2012.693428

ⴱ

von Suchodoletz, A., Uka, F., & Larsen, R. A. A. A. (2015). Self-

regulation across different contexts: Findings in young Albanian chil-

dren. Early Education and Development, 26, 829– 846. http://dx.doi.org/

10.1080/10409289.2015.1012189

ⴱ

Vukovic, R. K. (2006). The development of numeracy: A longitudinal

study of children from first through fourth grade (Doctoral dissertation).

The University of British Columbia, Vancouver, BC, Canada.

ⴱ

Vukovic, R. K., Fuchs, L. S., Geary, D. C., Jordan, N. C., Gersten, R., &

Siegler, R. S. (2014). Sources of individual differences in children’s

understanding of fractions. Child Development, 85, 1461–1476. http://

dx.doi.org/10.1111/cdev.12218

ⴱ

Vukovic, R. K., & Lesaux, N. K. (2013a). The language of mathematics:

Investigating the ways language counts for children’s mathematical

development. Journal of Experimental Child Psychology, 115, 227–244.

http://dx.doi.org/10.1016/j.jecp.2013.02.002

ⴱ

Vukovic, R. K., & Lesaux, N. K. (2013b). The relationship between

linguistic skills and arithmetic knowledge. Learning and Individual

Differences, 23, 87–91. http://dx.doi.org/10.1016/j.lindif.2012.10.007

Vygotsky, L. S. (1986). Thought and language. Cambridge, MA: MIT

Press.

ⴱ

Wade, M., Jenkins, J. M., Venkadasalam, V. P., Binnoon-Erez, N., &

Ganea, P. A. (2018). The role of maternal responsiveness and linguistic

input in pre-academic skill development: A longitudinal analysis of

pathways. Cognitive Development, 45, 125–140. http://dx.doi.org/10

.1016/j.cogdev.2018.01.005

Wagner, R., Torgesen, J., Rashotte, C., & Pearson, N. A. (1999). CTOPP:

Comprehensive Test of Phonological Processing (2nd ed.). Austin, TX:

Pro-ed.

ⴱ

Wallace, W. L. (1950). Prediction of grades in specific college courses.

The Journal of Educational Research, 44, 587–598. http://dx.doi.org/10

.1080/00220671.1951.10881895

ⴱ

Wang, A. Y., Fuchs, L. S., & Fuchs, D. (2016). Cognitive and linguistic

predictors of mathematical word problems with and without irrelevant

information. Learning and Individual Differences, 52, 79–87. http://dx

.doi.org/10.1016/j.lindif.2016.10.015

ⴱ

Wanless, S. B. (2008). Measuring behavioral regulation in young chil-

dren (Doctoral dissertation). Oregon State University, Corvallis, OR.

ⴱ

Wanless, S. B., Kim, K. H., Zhang, C., Degol, J. L., Chen, J. L., & Chen,

F. M. (2016). Trajectories of behavioral regulation for Taiwanese chil-

dren from 3.5 to 6 years and relations to math and vocabulary outcomes.

Early Childhood Research Quarterly, 34, 104–114. http://dx.doi.org/10

.1016/j.ecresq.2015.10.001

ⴱ

Wanless, S. B., McClelland, M. M., Acock, A. C., Chen, F. M., & Chen,

J. L. (2011). Behavioral regulation and early academic achievement in

Taiwan. Early Education and Development, 22, 1–28. http://dx.doi.org/

10.1080/10409280903493306

ⴱ

Watson, C. S., Kidd, G. R., Homer, D. G., Connell, P. J., Lowther, A.,

Eddins, D. A.,...Watson, B. U. (2003). Sensory, cognitive, and

linguistic factors in the early academic performance of elementary

school children: The Benton-IU project. Journal of Learning Disabili-

ties, 36, 165–197. http://dx.doi.org/10.1177/002221940303600209

Wechsler, D. Wechsler adult intelligence scale–fourth edition (WAIS–IV).

San Antonio, TX: NCS Pearson, 22:498, 2008.

ⴱ

Wei, W., Lu, H., Zhao, H., Chen, C., Dong, Q., & Zhou, X. (2012).

Gender differences in children’s arithmetic performance are accounted

for by gender differences in language abilities. Psychological Science,

23, 320–330. http://dx.doi.org/10.1177/0956797611427168

ⴱ

Wei, W., Yuan, H., Chen, C., & Zhou, X. (2012). Cognitive correlates of

performance in advanced mathematics. The British Journal of Educa-

tional Psychology, 82, 157–181. http://dx.doi.org/10.1111/j.2044-8279

.2011.02049.x

Weiland, C., & Yoshikawa, H. (2013). Impacts of a prekindergarten

program on children’s mathematics, language, literacy, executive func-

tion, and emotional skills. Child Development, 84, 2112–2130. http://dx

.doi.org/10.1111/cdev.12099

ⴱ

West, G., Vadillo, M. A., Shanks, D. R., & Hulme, C. (2018). The

procedural learning deficit hypothesis of language learning disorders:

We see some problems. Developmental Science, 21, e12552. http://dx

.doi.org/10.1111/desc.12552

ⴱ

Wiese, M. J., Lamb, C., & Piersel, W. C. (1988). WISC-R factor scores

and student self-ratings of behavior as predictors of academic achieve-

ment. Psychology in the Schools, 25, 35–41. http://dx.doi.org/10.1002/

1520-6807(198801)25:1⬍35::AID-PITS2310250106⬎3.0.CO;2-B

ⴱ

Willoughby, M. T., Blair, C. B., Wirth, R. J., & Greenberg, M. (2012).

The measurement of executive function at age 5: Psychometric proper-

ties and relationship to academic achievement. Psychological Assess-

ment, 24, 226–239. http://dx.doi.org/10.1037/a0025361

Wilson, R. A., & Keil, F. (1998). The shadows and shallows of explana-

tion. Minds and Machines, 8, 137–159. http://dx.doi.org/10.1023/A:

1008259020140

ⴱ

Wright, D. (1987). Intelligence and achievement: A factor analytic and

canonical correlational study. Journal of Psychoeducational Assessment,

5, 236–247. http://dx.doi.org/10.1177/073428298700500306

ⴱ

Wright, J. C., Huston, A. C., Murphy, K. C., St. Peters, M., Piñon, M.,

Scantlin, R., & Kotler, J. (2001). The relations of early television

viewing to school readiness and vocabulary of children from low-

income families: The early window project. Child Development, 72,

1347–1366. http://dx.doi.org/10.1111/1467-8624.t01-1-00352

Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of

mathematical word problem-solving instruction on middle school stu-

dents with learning problems. The Journal of Special Education, 39,

181–192. http://dx.doi.org/10.1177/00224669050390030501

ⴱ

Zagoloff, Z. (2010). The mediating effect of language skill on academic

achievement among African American, Caucasian, and Latino first–

third grade students (Doctoral dissertation). Illinois Institute of Tech-

nology, Chicago, IL.

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

LANGUAGE AND MATHEMATICS

ⴱ

Zepp, R. A. (1981). Relationships between mathematics achievement and

various English language proficiencies. Educational Studies in Mathe-

matics, 12, 59–70. http://dx.doi.org/10.1007/BF00386046

ⴱ

Zhang, J., Fan, X., Cheung, S. K., Meng, Y., Cai, Z., & Hu, B. Y. (2017).

The role of early language abilities on math skills among Chinese

children. PLoS ONE, 12, e0181074. http://dx.doi.org/10.1371/journal

.pone.0181074

ⴱ

Zhang, X. (2016). Linking language, visual-spatial, and executive func-

tion skills to number competence in very young Chinese children. Early

Childhood Research Quarterly, 36, 178–189. http://dx.doi.org/10.1016/

j.ecresq.2015.12.010

ⴱ

Zhang, X. (2018). Letter-name knowledge longitudinally predicts young

Chinese children’s Chinese word reading and number competencies in a

multilingual context. Learning and Individual Differences, 65, 176–186.

http://dx.doi.org/10.1016/j.lindif.2018.06.004

ⴱ

Zhang, X., Hu, B. Y., Ren, L., & Fan, X. (2017). Pathways to reading,

mathematics, and science: Examining domain-general correlates in

young Chinese children. Contemporary Educational Psychology, 51,

366–377. http://dx.doi.org/10.1016/j.cedpsych.2017.09.004

ⴱ

Zhang, X., Koponen, T., Räsänen, P., Aunola, K., Lerkkanen, M. K., &

Nurmi, J. E. (2014). Linguistic and spatial skills predict early arithmetic

development via counting sequence knowledge. Child Development, 85,

1091–1107. http://dx.doi.org/10.1111/cdev.12173

ⴱ

Zhang, X., & Lin, D. (2015). Pathways to arithmetic: The role of visual-

spatial and language skills in written arithmetic, arithmetic word prob-

lems, and non-symbolic arithmetic. Contemporary Educational Psychol-

ogy, 41, 188–197. http://dx.doi.org/10.1016/j.cedpsych.2015.01.005

ⴱ

Zhang, X., & Lin, D. (2017). Does growth rate in spatial ability matter in

predicting early arithmetic competence? Learning and Instruction, 49,

232–241. http://dx.doi.org/10.1016/j.learninstruc.2017.02.003

ⴱ

Zhang, X., & Lin, D. (2018). Cognitive precursors of word reading versus

arithmetic competencies in young Chinese children. Early Childhood

Research Quarterly, 42, 55–65. http://dx.doi.org/10.1016/j.ecresq.2017

.08.006

ⴱ

Zhang, X., Räsänen, P., Koponen, T., Aunola, K., Lerkkanen, M. K., &

Nurmi, J. E. (2017). Knowing, applying, and reasoning about arithmetic:

Roles of domain-general and numerical skills in multiple domains of

arithmetic learning. Developmental Psychology, 53, 2304–2318. http://

dx.doi.org/10.1037/dev0000432

ⴱ

Zhang, X., Räsänen, P., Koponen, T., Aunola, K., Lerkkanen, M., &

Nurmi, J. (2020). Early cognitive precursors of children’s mathematics

learning disability and persistent low achievement: A 5-year longitudinal

study. Child Development, 91, 7–27. http://dx.doi.org/10.1111/cdev

.13123

Zwaan, R. A., & Radvansky, G. A. (1998). Situation models in language

comprehension and memory. Psychological Bulletin, 123, 162–185.

http://dx.doi.org/10.1037/0033-2909.123.2.162

Received April 13, 2019

Revision received February 20, 2020

Accepted March 5, 2020 䡲

This document is copyrighted by the American Psychological Association or one of its allied publishers.

This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

40 PENG ET AL.

A preview of this full-text is provided by American Psychological Association.

Learn more

Content available from Psychological Bulletin

This content is subject to copyright. Terms and conditions apply.

Mediation effect of mathematics vocabulary skills between reading comprehension abilities and mathematics performance

Article

Full-text available

Jun 2025

Mathematics requires both comprehension and competence, which, once developed, benefit learners in daily life. This descriptive-correlational and explanatory study filled the gap by determining the mediating effect of vocabulary skills on the relationship between comprehension abilities and mathematics performance of 146 grade 7 students, chosen through multi-stage sampling techniques, in two select schools in Cabuyao City, Philippines, in 2024–2025. The respondents answered valid and reliable instruments with ethical considerations. The study used weighted mean, standard deviation, multiple regression bootstrap technique, mediated regression bootstrap technique, and PLS-SEM. The outcomes showed high levels of mathematics vocabulary skills and reading comprehension abilities, while mathematics performance reached satisfactory levels among the students. Multiple regression bootstrap technique revealed mathematics vocabulary as the most important factor affecting students' mathematics performance, while reading comprehension abilities have no direct significant effect with the presence of mathematics vocabulary. Furthermore, mediated regression bootstrap technique and PLS-SEM displayed a significant total effect of reading comprehension abilities on mathematics performance and the indirect effect flowing through mathematics vocabulary skills was significant. Mathematical vocabulary skills entirely mediate the indirect effect of reading comprehension abilities on mathematics performance exemplifying full mediation. It suggests that mathematics vocabulary skills are essential in enhancing reading comprehension abilities, thereby reinforcing their crucial role in academic achievement. Educators are encouraged to integrate vocabulary-focused strategies, administrators to support professional development in math literacy, and local officials to fund programs that strengthen foundational language skills in mathematics. Recommended Citation: Munda, N.P., Endrinal, J.R.H., & Nequinto, M.C. (2025). Mediation effect of mathematics vocabulary skills between reading comprehension abilities and mathematics performance. International Journal of Educational Management and Development Studies, 6(2), 167-187. https://doi.org/10.53378/ijemds.353205

Effects of Reading Strategy Intervention on Math Word Problems in Bilingual School-Age Students With Math Difficulties

Article

Full-text available

Jun 2025

Clinical Question: Do bilingual school-age children (P) who receive reading strategy alone interventions (I) show improvement in math word problems (O) relative to a multiple-target intervention or control condition (C)? Method: Systematic Review Study Sources: PsycInfo ® , Web of Science, JSTOR, PubMed, ERIC Search Terms: "bilingual*" OR "second language learner" OR "language learner" OR "English as a second language" OR "English as a foreign language" AND "math word problem" OR "math applied problems" AND "intervention" OR "treatment" OR "therapy" AND "school-age" OR "elementary" OR "primary" OR "grade" Number of Included Studies: 12 Primary Results: Bilingual students with math difficulties showed improvement in math word problems from reading strategy interventions and reading strategy interventions with math vocabulary instruction, content knowledge priming, and culturally relevant approaches. Bilingual students and teachers generally had positive feedback on various intervention approaches. Conclusions: An overall aim of reading strategy interventions for bilingual students with math difficulties is to actively regulate their reading behaviors to reduce the cognitive load on linguistic information to focus on solving math word problems. There are two high-level pieces of evidence showing that bilingual students with math difficulties benefit from reading strategy interventions alone or in combination with content knowledge priming. However, additional research is needed to evaluate the effectiveness of including math vocabulary instruction, the use of a culturally relevant approach, and the comparison of different reading strategies. These approaches only have minimal evidence (primarily single-subject design studies) yet have high social validity.

Mathematics Instruction for Students with Learning Disabilities

Article

Jan 2025

In this chapter, we present effective and evidence-based instructional practices to improve the mathematical literacy, concepts, knowledge, and skills of students with learning disabilities through (a) explicit instruction to teach mathematics vocabulary, (b) strategies promoting mathematical communication, (c) self-regulated strategy development to teach mathematical writing, (d) use of visual representations, (e) use of mathematical manipulatives, and (f) cognitive and metacognitive strategies to teach mathematical problem-solving. Mathematical literacy characterizes the ability to comprehend, communicate, and solve real-word problems in learning mathematics. However, many students with learning disabilities often face challenges in learning these mathematics abilities. As such, instructional practices that foster the development of mathematical literacy beyond mathematical proficiency for students with learning disabilities can lead to advancing their understanding and use of mathematical concepts, knowledge, and skills. We also describe inclusive practices and assessments that could be used as instructional frameworks for all learners, including those with learning disabilities. These include Universal Design for Learning, accommodations and modifications, data-based individualization, assistive technology, and emerging technology (e.g., artificial intelligence). As a provision of appropriate support tailored to mathematics instruction, these instructional practices will extend and promote students’ active engagement in learning mathematics.

A Comparative Assessment of Mathematical Vocabulary, Operations and Problem-Solving Skills in 5th Grade children with ADHD and SLD

Preprint

Apr 2025

This study aimed to conduct a comparative assessment of mathematical competence-including vocabulary, operations, and problem-solving-in children diagnosed with Specific Learning Disability (SLD) and Attention-Deficit/Hyperactivity Disorder (ADHD). Individual assessments were administered to evaluate intelligence quotient (IQ), mathematical competence, reading, and written language for both groups (SLD: N = 17; ADHD: N = 17). The results revealed statistically significant differences between the groups in several WISC subtests: Verbal IQ, Information (factual knowledge, long-term memory, recall), Arithmetic (attention, concentration, numerical reasoning), Digit Span (short-term auditory memory, concentration), Picture Arrangement (planning, logical thinking, social knowledge), Verbal Comprehension Index (VCI), and Freedom from Distractibility Index (FDI), as well as in Mathematical Operations and Mathematical Problem Solving. Both groups demonstrated difficulties across all assessed domains. To explore these difficulties in greater depth, canonical correlation analyses (CCA) were conducted on three variable sets. Findings suggest that while both SLD and ADHD are associated with cognitive challenges, they present largely distinct patterns of cognitive deficits. The implications of these results are discussed in the context of educational assessment and intervention.

فاعلية استخدام مدخل التعلم التكاملي بين المحتوى واللغة (CLIL) في تنمية مهارات التواصل الرياضي والثقة التدريسية لدى طلاب الدبلوم المهني "شعبة الرياضيات باللغة الإنجليزية" The Effectiveness of Using CLIL Approach in Developing Mathematical Communication Skills and Teaching Confidence for Students of the Professional Diploma "Mathematics Department in Englis

Article

Jan 2025

زيزي السيد عبد العزيز عبد الحي

Indigenous vs. Eurocentric Teaching Methods: The Place of Afro-Centric Games in South African Primary School Mathematics Curriculum

Chapter

Nov 2024

Austin Musundire

This paper addresses disparities in Mathematics teaching between Indigenous and Eurocentric methods in South African primary schools, aiming to improve mathematical performance in underprivileged settings. Through systematic literature review, action research, and action learning, it identifies Afro-centric games like nhodo, tsoro, and pada as effective tools for teaching basic math concepts. The study reflects the potential of integrating these games into the South African curriculum to enhance learning outcomes.

Examine the Longitudinal Association Between Prior and Subsequent Mathematics Using Meta-Analytic Structural Equation Modeling Approach

Article

Full-text available

Jun 2025
EDUC PSYCHOL REV

The current meta-analysis investigates the longitudinal association between prior and subsequent mathematics performance, involving mathematics measured at three time points, and to identify potential factors that could moderate this association, including age, time lag, and types of mathematics. Our analysis included 105 studies, comprising 111 independent samples and involving 413,541 individual students. Our findings revealed that early mathematics knowledge at Time 1 was associated with later performance at Time 3, both directly and indirectly through intermediate performance at Time 2, after controlling for working memory and language comprehension. Notably, the stability of the association between Time 1 and Time 3 mathematics remained robust across increasing age and time lag, while the association between Time 1 and Time 2 weakened as the time lag grew. Additionally, stronger associations were observed when mathematics at Time 1 and Time 3 involved similar or more comprehensive tasks. These findings suggest snowballing effect is more likely to occur within similar types of mathematics tasks, whereas a steppingstone effect is more likely between prior foundational mathematics and later higher level mathematical concepts.

Comorbidity of reading and math learning difficulties in a Chinese sample

Article

May 2025
LEARN INDIVID DIFFER

Development of a Mathematics Vocabulary Test: Evidence of Validity and Reliability in a Multilingual Context

Article

Full-text available

Apr 2025

The aim of this study was to develop the Mathematics Vocabulary Test (MVT)—an instrument to identify young children with a limited mathematics vocabulary—in a multilingual majority country—South Africa. This study consists of two substudies with children aged 3–8.5 years (N = 988, ngirls = 429). In Study 1, a 26-item MVT was developed by multiprofessional expert panels and piloted in four languages, isiZulu (n = 229), Sesotho (n = 83), English (n = 89), and Afrikaans (n = 216). Study 1 provided evidence of content validity, and the MVT was further revised based on the results. In Study 2, additional samples were assessed with the revised version of the MVT in English (Stage 1, n = 270) and isiZulu (Stage 2, n = 101) to provide further evidence of reliability and validity for these two language versions of the test. Confirmatory factor analyses supported structural validity of a unidimensional structure, including 20 items in the English version and 16 items in the isiZulu version. The structure of the English MVT showed stability across time (T2 5 months after T1). Both versions showed good reliability in terms of internal consistency. Our findings also provided evidence of concurrent and known-group validity for both language versions, as well as predictive validity of the English version of the test. The English and isiZulu MVT can be used as a measure of mathematics vocabulary in educational practice and research with young children.

Analysing the Role of Language in Mathematics Instruction: Challenges of Teaching Mathematics in a Multilingual Context in Kalomo District

Preprint

Full-text available

Apr 2025

Kadonsi Kaziya

This study explores how language shapes the teaching and learning of mathematics in Kalomo District, Zambia—a region where students grow up speaking local languages but are expected to switch to English as the language of instruction by Grade 5. Using a sequential mixed-methods approach, the research investigates how this linguistic shift impacts student performance, how teachers cope with language-related challenges, and what Zambia’s language-in-education policy means for everyday classroom practice. Data from mathematics tests and surveys involving 200 students and 30 teachers show a strong link between English proficiency and math achievement (r = 0.65, p < 0.05), with language ability explaining 34% of the differences in student performance. Interviews and classroom observations further reveal the difficulties students face in grasping abstract math concepts when taught in a language they are still learning. Teachers try to bridge the gap by code-switching, using visual aids, and incorporating culturally familiar examples. Despite their efforts, they continue to face challenges like limited bilingual resources and insufficient training. The study calls for a more gradual transition to English, backed by bilingual teaching materials and targeted teacher support. These findings highlight the importance of context-sensitive strategies in multilingual classrooms and offer practical recommendations for improving math education in linguistically diverse settings.

Long-Term Working Memory

Article

Full-text available

Apr 1995

To account for the large demands on working memory during text comprehension and expert performance, the traditional models of working memory involving temporary storage must be extended to include working memory based on storage in long-term memory. In the proposed theoretical framework cognitive processes are viewed as a sequence of stable states representing end products of processing. In skilled activities, acquired memory skills allow these end products to be stored in long-term memory and kept directly accessible by means of retrieval cues in short-term memory, as proposed by skilled memory theory. These theoretical claims are supported by a review of evidence on memory in text comprehension and expert performance in such domains as mental calculation, medical diagnosis, and chess.

Mathematical Disabilities: Cognitive, Neuropsychological, and Genetic Components

Article

Full-text available

Sep 1993

David C Geary

Cognitive, neuropsychological, and genetic correlates of mathematical achievement and mathematical disability (MD) are reviewed in an attempt to identify the core deficits underlying MD. Three types of distinct cognitive, neuropsychological, or cognitive and neuropsychological deficits associated with MD are identified. The first deficit is manifested by difficulties in the representation or retrieval of arithmetic facts from semantic memory. The second type of deficit is manifested by problems in the execution of arithmetical procedures. The third type involves problems in the visuospatial representation of numerical information. Potential cognitive, neuropsychological, and genetic factors contributing to these deficits, and the relationship between MD and reading disabilities, are discussed. Finally, suggestions for the subtyping of mathematical disorders are offered.

A Capacity Theory of Comprehension: Individual Differences in Working Memory

Article

Full-text available

Jan 1992

A theory of the way working memory capacity constrains comprehension is proposed. The theory proposes that both processing and storage are mediated by activation and that the total amount of activation available in working memory varies among individuals. Individual differences in working memory capacity for language can account for qualitative and quantitative differences among college-age adults in several aspects of language comprehension. One aspect is syntactic modularity: The larger capacity of some individuals permits interaction among syntactic and pragmatic information, so that their syntactic processes are not informationally encapsulated. Another aspect is syntactic ambiguity: The larger capacity of some individuals permits them to maintain multiple interpretations. The theory is instantiated as a production system model in which the amount of activation available to the model affects how it adapts to the transient computational and storage demands that occur in comprehension.

Factor Analysis of the Wechsler Adult Intelligence Scale-Revised for Persons 75 Years and Older

Article

Full-text available

Jun 1990

We factor analyzed the WAIS-R protocols of 130 normal elderly. For age and education, Ms = 81.24 years (SD = 5.24) and 9.54 years (SD = 2.50) . Results indicated that the WAIS-R may be interpreted as a 1-, a 2-, or a 3-factor battery. In the 1-factor solution, interpretative emphasis was placed on the Full Scale IQ as a measure of g. In the 2-factor solution, a Verbal Comprehension factor consisted of Information, Digit Span, Vocabulary, Comprehension, and Similarities. A Perceptual Organization factor comprised Block Design, Object Assembly, and Digit Symbol. In the 3-factor solution, the subtest alignments for the Verbal Comprehension and Perceptual Organization factors remained highly similar, whereas Arithmetic constituted a Freedom From Distractibility factor. Overall, 1- or 2-factor models seem to offer the most plausible and parsimonious structures for this sample. 7 subtests had high or intermediate levels of specific variance.

Closing the Word-Problem Achievement Gap in First Grade: Schema-Based Word-Problem Intervention With Embedded Language Comprehension Instruction

Article

Full-text available

Feb 2020

The main purpose of this study was to test the effects of word-problem intervention, with versus without embedded language comprehension instruction, on at-risk 1st graders' word-problem performance. We also isolated the need for a structured approach to word-problem intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n=391; mean age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based word-problem intervention with embedded language instruction, the same word-problem intervention but without language comprehension instruction, structured number knowledge intervention without a structured word-problem component, and a control group. Each intervention included 45 30-min sessions. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based word-problem intervention at 1st grade, with both word-problem conditions outperforming the number knowledge condition and the control group. Yet, word-problem performance was significantly stronger for the schema-based condition with embedded language comprehension instruction compared to the schema-based condition without language comprehension instruction. Number knowledge intervention conveyed no word-problem advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to word-problem intervention; the efficacy of schema-based instruction at 1st grade; and the added value of language comprehension instruction within word-problem intervention. Results also provide causal evidence on the role of language comprehension in word-problem solving.

Are the Relations of RAN with Reading and Mathematics Accuracy and Fluency Bidirectional? Evidence From a 5-Year Longitudinal Study with Chinese Children

Article

Full-text available

Jan 2020

Despite the widespread use of Rapid Automatized Naming (RAN) tasks in reading and mathematics research, little is known about the direction of their relation. Thus, in this longitudinal study, we examined the direction of the relation between RAN and reading/ mathematics accuracy and fluency. One hundred eighty-three Grade 1 Chinese children from Shanghai (84 girls and 99 boys; Mage = 85.98 months, SD = 3.76) were followed until Grade 5 and were assessed annually on RAN, reading, and mathematics. The results of standard cross-lagged analyses indicated that the effects were unidirectional (earlier RAN predicted future reading and mathematics fluency), specific (earlier RAN predicted further growth only in fluency outcomes), and consistent (with one exception, earlier RAN predicted every subsequent reading and mathematics fluency). Theoretical implications of these findings are discussed in light of the language in which the study was conducted and the developmental span covered.

The Development of Academic Achievement and Cognitive Abilities: A Bidirectional Perspective

Article

Full-text available

Jan 2020
CHILD DEV PERSPECT

Developing academic skills and cognitive abilities is critical for children's development. In this article, we review evidence from recent research on the bidirectional relations between academic achievement and cognitive abilities. Our findings suggest that (a) reading/mathematics and cognitive abilities (i.e., working memory, reasoning, and executive function) predict each other in development, (b) direct academic instruction positively affects the development of reasoning, and (c) such bidirectional relations between cognitive abilities and academic achievement seem weaker among children with disadvantages (e.g., those with special needs or low socioeconomic status). Together, these findings are in line with the theory of mutualism and the transactional model. They suggest that sustained and high‐quality schooling and education directly foster children's academic and cognitive development, and may indirectly affect academic and cognitive development by triggering cognitive‐academic bidirectionality. Developing academic skills and cognitive abilities is critical for children's development. In this article, we review evidence from recent research on the bidirectional relations between academic achievement and cognitive abilities. Our findings suggest that (a) reading/mathematics and cognitive abilities (i.e., working memory, reasoning, and executive function) predict each other in development, (b) direct academic instruction positively affects the development of reasoning, and (c) such bidirectional relations between cognitive abilities and academic achievement seem weaker among children with disadvantages (e.g., those with special needs or low socioeconomic status). Together, these findings are in line with the theory of mutualism and the transactional model. They suggest that sustained and high‐quality schooling and education directly foster children's academic and cognitive development, and may indirectly affect academic and cognitive development by triggering cognitive‐academic bidirectionality.

What’s the Best Way to Characterize the Relationship Between Working Memory and Achievement?: An Initial Examination of Competing Theories

Article

Full-text available

Jul 2019

Although studies have demonstrated a relationship between working memory and achievement in math and reading, it is still unclear why working memory might be related to these abilities. In the present article, we examined the viability of several possible theories in 2 separate analyses of math and reading. In each case, we contrasted the predictions of a cognitive filter model, a transactional model, and a positive manifold model using data from the 2011 Early Childhood Longitudinal Study Kindergarten (ECLS-K). Results of path analyses in a structural equation modeling (SEM) framework indicated an excellent fit for the transactional model, while a poor fit was shown for the other 2 models for both math and reading. Findings across these analyses suggested that working memory and achievement interact in a reciprocal, recursive manner over time. Findings are discussed in terms of their implications for theory, practice, and future research.

The Origin of Concepts

Book

Aug 2009

Susan Carey

The relation between mathematics vocabulary and mathematics performance among fourth graders

Article

Nov 2019
LEARN INDIVID DIFFER

Examining the Mutual Relations Between Language and Mathematics: A Meta-Analysis

Abstract and Figures

Recommended publications

Language Skills of Children With and Without Mathematics Difficulty

Investigating the Unique Predictors of Word-Problem Solving Using Meta-Analytic Structural Equation...

The Roles of Initial Mathematics, Reading, and Cognitive Skills in Subsequent Mathematics Performanc...

What is the Source of the Correlation Between Reading and Mathematics Achievement? Two Meta-Analytic...