Jo-Anne Lefevre

Carleton University · Institute of Cognitive Science

Early knowledge of numbers, relations, and operations are foundations for student success. Weak foundational number skills can lead to later difficulties, thus early identification and targeted interventions for students with weak number skills can help stop them from falling further behind. In the current study, we tested the effectiveness of MATm...

There is a need for valid and reliable screeners to assess students’ early math skills and help educators identify students who are at-risk for math difficulties. The Early Math Assessment @School (EMA@School) has been used to test the foundational number skills (i.e., numbers, relations, and operations) of over 200,000 Canadian students. In this s...

Dans cet article, je décris mon parcours académique en tant que chercheuse canadienne dans le domaine de la cognition mathématique. L’article est une version du discours que j’ai prononcé lorsque j’ai reçu le prix Donald O. Hebb de la Société canadienne des sciences du cerveau, du comportement, et de la cognition (SCSCCC) en juillet 2023 à l’Univer...

Does mathematical vocabulary predict the change in students’ performance on mathematical tasks from one academic year to the next? Chilean Spanish-speaking students (N = 87) completed measures of mathematical vocabulary, mathematical skills (i.e., arithmetic fluency, calculation, and applied problems), receptive vocabulary, and working memory in Gr...

The home mathematics environment of preschoolers is related to their mathematical performance. Information about the home mathematics environment in China is sparse, however. Accordingly, we developed and tested a culturally relevant home mathematics environment questionnaire for Chinese families. In Study 1 (n = 376), exploratory factor analysis o...

Les compétences mathématiques peuvent être conceptualisées comme des couches de connaissances, les compétences en numératie constituant le noyau de base et les compétences mathématiques plus complexes étant les couches supplémentaires enveloppant le noyau. Dans cette étude, nous avons testé un modèle élargi d’intégration hiérarchique des symboles (...

Student’s understanding of the meaning of the equal sign develops slowly over the primary Grades. In addition to updating their repre-sentations of equations to recognize that the equal sign represents an equivalence relation rather than signaling an operation, students need to move beyond full computation to efficiently solve equivalence problems....

Children's knowledge of the ordinal relations among number symbols is related to their mathematical learning. Ordinal knowledge has been measured using judgment (i.e., decide whether a sequence of three digits is in order) and ordering tasks (i.e., order three digits from smallest to largest). However, the question remains whether performance on th...

Is the development of number line estimation (NLE) similar across regions? Data from Canada (Quebec, n = 67, Mage = 7.9 years; Manitoba, n = 177, Mage = 7.8 years), Chile (n = 81, Mage = 7.9 years), and Northern Ireland (n = 171, Mage = 7.3 years) were analyzed. Twice, approximately one year apart, students completed a 0–1000 NLE task and other mat...

Transcoding is the process of translating between spoken and written numbers, and it is correlated with other mathematical skills. In the present study, we investigated the link between French number writing of 49 students in the third grade (aged 7 to 9 years) and their language skills. Transcoding in French is of particular interest because the s...

In the current study, we used a multi-method approach to understand the quality of math homework-helping interactions between parents and their children and how parents’ and children’s own math achievement and math anxiety relate to the quality of the interaction. Forty Canadian parents and their children (ages 10–12 years; grades 5 to 7) completed...

Introduction Children’s involvement in mathematics-related activities in the home environment is associated with the development of their early numeracy over the preschool years. Intervention studies to promote parents’ awareness and provision of mathematics-related home activities are however scant. In this study we developed and tested the effect...

Background Slowed processing speed is the most frequently reported cognitive deficit for people with multiple sclerosis (MS). However, measures used to assess processing speed may also recruit other cognitive abilities. The present objective was to determine the contributions of different cognitive functions to performance on two commonly used proc...

The home learning environment includes parental activities, attitudes, affect, knowledge, and resources devoted to supporting children’s development, including literacy and mathematics skills. These factors are related to the academic performance of preschool children (aged 3 to 6 years), before formal schooling and possibly beyond. In the present...

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753–1767], children’s cognitive skills in three domains—linguistic, attentional, and quantitative—predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a...

How do whole number arithmetic skills support students’ understanding of fraction magnitude during the emerging stages of fraction learning? Chinese students in Grade 4 (N = 1038; Mage = 9.9 years; 55.6% boys) completed assessments of whole number arithmetic skills (i.e., addition, subtraction, multiplication, and division), fraction mapping (i.e.,...

We examined developmental trajectories of attention‐deficit/hyperactivity disorder (ADHD) symptoms, standardized achievement, and school performance for adolescents with and without ADHD who did and did not enroll in postsecondary education (PSE; N = 749; 79% boys; 63% White, 17% non‐Hispanic Black, 10% Hispanic, and 10% other ethnicities). In a mu...

We investigated whether home math activities were related to children's math performance in kindergarten and the first three years of primary school. Participants were Chilean parents and their children in kindergarten, Grade 1, Grade 2, and Grade 3 (n s = 101, 95, 87, and 84, respectively). Mothers and fathers independently answered questions abou...

Background. Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students’ understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students’ understanding of measurement interp...

Home numeracy and literacy environments are related to the development of children’s early academic skills. However, the home learning environments of preschool children have been mainly explored with children from North America, Europe, and Asia. In this study we assessed the home numeracy and literacy environments of three-to-five-year-old childr...

Canadian students enrolled in either French-immersion or English-instruction programs were followed from Grades 2 to 3 (Mage = 7.8 years to 8.9 years; N = 244; 55% girls). In each grade, students completed two mathematical tasks that required oral language processing (i.e., word-problem solving and number transcoding from dictation) and two that di...

Math story problems are difficult for many solvers because comprehension of mathematical and linguistic content must occur simultaneously. Across two studies, we attempted to conceptually replicate and extend findings reported by Mattarella-Micke and Beilock (2010, https://doi.org/10.3758/PBR.17.1.106) and Jarosz and Jaeger (2019, https://doi.org/1...

Language skills play an important role in mathematics development. Students (7 to 10 years of age) learning school mathematics either in the same language used at home (first-language learners; n = 103) or in a different language (second-language learners; n = 57) participated in the study. Relations among cognitive skills (i.e., receptive vocabula...

Children’s performance on number line tasks reflects their developing number system knowledge. Before 5 years of age, most children perform poorly on even the simplest number lines (i.e., 0–10). Our goal was to understand how number line skills develop before formal schooling. Chilean preschoolers attempted a 0–10 number line task three times over...

What is the foundational knowledge that children rely on to provide meaning as they construct an exact symbolic number system? People and animals can quickly and accurately distinguish small exact quantities (i.e., 1 to 3). One possibility is that children’s ability to map small quantities to spoken number words supports their developing exact numb...

This article synthesizes findings from an international virtual conference, funded by the United States National Science Foundation, focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children’s outcomes, the purpose of the conference was to discuss actiona...

In this study, we extended a model of the relations among ADHD symptoms, anxiety, and academic performance. Undergraduates (N = 515) completed self-report measures of anxiety (i.e. trait, test, math, and literacy) and ADHD symptoms. During the study, they completed math and literacy measures and reported their current (i.e. state) anxiety three tim...

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 – 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All familie...

Math anxiety is a common correlate of math performance for adults. Research on young chil- dren’s emotional reactions to math is limited, but critical for determining how math anxiety develops. Students (N=244) completed math measures (i.e., number comparison, arithmetic fluency, and math problem solving) and math anxiety assessments twice, in grad...

We explored the home learning environments of 173 Mexican preschool children (aged 3–6 years) in relation to their numeracy performance. Parents indicated the frequency of their formal home numeracy and literacy activities, and their academic expectations for children’s numeracy and literacy performance. Children completed measures of early numerac...

Does providing an explicit midpoint affect adults’ performance differently for typical and atypical number line tasks? Participants (N=29) estimated the location of target numbers on typical (i.e., 0–10,000) and atypical (i.e., 0–7,000) number lines with either an explicitly labelled midpoint or no midpoint. For the typical number line, estimation...

How do children develop associations among number symbols? For Grade 1 children (n = 66, M = 78 months), sequence knowledge (i.e., identify missing numbers) and number comparison (i.e., choose larger number) predicted addition, both concurrently and indirectly at the end of Grade 1. Number ordering (i.e., touch numbers in order) did not predict add...

The written language of mathematics is dense with symbols and with conventions for combining those symbols to express mathematical ideas. For example, reading a factored polynomial function such as f(x) = x²(2x + 15) requires the knowledge that parenthesis can be used to signify function notation in one context and multiplication in another. Mathem...

The aim of the present study was to investigate longitudinal associations between formal home numeracy activities and children’s arithmetic fluency skills. Children were followed during the transition from the end of kindergarten (T1; Mage = 6.87 years) to the beginning of Grade 1 (T2), and again at the end of the Grade 1 (T3). Participants were Li...

This study investigated the longitudinal associations between children's early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, M age = 4:7 [years:months]), and at the end of kindergarten in 2017...

Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in Ch...

Are ADHD symptoms uniquely related to affect about mathematics in university students? Undergraduates (n = 425) completed three math performance measures (i.e., arithmetic, computational skills, and word problem solving) and self-report measures of ADHD symptoms, state anxiety, and confidence about math and literacy (i.e., affect and perceived self...

Adults (N = 72) estimated the location of target numbers on number lines that varied in numerical range (i.e., typical range 0-10,000 or atypical range 0-7,000) and spatial orientation (i.e., the 0 endpoint on the left [traditional] or on the right [reversed]). Eye-tracking data were used to assess strategy use. Participants made meaningful first f...

Before achieving arithmetic automaticity (direct answer recall), learners self-compute answers or use calculators/tables. Mechanisms supporting arithmetic automaticity are of interest because automaticity predicts math achievement and employment outcomes. Future recall is enhanced when, during study, learners attempt to recall the to-be-learned inf...

We used structural equation modeling to evaluate an enhanced version of the Home Numeracy Model proposed by Skwarchuk and colleagues (2014, Journal of Experimental Child Psychology, 121, 63–84). Participants were 390 Chilean preschool children and their parents. Children completed numeracy and literacy tasks at the beginning of preschool (mean age:...

INTRODUCTION. Children’s ability to place numbers on a line, where only the endpoints are marked, is related to other aspects of their mathematical understanding. In the present research, we examined the effects of a midpoint reference (e.g., marking the location of 5 on a 0-10 number line) on young children’s performance (3- to 5-year-olds) on a n...

We examined how children's strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34–18) and described their solution strategies. In the first experiment, strategy selectio...

What causes math anxiety? According to a cognitive deficits view, early weaknesses in basic number and spatial skills lead to poor performance and hence negative affect. A strong version of this view suggests that the relation between math anxiety and math performance among adults will be explained by deficits in spatial and basic number skills. In...

Preschoolers (n = 62) completed tasks that tapped their knowledge of symbolic and non-symbolic exact quantities, their ability to translate among different representations of exact quantity (i.e., digits, number words, and non-symbolic quantities), and their non-symbolic, digit, and spoken number comparison skills (e.g., which is larger, 2 or 4?)....

Résumé Les adultes qui ont recours à des procédures de calcul mental autres que la récupération directe pour résoudre des problèmes arithmétiques simples font généralement plus d’erreurs et répondent moins vite que ceux qui se fient exclusivement à la récupération. La présente étude a examiné comment ce temps supplémentaire était réparti entre les...

Many children in the USA and Canada have access to a wide range of experiences that can support their early numeracy development. Nevertheless, children’s early numeracy knowledge varies considerably in these countries as a function of parents’ education, socioeconomic conditions, parents’ attitudes, beliefs, knowledge about mathematics, and presch...

Children’s numeracy knowledge and performance varies across countries, regions, and languages. These cross-cultural differences occur even prior to formal schooling. Much existing cross-cultural numeracy research was focused on the role of language in accounting for these differences in children’s early numeracy development and performance. However...

Research Findings: Children who speak English are slower to learn the counting sequence between 11 and 20 compared to children who speak Asian languages. In the present research, we examined whether providing children with spatially relevant information during counting would facilitate their acquisition of the counting sequence. Three-year-olds (n...

Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8) and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6). Pa...

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of...

In this article, I provide a historical overview of the field of numerical cognition. I first situate the evolution and development of this field in the more general context of the cognitive revolution, which started in the mid-1950s. I then discuss the genesis of numerical cognition from 6 areas: psychophysics, information processing, neuropsychol...

Do eye-movement patterns of addition and multiplication problems differ? Participants (n = 41) solved addition and multiplication problems in one mixed and two pure blocks. Eye movement patterns in pure blocks were similar to those observed in previous studies. Participants looked longer at the operation sign than at the operands. In the mixed bloc...

Do eye-movement patterns of addition and multiplication problems differ? Participants (n = 41) solved addition and multiplication problems in one mixed and two pure blocks. Eye movement patterns in pure blocks were similar to those observed in previous studies. Participants looked longer at the operation sign than at the operands. In the mixed bloc...

Comprehensive Paper, Submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Psychology, Carleton University, Ottawa, Ontario June 2005

INTRODUCTION: Prospective memory allows people to complete intended tasks in the future. Prospective memory failures, such as pilots forgetting to inform pattern traffic of their locations, can have fatal consequences. The present research examined the impact of system factors (memory cue salience and workload) and individual differences (pilot age...

There is an emerging consensus that spatial thinking is fundamental to later success in math and science. The goals of this study were to design and evaluate a novel test of three-dimensional (3D) mental rotation for 4- to 8-year-old children (N = 165) that uses tangible 3D objects. Results revealed that the measure was both valid and reliable and...

Experiences that children have at home can establish a foundation for numeracy learning, and serve as an important transition toward school entry. However, Canadian parents and other caregivers do not often have a good understanding of numeracy learning, they may not be prepared to provide appropriate activities, and some may avoid numeracy activit...

The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with simp...

How important is the regularity of a number naming system when young children are learning to count? Three- and four-year-old English- and Turkish-speaking children (N = 75) played one of two versions of a board game. The number game involved counting and naming numbers from 1 to 20 whereas the color game involved naming colors. All of the Turkish-...

This book provides a comprehensive overview of numerical cognition by bringing together writing by leading researchers in psychology, neuroscience, and education, covering work using different methodological approaches in humans and animals. During the last decade there had been an explosion of studies and new findings with theoretical and translat...

One hundred and ten English-speaking children schooled in French were followed from kindergarten to Grade 2 (Mage : T1 = 5;6, T2 = 6;4, T3 = 6;11, T4 = 7;11). The findings provided strong support for the Home Literacy Model (Sénéchal & LeFevre, ) because in this sample the home language was independent of the language of instruction. The informal l...

Individuals who do well in mathematics and science also often have good spatial skills. However, the predictive direction of links between spatial abilities and mathematical learning has not been firmly established, especially for young children. In the present research, we addressed this issue using a sample from a longitudinal data set that spann...

Children's involvement in home literacy and numeracy activities has been linked to school achievement, but the subtleties in the home environment responsible for these gains have yet to be thoroughly investigated. The purpose of this study was to determine how children's interests and collaborative parent–child interactions affect exposure to home...

The Relative Consequence Model proposes multiple sclerosis (MS) patients have a fundamental deficit in processing speed that compromises other cognitive functions. The present study examined the mediating role of processing speed, as well as working memory, in the MS-related effects on other cognitive functions for early relapsing-remitting patient...

Does solving subtraction problems with negative answers (e.g., 5–14) require different cognitive processes than solving problems with positive answers (e.g., 14–5)? In a dual-task experiment, young adults (N=39) combined subtraction with two working memory tasks, verbal memory and visual-spatial memory. All of the subtraction problems required verb...

The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (200537. Siegler , R. S. , & Araya , R. ( 2005 ). A com...

We examined the role of executive attention, which encompasses the common aspects of executive function and executive working memory, in children's acquisition of two aspects of mathematical skill: (a) knowledge of the number system (e.g., place value) and of arithmetic procedures (e.g., multi-digit addition) and (b) arithmetic fluency (i.e., speed...

Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation between multiplication and division than that between addition and subtraction. We reviewed research on children and adults’ use of shortcut procedures that make use of the inverse relation on two kinds of problems: inversion...

Prospective memory is the ability to remember to perform acts in the future and is essential in the aviation domain because it supports remembering to complete radio communications. In the laboratory younger adults tend to outperform older adults on prospective memory tasks; yet in naturalistic settings older adults perform as well as younger adult...

Imbo and LeFevre (2009) observed that Asians (responding in their 2nd language) selected strategies less adaptively than did non-Asians (responding in their 1st language). In the present research, we tested whether adaptive strategy selection is (a) really more resource demanding for Asians than for non-Asians or (b) more resource demanding for par...

Why is subsequent recall sometimes better for self-generated answers than for answers obtained from an external source (e.g., calculator)? In this study, we explore the relative contribution of 2 processes, recall attempts and self-computation, to this generation effect (i.e., enhanced answer recall relative to when problems are practiced with a ca...

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial a...

Thirty-two Chinese-speaking adults solved single-digit multiplication problems. As compared to samples of English-, French-, and Dutch-speaking adults from other studies, the Chinese adults in the present study made more errors that indicated interactions between phonological codes activated at encoding and production of answers. For example, Chine...

Children’s experiences with early numeracy and literacy activities are a likely source of individual differences in their preparation for academic learning in school. What factors predict differences in children’s experiences? We hypothesised that relations between parents’ practices and children’s numeracy skills would mediate the relations betwee...

Two experiments were conducted to test cultural differences in the role of phonological and visual working memory in complex arithmetic. Canadian- and Chinese-educated students solved complex subtraction problems (e.g., 85 - 27; Experiment 1) and complex multiplication problems (e.g., 6 x 13; Experiment 2) under phonological and visual working memo...

Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 - 4 and recasted versions that included explicit negative signs-that is, 3 - (-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slo...

In the present study, the authors tested the effects of working-memory load on math problem solving in 3 different cultures: Flemish-speaking Belgians, English-speaking Canadians, and Chinese-speaking Chinese currently living in Canada. Participants solved complex addition problems (e.g., 58 + 76) in no-load and working-memory load conditions, in w...