Sarah R Powell

• Vanderbilt University
• Professor (Associate) at University of Texas at Austin

Mathematics learning is sequential and builds in complexity as children learn more advanced skills. The transition that many schools are making to the Common Core State Standards may require that some mathematics skills are introduced at earlier grades. Current focus on high-stakes assessments to understand student achievement may lead to external...

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be influ...

Students often experience difficulty with attaching meaning to mathematics symbols. Many students react to symbols, such as the equal sign, as a command to “do something” or “write an answer” without reflecting upon the proper relational meaning of the equal sign. One method for assessing equal-sign understanding is through nonstandard equations (e...

The focus of the present study was enhancing word problem and calculation achievement in ways that support prealgebraic thinking among second-grade students at risk for mathematics difficulty. Intervention relied on a multitier support system (i.e., responsiveness to intervention, or RTI) in which at-risk students participate in general classroom i...

Teachers and parents often use trade books to introduce or reinforce mathematics concepts. To date, an analysis of the early numeracy content of trade books has not been conducted. Consequently, this study evaluated the properties of numbers and counting within trade books. We coded 160 trade books targeted at establishing early numeracy skill in c...

A joint position statement issued in December 2024 by the National Council of Teachers of Mathematics (NCTM) and the Council for Exceptional Children (CEC) on teaching mathematics to students with disabilities lacked substantive, actionable, research-validated recommendations to support the work of practitioners in the field. Herein, we provide a r...

The present study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra’s initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 s...

We examined how generalized and mathematics-specific language skills predicted the word-problem performance of students with mathematics difficulty. Participants included 325 third-grade students in the southwestern United States who performed at or below the 25th percentile on a word-problem measure. We assessed generalized language skills in word...

Word problem-solving (WPS) poses a significant challenge for many students, particularly those with mathematics difficulties (MD), hindering their overall mathematical development. To improve WPS proficiency, providing individualized and intensive interventions is critical. This umbrella review examined 11 medium- to high-quality meta-analyses to i...

Establishing validated science programs for students with or at risk for learning disabilities requires testing treatment effects and exploring differential response patterns. This study explored whether students’ initial mathematics and reading skills influenced their treatment response to a whole-class, second-grade science program called Scienti...

This study reports a secondary analysis from a randomized control trial study conducted with third graders with mathematics difficulty (MD; N = 75). We used simple linear regression to investigate whether students’ performance on a word-problem vocabulary assessment predicted their performance on a measure of word-problem solving. Additionally, we...

Read-alouds provide teachers with an efficacious method for introducing vocabulary and content to young children. In this study, kindergarten teachers were randomly assigned to implement a mathematics-focused extended read-aloud program called TEMPLE (Teaching Early Math by Providing Language Exploration) with kindergarten children ages 5–6 (19 tea...

In the last decade, researchers have focused more on how to provide instructional supports for mathematics writing (Powell et al., 2017). In this synthesis, we examined 22 studies about mathematics writing to determine the overall mathematics-writing and mathematics outcomes of mathematics-writing instruction, the mathematics-writing and mathematic...

The efficacy of mathematics interventions for students with mathematics difficulties is a critical concern in educational research, particularly in light of the increasing demand for effective instructional strategies. While previous meta-analyses have explored various aspects of mathematics interventions, our study uniquely focuses on a broad rang...

In this synthesis, we analyzed 10 prealgebraic reasoning interventions for students with mathematics difficulty (MD) in Grades 6 through 8. All interventions focused on one or more prealgebraic concepts including integer operations, algebraic expressions and equations, and functions. Of the 10 intervention studies, six employed single-case design m...

This chapter focuses upon research related to building pre-service teachers' (PSTs') own competencies in mathematics writing (MW) as well as their skills in teaching MW and integrating MW into their future K-12 classrooms. The authors provide a review of the research with PSTs and MW. Although there is limited research on PSTs and MW, it is likely...

Developing mathematics proficiency requires an understanding of mathematics vocabulary. Although previous research has developed several measures of mathematics vocabulary at different grade levels, no study focused solely on fraction vocabularies. We developed and tested a measure of fraction vocabulary for students in Grade 4 to determine the int...

As students enter the upper elementary grades, word problems become a main component of mathematics instruction, increasing in complexity as students advance through the curriculum. For students identified as emergent bilinguals with mathematics difficulty (MD), the linguistic complexity inherent in word problems may serve as a barrier to word‐prob...

This study examined the influence of addition and subtraction practice embedded within a word‐problem intervention for Grade 3 students experiencing word‐problem difficulty. Students ( N = 448) were randomly assigned to one of two variants of a word‐problem intervention or a business‐as‐usual comparison condition. Within the word‐problem interventi...

In the present study, we investigated the impact of a word-problem intervention in retention and acquisition of knowledge after the intervention ended. We based analyses upon Grade 4 students experiencing mathematics difficulty (average age at pretest = 8.77) who received one of two variants of a word-problem intervention (with [n = 111] vs. withou...

Mathematical writing has gained attention as an essential component of discourse. Assessing and scoring students' writing pieces about mathematics has the potential to allow teachers and researchers to gain insights into the depth of students' understanding beyond what they can express orally, including their use of visual representations and symbo...

This meta-analysis systematically investigated the pathways to the Quantity-Number Competencies (QNC) model based on 78 studies involving 21,860 children. The QNC model assumes children acquire early numeracy via three developmental levels: QNC Level I (Basic numerical skills), QNC Level IIa (imprecise quantity to number-word linkage) and QNC Level...

Increasingly, students must demonstrate knowledge in mathematics through mathematics writing, yet research lags in understanding how students engage in mathematics-writing tasks. Most available research on mathematics writing focuses on typically achieving students without considering students with mathematics difficulty (MD). In this study, we exp...

Data-based individualization (DBI) is a framework that allows educators to make timely and informed decisions about student progress in academics or behavior. In this article, we focus on the DBI framework as applied to math intervention within a tiered support model for students experiencing math difficulty. We review how DBI starts with an instru...

Many students who experience difficulty with mathematics may also require behavioral support. We suggest educators create an appropriate scope and sequence for mathematics intervention by focusing on the critical mathematics content. Educators can then design the intervention with a common session structure. Finally, educators can embed and intensi...

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (R...

In intervention studies, high rates of implementation fidelity are important markers of a study’s success; however, the definition of implementation fidelity is both complex and dynamic. In this synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a mathematics interventi...

It is crucial that special education teachers are equipped with the knowledge and skills necessary to improve outcomes for students with disabilities. Despite federal legislation and efforts of the field to identify and disseminate evidence-based practices for students with disabilities, it is uncertain whether all special education teachers provid...

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (n = 76) were randomly assigned to word-problem intervention (n = 56) o...

In the present meta-analysis, we systematically investigated the relative contributions of students’ initial mathematics, reading, and cognitive skills on subsequent mathematics performance measured at least 3 months later. With One-Stage Meta-Analytic Structural Equation Modeling (MASEM), we conducted analyses based on 580,437 students from 265 in...

With a Meta-Analytic Structural Equation Modeling approach, we investigated the role of whole-number knowledge on fraction performance, accounting for domain-general skills, age, and mathematics-difficulty status. We conducted analyses based on 6,096 students from 39 independent samples within 29 studies. Findings suggested conceptual whole-number...

In this systematic review, we explored mathematics interventions for middle school (Grades 6, 7, and 8) implemented with students who experienced difficulty in the area of mathematics, including students with an identified learning disability in mathematics. A total of 72 single‐subject and group comparison studies met inclusion criteria, with 59 s...

We conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a pre-algebraic reasoning component (rela...

This study, which was reviewed through the Registered Report process, examined the initial efficacy of the Scientific Explorers program (Sci2) on second-grade students’ science achievement. Sci2 is grounded in the growing body of empirical research on science instruction, embedding principles of explicit instruction within a guided inquiry-based de...

Students in the elementary and secondary grades may use mathematics writing to express ideas and reasoning about mathematics. To understand current classroom practices related to the assessment and instruction of mathematics writing, we conducted a survey of kindergarten through Grade 12 educators across the United States who taught mathematics, wi...

Peer-Assisted Learning Strategies (PALS) is a peer tutoring program available in the areas of reading and mathematics that incorporates peers as change agents in academic intervention. Developed at Vanderbilt University by Douglas Fuchs, Lynn S. Fuchs, and their colleagues, PALS is currently available in reading from kindergarten through high schoo...

The purpose of this explorative study was to examine the use and understanding of key components of data-based decision making by educators in two countries—Germany and the United States. Educators responded to a survey that asked about data use and characteristics related to data-based decision making (DBDM). Results suggest educators in both coun...

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4‐year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's respo...

In this meta-analysis of single-case designs, the researchers investigated the effects of word-problem instruction for students with learning disabilities in Grades 1 through 12, as reported in 20 peer-reviewed articles published between 1975 and 2020. A two-level multilevel model with a robust variance estimation method was implemented to calculat...

In this meta-analysis of single-case designs, the researchers investigated the effects of word-problem instruction for students with learning disabilities in grades 1 through 12, as reported in 20 peer-reviewed articles published between 1975 and 2020. A two-level multilevel model with a robust variance estimation method was implemented to calculat...

Although the complexity of children’s number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children’s books, however, categorized a distinct subset of books about number as counting books. These counting books were complex with regard to portrayal of counting sequences, ex...

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The pre...

The purpose of this study was to examine the word-problem performance and strategies utilized by 3rd-grade students experiencing mathematics difficulty (MD). We assessed the efficacy of a word-problem intervention and compared the word-problem performance of students with MD who received intervention (n = 51) to students with MD who received genera...

Project STAIR (Supporting Teaching of Algebra: Individual Readiness) aims to develop and iteratively refine a framework for using data-based individualization (DBI) to support the readiness for algebra of middle-school students with mathematics learning difficulty. Project STAIR was tested in four middle schools in the United States to assess the i...

Some elementary students may exhibit challenging externalizing or internalizing behaviors in addition to difficulty with mathematics. In this study, we explored the behavioral patterns of 441 third-grade students with and without mathematics difficulty (MD). Compared with students without MD, students with MD demonstrated higher rates of externaliz...

In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word problem-so...

The purpose of this study was to measure the mathematics-vocabulary performance of 3rd graders to determine if performance differences existed among English learners (ELs) and non-ELs with and without mathematics difficulty (MD). Using screening data from a large-scale intervention study, we categorized students into four groups based on equation s...

Current mathematics curricula and assessments emphasize students’ ability to communicate mathematical reasoning in writing. Limited research exists, however, on what mathematics writing (MW) is and how to assess the quality of MW. Therefore, based on our definition of MW construct, we explored 4 approaches to scoring MW: (a) holistic rubric scoring...

In this synthesis, we reviewed 65 studies involving elementary students (i.e., grades 1–5) identified with mathematics difficulty (MD) in which authors implemented a mathematics intervention. Of these studies, we identified 33 group designs, 9 quasi-experimental designs, and 23 single-case designs. We aimed to synthesize performance differences bet...

Conventional research methods for understanding sources of individual differences in word-problem solving (WPS) only permit estimation of average relations between component processes and outcomes. The purpose of the present study was instead to examine whether and if so how the component processes engaged in WPS differ along the spectrum of WPS pe...

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve s...

This article is about a school‐district‐initiated partnership with university faculty and their effort to implement a mathematics multi‐tiered system of support (MTSS). In addition to reporting research about MTSS implementation, we describe how this district translated research into practice. We also share the perceptions of key stakeholders about...

Word problems require students to read a language-based problem, identify necessary information to answer a prompt, and perform calculation(s) to develop a problem solution. Solving word problems proves particularly challenging for students with mathematics difficulties because skill in reading, interpretation of language, and mathematics are requi...

Proficiency with algebra is difficult for students, even students at the college level. We administered an assessment of algebra to 362 college students. Students also completed measures of rational numbers, mathematics fact fluency, mathematics anxiety, reading fluency, and spelling accuracy. A dominance analysis revealed that, of the 5 variables,...

High‐stakes mathematics assessments require students to write about mathematics, although research suggests students exhibit limited proficiency on such assessments. Students with LD may have difficulties with writing, mathematics, or both. Researchers employed an intervention for teaching students how to organize mathematics writing (MW). Research...

Mathematical achievement is an early predictor of students’ academic outcomes, and mathematics achievement continues to be important throughout life. Thus, it is essential to examine instructional methods that enhance mathematical learning. One method that may impact mathematical learning is the use of gestures, yet a comprehensive methodical revie...

Proficiency with mathematics requires an understanding of mathematical language. Students are required to make sense of both spoken and written mathematical terms. An essential component of mathematical language involves the understanding of the vocabulary of mathematics in which students connect vocabulary terms to mathematical concepts or procedu...

To understand mathematics, children must interpret mathematics symbols. In this study, we designed a brief assessment of mathematics symbols for children in the elementary grades. For each of 23 symbols, children identified the symbol, provided the meaning of the symbol, and used the symbol. We assessed 297 children in Grades 1, 3, and 5. Internal...

Some students may be diagnosed with a learning disability in mathematics or dyscalculia, whereas other students may demonstrate below-grade-level mathematics performance without a disability diagnosis. In the literature, researchers often identify students in both groups as experiencing math difficulty. To understand the performance of students wit...

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure of...

The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of 5th-grade students. Students (N = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and ge...

The purpose of this review was to conduct a meta-analysis of 25 years of mathematics interventions for students with mathematics difficulty or disability in Grades 4 through 12. A search of the literature yielded 25 studies that met the inclusion criteria. Studies were coded to extract important study information (e.g., participant information, res...

We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned...

To read mathematics textbooks, answer questions on mathematics assessments, and understand educator and student communication, students must develop an understanding of the academic language of mathematics. A primary aspect of academic language is vocabulary. In this study, we focused on the mathematics-vocabulary performance of students in 3rd and...

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., add, more, triangle). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary measure for first grade and piloted the a...

Word problems are prevalent on high-stakes assessments, and success on word problems has implications for grade promotion and graduation. Unfortunately, English Language Learners (ELLs) continue to perform significantly below their native English-speaking peers on mathematics assessments featuring word problems. Little is known about the instructio...

This chapter discusses mathematics assessment of students with disabilities: summative, formative, and diagnostic assessments, and how and when these assessment types are appropriate for school-age students with disabilities from pre-kindergarten through high school. The chapter also presents a case study, which utilizes all three types of mathemat...

Mathematics standards in the United States describe communication as an essential part of mathematics. One outlet for communication is writing. To understand the mathematics writing of students, we conducted a synthesis to evaluate empirical research about mathematics writing. We identified 29 studies that included a mathematics-writing assessment,...

Mathematics is an area of difficulty for most children and adolescents with Down syndrome (DS). Researchers have suggested tailoring academic interventions based on the behavioral phenotype of DS could improve mathematics outcomes. The purpose of this review was to examine whether children and adolescents with DS perform differentially compared to...

Mathematics standards expect students to communicate about mathematics using oral and written methods, and some high-stakes assessments ask students to answer mathematics questions by writing. Assumptions about mathematics communication via writing include (a) students possess writing skill, (b) students can transfer this writing skill to mathemati...

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculatio...

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and...

This white paper describes the Elementary Mathematical Writing Task Force's recommendations for the types of and purposes for elementary mathematical writing. It presents how the group distinguished "mathematical writing" from other kinds of writing that take place in mathematics classrooms and considerations of this work. Download at http://mathwr...

Legislations mandates that educators use evidence-based practices (EBPs) that are supported by scientifically based research. EBPs have demonstrated a likelihood to work for students with disabilities. EBPs should match targeted needs of the student receiving the instruction, which sometimes requires educators to search for the best intervention to...

Students who demonstrate persistent mathematics difficulties and whose performance is severely below grade level require intensive intervention. Intensive intervention is an individu- alized approach to instruction that is more demanding and concentrated than Tier 2 intervention efforts. We present the elements of intensive intervention that teache...

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring w...

Students often misinterpret the equal sign (=) as operational instead of relational. Research indicates misinterpretation of the equal sign occurs because students receive relatively little exposure to equations that promote relational understanding of the equal sign. No study, however, has examined effects of nonstandard equations on the equation...

As highlighted in this book and elsewhere, peer tutoring is a beneficial strategy for teaching students across elementary, middle, and high school (Bowman-Perrott et al., 2013; Codding, Chan-Iannetta, George, Ferreira, & Volpe, 2011). In this chapter, we focus on peer tutoring in mathematics with the Peer-Assisted Learning Strategies (PALS) program...

Students with mathematics difficulty demonstrate lower mathematics performance than typical-performing peers. One contributing factor to lower mathematics performance may be misunderstanding of mathematics symbols. In several studies related to the equal sign (=), students who received explicit instruction on the relational definition (“the same as...

Over the past two decades, changes in legislation and mathematics standards, along with the increased placement of students with disabilities in general education settings, have resulted in higher expectations for what students with disabilities will be able to know and do related to mathematics. To adequately prepare for the demands of teaching ma...