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Opportunities for practice play a critical role in learning complex behaviors. In the context of explicit mathematics instruction, practice facilitates systematic opportunities for students with mathematics difficulties to learn new mathematics content and apply such knowledge and skills to novel mathematics problems. This study explored whether there is an optimal...
This article focuses on two ways in which math language could be improved in middle school. First, educators can use formal language instead of informal language. Second, educators can be more precise with math terms that are closely related but have distinct meanings and characteristics. These terms may cause confusion...
Mathematics interventions to accelerate the learning of students with mathematics difficulties should be developed through a design science approach such as the Curriculum Research Framework. Precision Mathematics is a National Science Foundation-funded DRK–12 Design and Development project focused on building mathematical proficiency with the critical concepts and problem-solving...
English learners (ELs) represent a rapidly growing subgroup in U.S. schools. Yet converging evidence suggests that a concerning number of ELs struggle to reach proficient levels in mathematics. The purpose of this multisite randomized controlled trial was to examine the treatment effects of a Tier 2 mathematics intervention on...
The authors conducted 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, research design, description of treatment and...
Many general and special education teachers across the United States teach word problems by defining problems as a single operation (e.g., “Today, we’re working on subtraction word problems.”) and linking key words (e.g., more, altogether, share, twice) to specific operations (e.g., share...
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, the authors assessed 478 third-grade students on a measure of mathematics computation....
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 with math difficulty,...
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. This study focused on the mathematics-vocabulary performance of students in third and fifth...
This study investigated the effects of an early numeracy intervention delivered by kindergarten teachers to students identified as having mathematics difficulties. A design of multigroup growth modeling with random assignment to intervention condition was employed. Thirty-two teachers were randomly assigned to the treatment or comparison condition. A total of 71 students...
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, intervention, or survey for...
Researchers design scripted supplemental mathematics programs for struggling students, such as students with learning disabilities, to encourage an evidence-based presentation of concepts and use of instructional language in teachers’ implementation. In practice, teachers may or may not implement these programs with high fidelity, resulting in slight to...
Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models) can be used. This article discusses ...
Objectives: The goals were to (1) provide a review of the typical and atypical development of early numeracy; (2) present what is known about the neurocognitive underpinnings of early numeracy; and (3) discuss the implications for early assessment and intervention. Method: Studies on the development of typical and atypical early...
Children with disabilities perform lower in mathematics than their peers without disabilities, and this gap widens from ages 7 to 13 (Wei, Lenz, & Blackorby, 2013). Of even greater concern is that fifth-grade children with mathematics disabilities continue to perform in the bottom quartile of their grade in high school (Shalev, Manor, &...
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. The authors created a 64-item mathematics-vocabulary measure for first grade and piloted...
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). To develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and use writing features to...
Clarke et al. (2014) provide a persuasive case for the role of a theory-of-change model to guide the nature of curriculum development work embodying both a theoretical and empirical knowledge foundation. They illuminate the components of their model, which were used to design and test the efficacy of a Tier 2 intervention...
The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and...
Researchers design scripted supplemental mathematics programs for struggling students, such as students with learning disabilities (LD), to encourage an evidence-based presentation of concepts and use of instructional language in teachers’ implementation. In practice, teachers may or may not implement these programs with high fidelity, resulting in...
This study synthesized intervention studies focusing on instruction to improve fraction skills. Seventeen studies met the inclusion criteria: being published in English-language peer-reviewed journals or dissertations between 1975 and 2014, and targeting 3rd- through 12th-grade students struggling to learn mathematics. From the Common Core State Standards for Mathematics, addition and subtraction...
This study investigated the effects of explicit, strategic intervention with iPad application practice on the multiplication fact performance and strategy use of elementary students with learning disabilities (LD) using a single-case, multiple-probe design across participants. Four fifth-grade students with LD received 15 1:1 intervention sessions in multiplication facts. Results indicated that all...
Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students may face understanding...
This review provided a systematic analysis of mathematics interventions for individuals with autism. Using success estimates, strength-of-evidence ratings, and percentage of nonoverlapping data, the authors identified 13 studies that provided evidence of effective to very effective outcomes using mathematics accuracy measures for at least one intervention. Five studies with measurements...
The authors discuss the challenges related to solving math word problems. Then, they discuss each of the addition and subtraction word problem schemas and provide a framework for introducing these schemas to students who experience difficulty with math.
This article won the Kirk Award for the best practice article in Learning Disabilities Research & Practice of 2015. Students who demonstrate persistent mathematics difficulties and whose performance is severely below grade level require intensive intervention. Intensive intervention is an individualized approach to instruction that is more...
Opportunities to respond (OTR) and specific praise are two practices that may be particularly beneficial to students learning in secondary inclusive classrooms. Yet, there is relatively little research on effective inclusion practices involving secondary students with learning disabilities or studies at the secondary level. This study sought to extend the...
Many students with learning disabilities in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic thinking, teachers should ask questions in...
Although research on Tier 2 interventions for early mathematics is accumulating, such efforts remain far behind those for reading, especially regarding specific features such as the ideal time to begin an intervention. The present study investigated the effectiveness of a Tier 2 intervention by using a single-subject multiple-baseline, across-groups design with two...
Students with mathematics difficulties and learning disabilities typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to use when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word problems that employ specific word...
The special issue provides content knowledge about specific mathematics skills and concepts and evidence-based practices for teaching this content to students who have mathematics learning disabilities or are struggling with mathematics but may not have an identified mathematics disability. The intent of this issue is to provide readers...
Instructional applications are educational software programs that can be accessed via mobile technologies and used to help students acquire various academic skills, including mathematics. Although research suggests that app-based instruction (AI) can be effective, there is a paucity of research comparing AI to teacher-directed instruction (TDI) or to a...
Students with mathematics learning disabilities have a weak understanding of mathematical concepts that underlie success in algebra I, such as ratios and proportional reasoning. In this study, researchers used a multiple-baseline across participants design to evaluate the effects of a intervention based on an instructional trajectory of how students come...
This study investigated the effects of the Good Behavior Game (GBG) on classwide off-task behavior in two ninth-grade basic algebra resource classes. Ten students with a variety of disabilities in two classrooms and their special education resource teacher participated in this study. A reversal design was employed, in...
Research-Based Practices in Special Education, the book in which this chapter appears, aims to help special educators combat the gap between research and practice by identifying specific practices proven through research to work for students with special needs. Geared toward practitioners, teacher educators, and policymakers,...
This study synthesized the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that...
This study evaluated the stability of mathematics learning difficulties over a 2-year period and investigated several factors that might influence this stability (categorical vs. continuous change, liberal vs. conservative cut point, broad vs. specific assessment); the prediction of mathematics performance over time and by performance level were also evaluated....
Shared story reading is used successfully to promote literacy skills for all students. However, the benefits of shared story reading are not exclusive to literacy instruction and should carry into other disciplines, such as mathematics. Using shared story reading to teach mathematics concepts can play an important role in mathematics...
Research-Based Practices in Special Education, the book in which this chapter appears, is a collection of techniques shown to work for students with disabilities. The book aims to help practitioners, teacher educators, and policymakers combat the gap between research and practice. The chapters offer a consistent format, including definition of...
Pacific Coast Research Conference (February 2009) Sun A Kim, Kathleen Hughes, Jennifer Porterfield, Diane P. Bryant, Brian R. Bryant, Minyi Shih: A Synthesis of Middle School Mathematics Intervention Research for Students With Learning Disabilities
Visit the Early Mathematics Intervention website : http://3tiermathmodel.org/
Institute of Education Sciences (June 2008) Diane P. Bryant, Brian R. Bryant: Mathematics Interventions: Courage to Risk
Pacific Coast Research Conference (February 2009) Brian R. Bryant, Diane P. Bryant, Greg Roberts, Sharon Vaughn, Andrea Arthur, Sarojani S. Mohammed, Sun A Kim: The Effects of a Tier 2 Intervention on the Early Numeracy Performance of First-Grade Students with Mathematics Difficulties. ANCOVA and RDD: What We’re Learning
Council for Exceptional Children (April 2009) Diane P. Bryant, Brian R. Bryant, Jennifer Porterfield, Kathleen Hughes: Early Numeracy: Response to Intervention: Tier 2 Intervention
Council for Learning Disabilities (October 2009) David Chard, Diane P. Bryant: Evidence-Based Interventions for Students With Learning Disabilities: How Research Can Inform Practice
Society for Research on Educational Effectiveness (March 2010) Diane P. Bryant, Greg Roberts: Validating a Response to Intervention Multitiered Model for Primary Grade Students With Mathematics Difficulties
Council for Exceptional Children (April 2011) Diane P. Bryant, Brian R. Bryant, Greg Roberts, Kathleen Pfannenstiel, Jennifer Porterfield: Effects of an Early Intervention for Second-Grade Students At Risk for Mathematics Difficulties
Pacific Coast Research Conference (February 2010) Brian R. Bryant, Diane Bryant, Kathleen Hughes, and Jennifer Porterfield: Response to Intervention for Grade 1 Mathematics: Assessment and Intervention
Council for Exceptional Children (April 2010) Diane Pedrotty Bryant, Brian Bryant, Kathleen Hughes: Early Mathematics Tier 3 Intervention: What We Are Learning
Pacific Coast Research Conference (February 2011) Kathleen Hughes Pfannenstiel, Danielle SoRelle, Diane Bryant: Teacher Ratings of Math Ability Versus Actual Ability: A Longitudinal Study
Pacific Coast Research Conference (February 2011) Diane Bryant, Brian Bryant, Kathleen Hughes Pfannenstiel, Greg Roberts: The Effects of Tier 2 Mathematics Intervention for At-Risk students in Grades 1 and 2
This article introduces a special mathematics series in Learning Disability Quarterly.
This study determined the effects of an early numeracy, preventative, Tier 2 intervention on the mathematics performance of first-grade students expressing mathematics difficulties. The study used a pretest-postest design with random assignment of 139 subjects to the Tier 2 treatment and 65 students to the control group. Study instruments were progress-monitoring measures and a...
This article provides a review of research in cognitive strategy instruction for improving mathematical problem solving for students with learning disabilities (LD). The particular focus is on one of the salient components of this instructional approach - self-regulation. Seven studies utilizing this approach for teaching problem solving to students with...
Concern about poor mathematics achievement in U.S. schools has increased in recent years. In part, poor achievement may be attributed to a lack of attention to early instruction and missed opportunities to build on young children's early understanding of mathematics. This study examined the development and feasibility testing...
This article introduces a two-stage framework for the remediation of number combination deficits. The authors summarize the research and use research program studies to illustrate three approaches to remediation. The framework's less intensive stage, implementing one of three intervention approaches hypothesized to be most productive, uses a validated protocol...
In third grade, serious mathematics deficits become clearly established, and identification of mathematics disabilities typically begins to occur. This article provides background information on two aspects of mathematical cognition that present major challenges for students in the primary grades: number combinations and story problems. The article then focuses on seven...
This study examined the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. The study used a regression discontinuity design. Participants included 126 (Tier 2, n = 26) first-graders and 140 (Tier 2, n = 25) second-graders. Tier 2 students received 15-minute intervention booster lessons...
This article presents the results of a study that examined the effects of Tier 2 intervention on the performance of first-grade students identified as being at risk for mathematics difficulties. Participants included 161 (Tier 2, n = 42) first-graders. Tier 2 students received 20-minute intervention booster lessons in number and operation skills and concepts for 23 weeks....
This study examined lessons from kindergarten, first-grade, and second-grade basal mathematics textbooks to determine the extent to which 11 evidence-based critical features of instruction were present. High-quality core instruction in these grades is critical to prevent mathematics difficulties. Overall, results showed an "Approaching Acceptable" rating, meaning that the features were not...
The authors examined 31 research articles to investigate the empirical evidence for using assistive technology to support people with intellectual disabilities, in relation to the seven domains of support in the Supports Intensity Scale. Results indicate that assistive technology can be a viable support throughout individuals’ lifespan and across a...