Mathematics Instruction and Interventions for Students with Disabilities
- LAST MODIFIED: 28 September 2016
- DOI: 10.1093/obo/9780199756810-0163
- LAST MODIFIED: 28 September 2016
- DOI: 10.1093/obo/9780199756810-0163
Prior to the passing of the Elementary and Secondary Education Act (ESEA) in 1965, and the Education for All Handicapped Children Act (EHA) in 1975, the majority of children in the United States with visible disabilities and severe cognitive impairments had limited opportunities and limited access to formal education. Those with hidden disabilities did attend school, but they often failed because there were limited resources and limited understanding about teaching students with disabilities. By the time EHA was reauthorized in 1990, with an ensuing name change to the Individuals with Disabilities Education Act (IDEA), many improvements had occurred for students with disabilities including a better understanding of hidden disabilities, such as learning disabilities (LD) and mental health issues, as well as improved teacher training and research to determine evidence-based practices. With the focus on evidence-based practices, there have been increased research studies published on instruction and interventions for students with disabilities in pre-K–12 education. However, the literature is limited for mathematics in comparison to reading, even though math is a core subject that has a direct impact in life. It is often noted that increased proficiency in math is linked to student success across the education continuum, workforce competitiveness, and overall quality of life. Specifically, success in algebra is highly regarded as the gateway to higher mathematics course-taking; postsecondary educational opportunities; and science, technology, engineering, and mathematics (STEM) careers. In terms of careers, Geary’s “Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics” (Journal of Developmental & Behavioral Pediatrics 32.3, 2011, p. 250) summarizes studies reporting consequences of underdeveloped mathematical competencies on employment outcomes in Great Britain and in the United States. Geary reported that poor math skills were linked to lower rates of full-time employment and higher rates of employment in lower-paying occupations, as well as limited opportunities for promotion. Thus, significantly, students miss opportunities to attend college and to acquire high-paying jobs because of math difficulties and poor performance in math (Mazzocco, M. M. M., and Thompson, R. E. “Kindergarten Predictors of Math Learning Disability,” Learning disabilities research & practice?: A publication of the Division for Learning Disabilities, Council for Exceptional Children, 20.3, 2005, pp. 142–155). Though limited in comparison to reading research, there are still a lot of publications related to mathematics instruction and interventions for students with disabilities. Determining which publications are meaningful, and which interventions and instructional methods have evidence to support their effectiveness, is not always easy. Thus, this bibliography is written with the educator in mind. The information is presented with a focus on educators, and on what information is useful in mathematics teaching today. With the adoption of the Common Core State Standards for Mathematics (CCSSM), the trend for general education and state assessments in mathematics has changed over the years. The CCSSM emphasize the development of conceptual understanding, reasoning, and problem solving rather than just procedural or fluency skill in math. This shift applies to all students, including students with disabilities. Therefore, for the most part, newer publications are included reflecting this trend. However, a few older publications, which are recognized as containing crucial foundational knowledge and are still relevant to today’s educators, are included. In addition, the authors have primarily included publications related to math instruction and interventions specifically for students with disabilities, other than several cases in which the publications are highly relevant to special educators. While it is recognized that many general education math programs are relevant to students with disabilities, the focus of this bibliography has remained narrow in an attempt to best assist the educators struggling to address the math learning needs of their students with disabilities. It is important to note that much of the published literature dealing with math and disabilities is focused on students with LD. This is logical, since students with LD are the largest subset of students with disabilities identified in the school setting. However, this often leaves teachers of students with other types of disabilities uncertain as to what interventions and instructional programs to use. Therefore, in an attempt to assist all educators, some of the information in this bibliography is presented under subheadings that present journal publications by grades.
The following citations are a sampling of some of the summative work done over the years. These articles present either a meta-analysis or a systematic review of literature, which are useful in quickly identifying the types of instructional techniques available or the effectiveness of interventions for a specific group of students. One of the citations is not specific to math interventions or instruction (Johnson, et al. 2010). This article is included in this bibliography because it is a meta-analysis of thirty-two studies that examined the cognitive processing differences between students with specific learning disabilities (SLD) and typically achieving peers. It is imperative that teachers of students with LD have an understanding of the cognitive processing issues often faced by students with LD. The remainders of the articles present a variety of analytical methods used to summarize existing research and literature associated with math interventions and instructional processes for students with disabilities. Gersten, et al. 2009; Maccini, et al. 2007; and McKenna, et al. 2015 synthesize research targeting students with LD. Some instructional approaches and strategies that yielded high effect size include an explicit instruction and heuristics approach for all students with LD (Gersten, et al. 2009), and some present a mnemonic strategy instruction and graduated instructional approach for adolescent students with LD (Maccini, et al. 2007). The use of explicit instruction was also noted as effective for a subset of students with LD—namely, students with math disabilities (MD)—along with the use of an advance organizer (Zheng, et al. 2013). Barnett and Cleary 2015 reviews research studies on math intervention for students with autism spectrum disorders (ASD). Six of the eleven studies utilized visual representations to develop math skills. Hord and Bouck 2012 reviews research studies on academic math interventions for students with mild intellectual disabilities (MID) in elementary grades up to twenty-three-year-olds. The majority of the studies Hord and Bouck reviewed focused on interventions to improve math facts or computation skills for basic arithmetic. Mulcahy, et al. 2015 focuses on students with emotional and behavioral disorders (EBD). All the studies reviewed utilized different instructional strategies and interventions, and thus no evidence-based practices were identified.
Barnett, J. E., and S. Cleary. 2015. Review of evidence-based mathematics interventions for students with autism spectrum disorders. Education and Training in Autism and Developmental Disabilities 50.2: 172–185.
This comprehensive literature review synthesized eleven studies of mathematics intervention strategies for students with ASD. The future implications presented are noteworthy in that the literature associated with teaching math to students with ASD is very limited—only eleven studies were reviewed, and many of these studies had a small sample size.
Gersten, R., D. Chard, M. Jayanthi, S. Baker, P. Morphy, and J. Flojo. 2009. Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research 79.3: 1202–1242.
This article presents the findings of forty-two randomized controlled trials and quasi-experimental research related to instructional approaches for teaching math to school-aged students with LD from 1971 to 2007. The authors use Hedges’s g effect size to show the effectiveness of each intervention approach. It is a resource for gaining access to research-based practices.
Hord, C., and E. C. Bouck. 2012. Review of academic mathematics instruction for students with mild intellectual disability. Education and Training in Autism and Developmental Disabilities 47.3: 389–400.
The authors reviewed the literature from 1999 to 2010 on academic mathematics interventions for students with MID. Seven articles were reviewed. Six of the seven focused on instructional strategies to improve procedural skills such as math facts using flashcards. There is a need for more research on conceptual understanding of math ideas for students with MID, given federal and state policies regarding higher-order math thinking.
Johnson, E. S., M. Humphrey, D. F. Mellard, K. Woods, and H. L. Swanson. 2010. Cognitive processing deficits and students with specific learning disabilities: A selective meta-analysis of the literature. Learning Disability Quarterly 33.1: 3–18.
A meta-analysis of thirty-two studies was conducted to examine the cognitive processing differences between students with SLD and typically achieving peers. The analysis found moderately large to large effect sizes in cognitive processing differences between groups of students with SLD and typically achieving students.
Kunsch, C. A., A. K. Jitendra, and S. Sood. 2007. The effects of peer‐mediated instruction in mathematics for students with learning problems: A research synthesis. Learning Disabilities Research & Practice 22.1: 1–12.
This synthesis summarizes the effectiveness of peer-mediated interventions on the mathematics performance of both students with disabilities and those at risk for mathematics disabilities. Results of seventeen studies indicate that peer-mediated interventions in mathematics are moderately effective for improving students’ mathematics performance.
Maccini, P., C. A. Mulcahy, and M. G. Wilson. 2007. A follow‐up of mathematics interventions for secondary students with learning disabilities. Learning Disabilities Research & Practice 22.1: 58–74.
Review of the literature from 1995 to 2006 yielded twenty-three articles that met the inclusion criteria. A number of practices demonstrated significant gains for secondary school students with LD, which focus on not only procedural but also conceptual knowledge in math aligned with the current math standards.
McKenna, J. W., M. Shin, and S. Ciullo. 2015. Evaluating reading and mathematics instruction for students with learning disabilities: A synthesis of observation research. Learning Disability Quarterly 38.4: 195–207.
Eleven studies focusing on academic instruction for students with LD were reviewed. Cognitive strategy instruction, differentiated instruction, and opportunities for independent application (e.g., text reading, problem solving) were reported infrequently across the published observational research.
Mulcahy, C. A., M. P. Krezmien, and J. Travers. 2015. Improving mathematics performance among secondary students with EBD: A methodological review. Remedial and Special Education 37.2: 113–128.
A systematic methodological review of single case studies of students with emotional and behavioral disorders (EBD) from 1975 to December 2012 yielded nineteen articles that met inclusion criteria. Only eight studies investigated academic interventions to improve math performance for secondary students with EBD. The remainder of the studies focused on behavioral interventions in math classes, and mathematics performance was a secondary variable.
Zheng, X., L. J. Flynn, and H. L. Swanson. 2013. Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly 36.2: 97–111.
This meta-analysis identified the sample characteristics and instructional components of effective intervention studies for enhancing mathematical word problem-solving proficiency in children with math disabilities (MD). The results suggest reading ability and specific instructional components such as sequencing, explicit practice, advanced organizers, and so on have a major influence on the outcomes.
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