Enhancing Mathematical Problem Solving for Secondary Students with or at Risk of Learning Disabilities: A Literature Review

Abstract

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as generalizing to different contexts; both requirements are particularly challenging for many students with learning disabilities. An in-depth review of research was completed to (1) demonstrate how interventions targeting mathematical problem solving are categorized into heuristic, semantic, or authentic approaches; (2) explore the degree to which generalization is presented in each approach; and (3) determine the efficacy of each intervention approach. Experimental studies (n = 17) demonstrating the effects of interventions designed to enhance mathematical problem solving for secondary students with or at risk of learning disabilities were analyzed. Findings indicate that the efficacy of the three intervention approaches varies, and that the real-world connections differ. Implications for research and practice are discussed.

Explicit Instruction: Historical and Contemporary Contexts

“…Instructional components of direct instruction were initially identified through correlational research (e.g., observations of what effective teachers do when they teach), and were followed by experimental research to verify the effectiveness of the identified teaching behaviors. These studies and their findings were summarized in the 1980s by Brophy and Good (1986) as well as others (e.g., Gage & Needles, 1989;Rosenshine & Stevens, 1986), and were followed by discussions of implications for special education (e.g., Christenson, Ysseldyke, & Thurlow, 1989;Gersten, 1998;Gersten, Baker, Pugach, Scanlon, & Chard, 2001).…”

“…There have been numerous descriptive literature reviews, syntheses, and meta-analyses published in peer-reviewed journals that identify effective instructional approaches used with students with LD across a variety of content areas. These reviews all identified explicit instruction as effective for teaching students with LD in the areas of math, reading, and writing (e.g., Christenson et al, 1989;Gersten, 1998;Graham & Harris, 2009;Graham, McKeown, Kiuhara, & Harris, 2012;Kroesbergen & Van Luit, 2003;Mastropieri, Scruggs, Bakken, & Whedon, 1996;Solis et al, 2012;Swanson, 2001;Vaughn et al, 2000).…”

Schema-Based Instruction for Mathematical Word Problem Solving: An Evidence-Based Review for Students With Learning Disabilities

“…As students learn more mathematical concepts, connections are continuously made within and across these different ideas, thus, building deeper mathematical understanding that leads to more sophisticated problem-solving skills. Schema is an essential element in helping students develop mathematical problem-solving skills; however, students with MD require additional instructional scaffolding to facilitate the development of schema (Hwang & Riccomini, 2016; Jitendra, DiPipi, & Perron-Jones, 2002).…”

“…Schemas based on visual representations are especially important for students with LD during problem-solving instruction and can take many different forms including schema diagrams, bar models, generic diagrams, graphic organizers, tables, and charts (Hwang & Riccomini, 2016). Whereas an addition word problem involving picking apples and cherries could be very simply represented by a pictorial illustration of apple and cherry trees (i.e., a drawing of a tree with apples on it), the same problem could be represented with schema diagram (e.g., bar model, graphic organizer illustrating essential problem features).…”

A Systematic Analysis of Experimental Studies Targeting Fractions for Students with Mathematics Difficulties

“…Rather than focusing specifically on the domain of fractions, the majority of studies have focused on general mathematics domains for struggling learners (e.g., Cheung & Slavin, 2013;Gersten et al, 2009;Kroesbergen & Van Luit, 2003;Swanson & Jerman, 2006); word problems (e.g., Fuchs et al, 2011;Hwang & Riccomini, 2016;Zheng, Flynn, & Swanson, 2013); or basic fact fluency (e.g., Codding, Burns, & Lukito, 2011). Only two syntheses addressed the overall effects of interventions designed to improve fraction achievement and examine effective instructional types for students with mathematics difficulties.…”