Challenges Students May Experience

A major component of mathematics instruction is solving word problems. Solving a word problem requires students to draw on multiple knowledge bases and skills both accu-rately and efficiently (Baroody, 2011; National Research Council, 2001). These knowledge bases include (a) concep-tual understanding, which refers to an integrated and func-tional understanding of mathematics concepts (e.g., rational numbers, fractions, decimals), operations (e.g., division), and relations (e.g., 0.05 is the same as 5/100 is the same as 5%); (b) procedural knowledge, or fluency, which refers to the skill in performing procedures (e.g., performing calcula-tions with fractions) efficiently, accurately, and appropri-ately; and (c) strategic and adaptive knowledge, or the ability to engage in mathematical inquiry, reflection, and justification as well as selecting appropriate methods and strategies for formulating, representing, and solving prob-lems (Baroody, 2011; National Research Council, 2001). Central to strategic and adaptive knowledge is the ability to represent a word problem. A diagram is an often-recommended approach for representing a word problem, particularly as students work toward higher levels of math-ematics in the middle or high school grades. In general, a diagram can be thought of as something that stands in place of something else, such as the expression of a concept (Smith, 2003). The strength of a diagram is that, like any visual representation, it can be used as a cognitive tool both to help understand a problem situation and, subse-quently, to solve the problem. Further, it provides a visual referent that students can use in a metacognitive manner to monitor progress and self-correct where necessary (van Garderen, 2006). Unfortunately, for many students, in par-ticular, students with learning disabilities (LD), their ability to use diagrams as a cognitive tool for solving word prob-lems is lacking