Teaching students with mathematics disabilities to solve multiplication and division word problems: the role of schema-based instruction

Abstract

Mathematical knowledge involving whole number multiplication and division is integral to understanding multiplicative structures such as ratios, slope, rate of change, and proportions, which are important in subsequent mathematical learning. In this study, we investigated the effectiveness of a research-based intervention, schema-based instruction (SBI), to teach multiplicative whole number word-problem solving to three-fifth-grade students with mathematics disabilities. SBI emphasizes the underlying mathematical problem structure, uses visual-schematic diagrams to show how quantities in a problem are related, focuses on problem solving procedures grounded in reasoning, and highlights metacognitive strategy knowledge to monitor and reflect on the problem-solving process. We used a multiple probe across participants design to evaluate the functional relation between the SBI intervention and word-problem solving performance. Immediately following treatment as well as 1–3 weeks later, results indicated acquisition and retention of word problem-solving skills by all three students. In addition, the percentage of student use of representations (i.e., drawing a diagram, writing a number sentence) increased from the baseline to the intervention phases. These findings and their relation to theory, research, and practice are discussed.