Improving students’ proportional thinking using schema-based instruction

Abstract

This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7 th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents. The SBI program emphasized the underlying mathematical structure of problems via schematic diagrams, focused on a 4-step procedure to support and monitor problem solving, and addressed the flexible use of alternative solution strategies based on the problem situation. Blocking by teacher at three middle schools, the authors randomly assigned the 21 classrooms to one of two conditions: SBI and control.Classroom teachers provided the instruction. Results of multilevel modeling used to test for treatment effects after accounting for pretests and other characteristics (gender, ethnicity) revealed the direct effects of SBI on mathematical problem solving at posttest. However, the improved problem solving skills were not maintained a month later when SBI was no longer in effect nor did the skills transfer to solving problems in new domain-level content.KEYWORDS: word problem solving, ratio and proportion, middle school students, schemabased instruction

“Concreteness fading” promotes transfer of mathematical knowledge

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The Effects of Paraphrasing Interventions on Problem‐Solving Accuracy for Children at Risk for Math Disabilities

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Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

“…Considerable research in mathematics education has focused on how to improve students' proportional reasoning (e.g., Behr, Harel, Post, & Lesh, 1992;Lamon, 2007;Lesh, Post, & Behr, 1988;Litwiller & Bright, 2002), with recommendations that include providing ratio and proportion tasks in a wide range of contexts (e.g., measurements, prices, rates) and ensuring that students have experienced conceptual instruction before presenting symbolic strategies for solving proportional problems. Accordingly, the purpose of the present randomized controlled study was to rigorously evaluate the effectiveness of one instructional intervention, schema-based instruction (SBI), which has shown promise in prior work in enhancing students' ability to solve problems with embedded ratio, proportion, and percent concepts (e.g., Jitendra, Star, Starosta, Leh, Sood, & Caskie, 2009;Jitendra, Star, Rodriguez, Lindell, & Someki, 2011). …”