Cultivating Knowledge of Mathematical Equivalence

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

This project will develop and test the effectiveness of a semester-long conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Participants in the research will be elementary- and middle- school students. Although many brief, single-session laboratory studies have suggested effective ways to promote equal sign knowledge in the short term, these studies have generally failed to produce practical guidelines for use by regular classroom teachers. This project will apply findings from laboratory studies over a longer time period with the goal of packaging a practical approach to developing students' knowledge of the equal sign for classroom teachers. The hypothesis is that improved equal sign knowledge will lead to improved access to algebra, an important pathway into higher mathematics and science that provides access to Science, Technology, Engineering, and Mathematics (STEM) fields that help power modern society. This project will explore the effectiveness of spaced, conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Multiple experimental studies have shown that brief, conceptually-based instructional interventions can lead to improvements in children's equal sign knowledge. The proposed research will test whether spacing such interventions over time can lead to more substantial and long-term gains in equal sign knowledge, and whether such knowledge, in turn, fosters algebraic reasoning. One component of the research will aim to optimize the conceptually based intervention. The other component will be a study that investigates the effects of the intervention over time, using a crossover design. The research will employ a measure of equal sign knowledge that is more sensitive than most commonly used measures, allowing for detection of relatively fine-grained gains in response to the instructional intervention. In total, the work will contribute to the field's understanding of how to improve equal sign knowledge and understanding of the causal impact of equal sign instruction on student competence in algebra. This project is co-funded by the Discovery Research preK-12 program (DRK-12) that seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.