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Matthews receives NSF award to study ways to help students better understand the equal sign

September 26, 2018

UW-Madison’s Percival Matthews is the principal investigator on a new National Science Foundation (NSF) grant that’s designed to examine ways to promote equal sign knowledge among school children.

The researchers will test the effectiveness of brief episodes of instruction over the course of a semester to build children’s understanding of the equal sign and associated gains in algebraic thinking. Participants in the research will be elementary- and middle- school students.

Percival Matthews
Matthews is an assistant professor with the School of Education's No. 1-ranked Department of Educational Psychology and he heads the Mathematics Education Learning and Development Lab. The research team will include co-principal investigators Martha Alibali and Ana Stephens. Alibali is a UW-Madison professor of psychology and an investigator with the School of Education’s Wisconsin Center for Education Research (WCER), while Stephens is an associate researcher with WCER.

The NSF award, for more than $670,000 over the next three years, is for a project titled, “Cultivating Knowledge of Mathematical Equivalence.”

The abstract notes that while brief, single-session studies have suggested effective ways to promote equal sign knowledge in the short term, such research has generally failed to produce practical guidelines for use by classroom teachers.

In particular, this project will examine whether spacing instruction over time can lead to more substantial and long-term gains in equal sign knowledge, and whether such knowledge, in turn, fosters algebraic reasoning.

The hypothesis, explains Matthews, is that improved equal sign knowledge will lead to improved access to algebra, which is an important pathway into higher mathematics and science.

“The equality relation symbolized by the equal sign is widely considered to be a ‘big idea’ in mathematics that provides a foundation of later competence,” says Matthews. “For instance, some of my recent work found that equal sign knowledge at second grade predicted fourth grade pre-algebraic thinking skills. This knowledge had a much bigger effect than things like IQ, attentive behavior and socioeconomic status, so finding ways to promote it is really important.”

The team ultimately hopes to be able to find ways of packaging a practical approach to developing students' knowledge of the equal sign for classroom teachers.

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.

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