UW-Madison Fractions & Algebra Project

A few weeks ago Shubhi, Snigdha, and Kairui presented their poster at the Undergraduate Research Symposium. Their poster investigated how students shift between fraction and decimal representations across different mathematical contexts. It was found that students exhibit distinct strategy profiles based on their representations, with some demonstrating greater flexibility than others. These patterns provide insight into how students’ representational choices are a strategic decision and how and when a person uses representational flexibility matters. Although there were no consistent or large differences between decimal use and individual characteristics (relational reasoning ability, fluid intelligence, working memory), they aim to test instructional strategies that may deepen these concepts in the future.

On April 17th, Ella presented her poster at the Undergraduate Research Symposium. She investigated the relationship between 7-9th grade students’ proportional reasoning strategies and fraction schemes. It was found that students who have a more sophisticated understanding of fractions are more likely to display strategy flexibility in proportional reasoning problems. This means that having a stronger understanding of fractions may allow students to correctly solve proportional reasoning problems in a variety of ways. Congratulations, Ella!

This morning we celebrated Labsgiving with a breakfast potluck and a great presentation from Sophie on students’ understanding of the equal sign! Wishing everyone a wonderful Thanksgiving break! 🦃🍂

Last week, Ana Stephens presented preliminary findings from Phase 1 of our research at the Psychology of Mathematics Education—North America conference at Penn State. We found that students who performed well on proportional reasoning tasks also had better fraction magnitude and arithmetic knowledge. We also found that students who demonstrated strategy flexibility on the proportional reasoning tasks (using two or more different strategies across four tasks) had higher fraction arithmetic scores and greater success placing fractions on a 0–5 number line. We will continue to share more results from Phase 1 as we continue our analyses!