Understanding Reducible Fractions

• In Event: Motivation in Mathematics

Abstract

Prior studies have focused on how children understand irreducible fractions, where no common factor can be extracted (e.g., 2/3). Here, we investigate how people reason about reducible fractions (e.g., 4/6). Mathematics instruction emphasizes always reducing fractions to lowest terms. We predict, then, that adults will do so automatically. To test this prediction, we developed a new fraction span task where automatic reduction of reducible fraction is task-irrelevant, i.e., should hurt performance. We also adapted the fraction comparison task so that automatic reduction is task-relevant, i.e., should enhance performance by supporting the use of efficient componential strategies. Our study of undergraduate students found initial support for these prediction, suggesting that fraction instruction should stress the task-relevance of reducing reducible fractions.

Authors

• Jimin Park, University of Minnesota - Twin Cities

• Sashank Varma, Georgia Tech