From Here to There! A Dynamic Algebraic Notation System Improves Understanding of Equivalence in Middle-School Students

Abstract

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among mathematically equivalent states. In the fall of 2019, 475 middle-school students participated in a randomized control trial where they worked in either FH2T or online problem sets with hints and feedback in ASSISTments over four 30-min sessions during their math class. We found that (a) students in both conditions improved their understanding of mathematical equivalence from pretest to posttest, (b) students in the FH2T condition performed better on posttest compared to students in the problem set condition, and (c) the condition effect was comparable between students with high versus low prior knowledge. Together, the findings suggest that FH2T is an effective intervention for improving middle-school students’ understanding of mathematical equivalence. The implications for research and practice on the usefulness of digital environments in mathematics education are discussed.