Comparing and Abstracting in a Programming-Enhanced Environment for Algebra Learning

• In Event: Virtual Poster Session
  In Virtual iPresentation Only: SIG-Research in Mathematics Education Virtual Poster Session

Abstract

Comparing and explaining multiple strategies for solving identical or isomorphic problems has been proven to enhance students’ conceptual understanding, procedural knowledge, and flexibility in mathematics. This study, anchored in the dynamic operations involved in mathematical problem-solving, extends previous research by modeling student thinking processes during comparisons across isomorphic problems and multiple methods in a programming-enhanced environment. Drawing on Piaget’s notion of abstraction, we examine how students assimilate and accommodate new knowledge during different types of comparison. Our models suggest that interconnected levels of empirical and reflective abstractions are involved when students compare programming outputs and computer programs. We conclude by discussing how characterizing these mental processes can inform task design and guide future research in mathematics education.

Authors

• Haoyi Wang, University of Toronto - OISE

• Biyao Liang, University of Hong Kong