Harmony and Dissonance: An Enactivist Analysis of the Struggle for Sense Making in Problem Solving

This work seeks to understand the emergent nature of mathematical activity mediated by learners' engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of the standard algorithm. In addressing the question, "How do learners make sense of and coordinate meanings across multiple representations of mathematical ideas?" we took an enactivist perspective and used tools of semiotics to analyze the ways they navigated the dissonance that arose as they sought to achieve harmony in meanings across multiple representations of ideas. Our findings reveal the value of such tool-mediated engagement as well as the complexity of problem solving more broadly. Implications for learning mathematics with multiple artifacts are discussed. [For the complete proceedings, see ED630060.]