Adding Up to Multiplicative Concepts: The Role of Embodied Reasoning

• In Event: Students’ Mathematical Thinking and Learning

Abstract

22 Grade 4-6 students participated in a design study that investigated the microgenesis of proportionality schemata via engaging in embodied-interaction problem-solving activities. Qualitative data analyses elucidate enduring theoretical and practical questions regarding the cognitive constitution of multiplicative concepts and in particular relations between additive and multiplicative forms of reasoning. We argue that unless multiplicative theorems-in-action are reenacted as iterated-adding, these efficient arithmetic procedures may remain ungrounded in schemata emerging from spatial–temporal interaction and, as such, remain conceptually inflexible, ungenerative. To support the plausibility of this claim, we compare across case studies of students who, asked how additive and multiplicative solution strategies result in the same systemic effect, struggled with varying success to coordinate recursive-iteration “analog” trans-locations and number-driven “digital” products.

Authors

• Dor Abrahamson, University of California - Berkeley

• Andrea Negrete, University of California - Berkeley

• Jose Francisco Gutierrez, University of California - Berkeley