Understanding and Cultivating the Connections between Students’ Natural Ways of Reasoning and Mathematical Ways of Reasoning

Many consider mathematical reasoning to be a basic mathematical skill and inseparable from knowing and using mathematics. Yet despite its importance, mathematics education research continues to paint a bleak picture of students' abilities to reason mathematically. In contrast, cognitive science research has revealed surprising strengths in children's abilities to reason in non-mathematical domains, suggesting that children are capable of developing complex and abstract causal theories, and of using powerful strategies of inductive inference. Thus, this raises something of a paradox: Why are children so good at reasoning in non-mathematical domains, yet often so poor at reasoning in mathematical domains? The purpose of this study is to explore this seeming paradox. In particular, our goal is to extend the cognitive science research into the domain of mathematics education and, more specifically, into the domain of middle school mathematics. We seek to understand the strengths and weaknesses of students' reasoning in and out of mathematics, to understand the connections between students' reasoning in different domains, and, ultimately, to improve students' abilities to reason mathematically.

Specifically, the goals of this project are: (i) to understand the relationship between students’ inductive reasoning strategies outside mathematics and their ways of reasoning within various mathematics domains, and (ii) to understand the relationship between students’ ways of reasoning inductively and their abilities to begin to reason deductively.