Ways of Reasoning About Integers: Order, Magnitude, and Formalisms

• In Event: Poster Session 17
  In Poster Session: Teaching and Learning Mathematics: Multiple Perspectives

Abstract

On the basis of analysis of interviews with 47 grades 1–4 students, we identified 3 ways of reasoning about integers that teachers could leverage to support sophisticated integer reasoning. Responses of children who had negative numbers in their domains fell primarily into 1 of 3 categories—ordinal, magnitude-based, or formal. We present three illustrative cases of these distinct ways of reasoning. Though individual children did not typically use a single way of reasoning across all problems, many were consistent in their problem-solving approaches and invoked a primary way of reasoning. Thus, we consider how a particular view of number, consistently applied across problems, both supported and constrained students’ integer understanding.

Authors

• Jessica Pierson Bishop, University of Georgia

• Lisa L. Lamb, San Diego State University

• Bonnie Schappelle, San Diego State University

• Ian Whitacre, Florida State University

• Melinda Lewis, San Diego State University

• Randolph A. Philipp, San Diego State University