Middle-Grade Teachers' Reasoning with Fraction Division Tasks

Abstract

This study provides a fine-grained analysis of teachers’ reasoning as they engage in quotitive fraction division tasks. In particular, this qualitative analysis considers the mathematical knowledge that six middle-grade teachers used in a professional development program and interviews. In all of the items, fraction division situations were approached through linear or area models. Analysis focused on three knowledge components with which teachers associated in reasoning fraction division tasks: partitioning operations, reasoning with quantitative units (referent units and levels of units), and interpretations of numerical expressions of division.

Keywords

• reasoning with quantitative units
• fraction division
• mathematical knowledge for teaching
• partitioning operations