Educating Teachers to Teach Multiplicative Structures in the Middle Grades

Abstract

The middle-grades mathematics related to multiplicative structures has undergone careful scrutiny over the past decade. Researchers have identified the types of reasonings involved; the difficulties students have with the concepts and why these difficulties might occur; and the interconnections within this content area. On the basis of this research we make four recommendations for the preparation and professional development of teachers. The recommendations deal with different but related forms of reasoning: quantitative reasoning, multiplicative reasoning, proportional reasoning, and reasoning with rational numbers. Problematic issues that follow from the recommendations are discussed.