Fostering prospective mathematics teachers’ proportional reasoning through a practice-based instruction

Abstract

ABSTRACT The purpose of this study was to investigate prospective middle school mathematics teachers’ proportional reasoning before and after receiving a practice-based instruction based on proportional reasoning. The Proportional Reasoning Test, semi-structured interviews and observations of student teachings were used to collect data about the participants’ proportional reasoning. The results indicated that prospective teachers improved their proportional reasoning by completing a practice-based instruction. Before the instruction, they generally applied algebraic procedures without associating meaning and used a limited number of strategies to solve problems. Furthermore, they had difficulties in distinguishing proportional from nonproportional situations. However, by the end of the instruction, while they mostly preferred to use informal strategies, they relied less on formal strategies. Additionally, they utilized a broader range of strategies to solve problems and made sense of these strategies. Further, they could determine whether the quantities in a situation were related additively, multiplicatively, or in some other way.