Prospective middle-school mathematics teachers’ quantitative reasoning and their support for students’ quantitative reasoning

Abstract

The aim of this research is to examine prospective mathematics teachers’ quantitative reasoning, their support for students’ quantitative reasoning and the relationship between them, if any. The teaching experiment was used as the research method in this qualitatively designed study. The data of the study were collected through a series of exploratory teaching interviews and debriefing interviews with nine focus group participants, and clinical interviews that the participants conducted with middle-school students. The results indicated that the participants with strong quantitative reasoning use problem-solving approaches that focused on the quantity, whereas the participants with poor quantitative reasoning use problem-solving approaches that focused on performing calculations, using formulas and procedures devoid of quantitative meaning in solving of the problem. During the questioning process, the participants with strong quantitative reasoning led their students to identify and interpret the quantities, determine relationships among the quantities, represent all the quantities and their interrelationships, whereas the participants with poor quantitative reasoning led their students to perform calculations, make algebraic manipulations and focus on numbers by ignoring the quantities in the problem. These results suggest that prospective mathematics teachers’ quantitative reasoning is strongly associated with their support for students’ quantitative reasoning in the problem-solving process.