Student constructs of mathematical problems: Problem types, achievement and gender

Abstract

This study aims to understand students’ constructs regarding mathematical problems. Fifty-one Taiwanese primary students’ constructs are elicited using interviews with the repertory grid technique based on their responses to creative and non-creative problems. The results of qualitative data analysis show that students’ initial constructs can be categorized into three cognitive constructs (perception, strategy, and goal, each with deep and surface orientation constructs) and one affective construct. The results of correlation analysis reveal that deep strategy for both creative and non-creative problems and affect for creative problems are related to mathematics achievement. The results of multivariate analysis of variance reveal that students have fewer surface strategies and more surface goals for creative problems than those for non-creative problems. No significant gender differences or interaction effects between problem types and genders occur for either construct. The results reveal implications for teachers in the development of effective pedagogy for teaching different types of mathematical problems.

Keywords

• mathematics learning
• personal constructs
• problem types
• repertory grid technique