Preservice mathematics teachers solving word problems: visual-spatial abilities, use of representations, and types of mathematical thinking

Abstract

The main purpose of this study was to examine preservice teachers’ types of mathematical thinking, use of visual-spatial representations, visual-spatial abilities, and mathematical problem solving performances and to investigate the relationships between these variables. The sample of the study consisted of 113 preservice mathematics teachers in a private and four public universities in Istanbul and Ankara. In order to investigate the research questions two instruments were used. Firstly, preservice teachers’ types of mathematical thinking were determined. Although problem solving performances were similar for each type of mathematical thinking, preservice teachers who adopted harmonic and geometric types of mathematical thinking preferred to use schematic representations more than analytic thinkers in their problem solving processes. Use of visual-spatial representations was related with problem solving performance and schematic representations were associated more strongly with correct solutions in comparison with pictorial representations. The participants’ visual-spatial abilities had a significant relationship only with their use of schematic representations. The findings provided an insight about preservice teachers’ preferences for visual approach and their implications for teacher education programs. Preservice teachers should have an opportunity to learn how a schematic representation can be created and teacher education programs should include visual approaches with consideration of their efficacies.