Exploring Mathematical Reasoning of Elementary Preservice Teachers

Abstract

The purpose of this study is to understand the characteristics of mathematical reasoning of elementary preservice teachers (EPTs). For this purpose, 68 EPTs were presented with two tasks related to mathematical reasoning, and their written responses were analyzed. The EPTs' mathematical reasonings were investigated on the one hand as a whole and on the other hand between the three groups -the full successful, partial successful, and unsuccessful provers-, with focusing on the affordances from and strategies for using examples proposed in the CAPS framework. As the results of this study, it was revealed that the EPTs had insufficient competencies in terms of exploring with examples, finding structural features, building generalizations, developing conjectures, and producing proofs. In contrast, the EPTs had great strength with regard to representing their chosen examples in formal expression, which was a decisive contributor on the one hand but an impediment on the other in producing valid justifications to the given conjectures. Based on the results, the implications for elementary preservice teacher education were suggested.

Keywords

• mathematical reasoning
• preservice elementary teacher
• example
• conjecture
• structure
• generalization
• justification
• proof