Cognitive Analysis of Constructing Algebraic Proof Processes: A Mixed Method Research

Abstract

This study aimed in order to investigate cognitive aspects of the processes of constructing algebraic proofs of pre-service and service secondary math teachers. We used explanatory sequential design from mixed research methods in the study. Secondary math teachers working in the province east of Turkey and pre-service secondary math teacher in this province participated to the study. Quantitative data of the study were collected through a “Proving Diagnostic Test” and qualitative data were gathered from the participants through a think aloud protocol. We used two different activity cards that each of them included one algebraic proof question in the think aloud protocol. Quantitative data were analyzed using descriptive and inferential statistics. Content analysis was applied to qualitative data. The study show that the cognitive skills performed by pre-service and service secondary math teachers emerge five categories: read the proposition of the proof, evaluating the correctness, determining strategies, carry out plans and heuristic shortcuts thinking strategy. Eight categories were identified in the theme (context of) of meta-cognitive skills. These categories are: facilitating the operations, questioning, awareness, planning, strategy determination, controlling, correlating, and analogical reasoning.