Exploring the opportunities for reasoning and proving in mathematical tasks designed by secondary prospective teachers

Abstract This article examines the opportunities for reasoning and proving (ORP) embedded in mathematical tasks designed by secondary prospective mathematics teachers (PSTs) in a capstone course, Mathematical Reasoning and Proving for Secondary Teachers . Drawing upon the commognitive framework, we establish a unified conceptualization for examining the mathematical reasoning processes and the logic-related constructs embedded in mathematical tasks. We analyze 551 questions designed by 15 PSTs who participated in the course and explore how mathematical reasoning and logic-related constructs are reflected and intertwined in the tasks. Findings revealed four types of ORP, explicating the differences between opportunities related to reasoning processes and logic-related constructs: limited ORP, mathematical-reasoning ORP, logic-related ORP, and fully-integrated ORP. We discuss the contribution of the four types of ORP for characterizing tasks, specifically those that include logic-related constructs, and potential implications for supporting teachers in integrating reasoning and proving in their classrooms.