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.
Weingarden, M. & Buchbinder, O. (2025). Exploring the opportunities for reasoning and proving in mathematical tasks designed by secondary prospective teachers. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-025-10440-x