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<p>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, <i>Mathematical Reasoning and Proving for Secondary Teachers</i>. Drawing upon the commognitive framework, we establish a unified conceptualization for examining the <i>mathematical reasoning processes</i> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月25日

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  • Merav Weingarden,
  • Orly Buchbinder

摘要

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.