Abstract We analyzed video data of five instructors teaching the Mean Value Theorem (MVT) in a first-semester calculus course as part of a broader project investigating how active learning strategies were being implemented and supported in calculus courses. We sought to identify the ways examples of functions that did or did not satisfy the conclusion of MVT were generated and used in instruction. Using thematic analysis, we identified four themes that serve as characterizations of examples, which then allowed for the analysis of trends and patterns. We propose that attention to the generation and use of examples serves as one lens for considering how students can be engaged in the mathematical activity of the classroom, with implications for learning. This work contributes to an evolving notion of what is entailed in students’ active learning of mathematics and the role of the instructor in facilitating active learning opportunities.

中文翻译：

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微积分课堂中图例的生成与使用：均值定理的案例

摘要 我们分析了在第一学期微积分课程中教授中值定理 (MVT) 的五位教师的视频数据，作为调查微积分课程中如何实施和支持主动学习策略的更广泛项目的一部分。我们试图确定在教学中生成和使用满足或不满足 MVT 结论的函数示例的方式。使用主题分析，我们确定了四个主题作为示例的特征，然后允许分析趋势和模式。我们建议将关注示例的生成和使用作为考虑学生如何参与课堂数学活动并对学习产生影响的一个镜头。