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Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction
Journal of Mathematics Teacher Education ( IF 1.786 ) Pub Date : 2019-11-26 , DOI: 10.1007/s10857-019-09450-3
Christine Andrews-Larson , Estrella Johnson , Valerie Peterson , Rachel Keller

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about inquiry-oriented instruction relative to vertices of the instructional triangle (content, students, and instructor). Through this lens, we analyze conversations of twenty-five mathematicians who elected to attend a workshop on inquiry-oriented instruction at a large national mathematics conference. Identifying differences in talk between two breakout groups, we argue that deeper mathematical engagement in task sequences designed for students supported deeper engagement in students’ mathematical reasoning and engendered reasoning about instruction that was more frequently accompanied by rationale based in mathematics or students’ reasoning about mathematics. Importantly, deeper mathematical engagement was observed when the discussion facilitator prompted participants to engage through a mathematical lens rather than an instructional lens.



中文翻译:

与数学家进行数学运算以支持关于探究式教学的教学推理

鉴于在大学数学教育中普遍存在着以学生推理为重点的研究以及利用学生推理的教学创新的发展,重要的是了解本科数学教师如何理解这些创新。我们描述了关于以查询为导向的教学相对于教学三角形的顶点(内容,学生和讲师)的教学推理。通过这个镜头,我们分析了25位数学家的对话,他们选择参加了一次大型全国数学会议上的面向查询的讲习班。确定两个分组讨论之间的谈话差异,我们认为,在为学生设计的任务序列中进行更深入的数学参与,可以支持更深入地参与学生的数学推理和产生关于教学的推理,而这种推理更多地伴随着基于数学的基本原理或学生对数学的推理。重要的是,当讨论主持人通过数学视角而非教学视角提示参与者进行互动时,观察到了更深层次的数学互动。

更新日期:2019-11-26
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