Studying the Practical Rationality of Mathematics Teaching: What Goes Into Installing: a Theorem in Geometry?
Studying the Practical Rationality of Mathematics Teaching: What Goes Into Installing: a Theorem in Geometry?
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DOI：
10.1080/07370008.2011.556833
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发表时间：
2011-01-01
影响因子：
3.3
通讯作者：
Chazan, Daniel
中科院分区：
文献类型：
--
作者：
Herbst, Patricio;Nachlieli, Talli;Chazan, Daniel
本文提出了一种研究数学教师在高中几何定理教学中运用合理性的方法。从更广泛的意义上讲，本研究阐述了如何激发理性，引导教师处理教学实践的需求。特别地，它说明了通过卡通人物动画表现的有问题的课堂场景如何促进实践者群体之间的思想实验。根据四组有经验的几何教师的学习小组会议的视频记录，该研究展示了如何解析和检查这些记录，以确定有经验的实践者与教学情况实例相关的感知和欣赏类别。该研究提供了支持一个理论推导假设的初步证据，即几何教师作为一个群体认识到，教师将认可或认可那些将被作为定理记住以供以后使用的命题的期望是规范的。在一个学生证明了一个命题而老师没有认定为定理的故事的互动中，该研究还显示了几何教师可以使用的战术资源，使学生能够重复使用这样的命题。
This article presents a way of studying the rationality that mathematics teachers utilize in managing the teaching of theorems in high-school geometry. More generally, the study illustrates how to elicit the rationality that guides teachers in handling the demands of teaching practice. In particular, it illustrates how problematic classroom scenarios represented through animations of cartoon characters can facilitate thought experiments among groups of practitioners. Relying on video records from four study group sessions with experienced teachers of geometry, the study shows how these records can be parsed and inspected to identify categories of perception and appreciation with which experienced practitioners relate to an instance of an instructional situation. The study provides initial evidence that supports a theoretically derived hypothesis, namely that teachers of geometry as a group recognize as normative the expectation that a teacher will sanction or endorse those propositions that are to be remembered as theorems for later use. In interacting with a story in which students had proven a proposition that the teacher had not identified as a theorem, the study also shows the kind of tactical resources that teachers of geometry could use to make it feasible for students to reuse such a proposition.