Leveraging a Categorization Activity to Facilitate Productive Generalizing Activity and Combinatorial Thinking
Leveraging a Categorization Activity to Facilitate Productive Generalizing Activity and Combinatorial Thinking
复制标题
利用分类活动促进富有成效的概括活动和组合思维
DOI：
10.1080/07370008.2021.1887192
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发表时间：
2021
影响因子：
3.3
通讯作者：
E. Lockwood
中科院分区：
文献类型：
--
作者：
Zackery Reed;E. Lockwood
摘要在本文中，我们提供了两个迭代教学实验的数据，涉及学生的四个基本计数问题的建设。教学实验的目的是利用相关和扩展的概括活动，为学生提供机会，以反映在构建这些公式时的初始组合活动。我们讨论了三种组合的思维方式，从他们的工作中出现在这个任务，并提供评论学生的概括活动和参与的新兴思维方式之间的相互作用。我们解决的实际目标，确定方法，学生富有成效的组合推理，我们提供了一个理论上的评论学生的活动，因为它发生在特定的概括行动的背景下的反思。
Abstract In this paper, we present data from two iterative teaching experiments involving students’ constructions of four basic counting problems. The teaching experiments were designed to leverage the generalizing activities of relating and extending to provide students with opportunities to reflect on initial combinatorial activity when constructing these formulas. We discuss three combinatorial ways of thinking that emerged from their work on this task and provide commentary on the interplay between the students’ generalizing activities and engagement in the emergent ways of thinking. We address the practical goals of identifying ways that students productively reason in combinatorics, and we provide a theoretical commentary on students’ reflection on activity as it occurs in the context of particular generalizing actions.