Appreciating mathematical structure for all
Appreciating mathematical structure for all
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所有人都能欣赏数学结构
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Watson
中科院分区：
文献类型：
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作者：
J. Mason;M. Stephens;A. Watson
我们把数学结构的意思是一般属性的识别，这些属性在特定情况下被实例化为一个集合的元素或元素子集之间的关系。因为我们认为欣赏结构是一种强大的生产力，所以关注结构应该是数学教学和学习的一个重要组成部分。这与教孩子数学结构不相混淆。我们观察到，儿童从很小的年龄就能够在比一些作者想象的更大的程度上欣赏结构。当然，引导学生欣赏结构意味着他们对结构的欣赏需要培养，以便加深和变得更加成熟。我们首先考虑一些最近的研究，支持这一观点，然后继续认为，除非学生被鼓励参加结构和从事结构思维，他们将被阻止从思考富有成效和深入的数学。我们提供了几个说明性的情况下，结构思维有助于弥合概念和程序的方法来教和学数学之间的神话鸿沟。最后，我们把我们的建议的背景下，如何在过去的几位作家试图探索结构在数学教学和学习的重要性。
We takemathematical structure to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set. Because we take the view that appreciating structure is powerfully productive, attention to structure should be an essential part of mathematical teaching and learning. This is not to be confused with teaching children mathematical structure. We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning.