Mathematicians’ Example-Related Activity when Exploring and Proving Conjectures
Mathematicians’ Example-Related Activity when Exploring and Proving Conjectures
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数学家在探索和证明猜想时的示例相关活动
DOI：
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发表时间：
2016
期刊：
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通讯作者：
Alison G. Lynch
中科院分区：
文献类型：
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作者：
E. Lockwood;Amy B. Ellis;Alison G. Lynch
例子在探索猜想和随后的证明过程中起着至关重要的作用。尽管证明一直是一个广泛研究的对象，但数学家在表述证明时利用例子的精确方法还有更多需要学习的地方。在本文中，我们提出了调查和采访数学家的结果，目标是例子在数学家的证明相关活动中的作用。他们的回答揭示了具体的与例子相关的活动（包括战略性的例子选择和使用）以及他们参与这些活动的总体方式（包括对泛化和元认知的关注）。我们分享了调查和访谈的说明性摘录，并讨论了结果的教育意义。
Examples can play a critical role in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, there is more to learn about the precise ways in which mathematicians leverage examples as they formulate proofs. In this paper, we present results from surveys and interviews with mathematicians that targets the role of examples in mathematicians’ proof-related activity. Their responses shed light on specific example-related activity (including strategic example selection and use) and on the overarching ways in which they engage in such activity (including a focus on generalization and metacognition). We share illustrative excerpts from the surveys and interviews and discuss educational implications of the results.