Proof as a Cluster Category
Proof as a Cluster Category
复制标题
作为聚类类别的证明
DOI：
10.5951/jresematheduc.2019.0007
复制
发表时间：
2020
影响因子：
2.8
通讯作者：
Keith Weber
中科院分区：
文献类型：
--
作者：
J. Czocher;Keith Weber
为了设计和改进数学证明的教学，数学教育者需要对证明进行充分的定义，该定义忠实于数学实践并与教学情境相关。在数学教育和数学哲学中，数学证明通常被定义为满足一系列必要和充分条件的证明类型。我们认为，以这种方式定义证明类别使得定义无法准确捕获类别成员资格的确定方式。我们提出了另一种账户——证明作为集群类别——并展示了它解决以前账户中固有的许多棘手挑战的潜力。我们还将证明，采用集群帐户对于如何研究和教授证明是有用的。
To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a collection of necessary and sufficient conditions. We argue that defining the proof category in this way renders the definition incapable of accurately capturing how category membership is determined. We propose an alternative account—proof as a cluster category—and demonstrate its potential for addressing many of the intractable challenges inherent in previous accounts. We will also show that adopting the cluster account has utility for how proof is researched and taught.