Characterizing how and when a way of proving develops in a primary mathematics classroom: A commognitive approach
Characterizing how and when a way of proving develops in a primary mathematics classroom: A commognitive approach
复制标题
描述小学数学课堂中如何以及何时发展一种证明方法：一种认知方法
DOI：
10.1080/0020739x.2021.1941365
复制
发表时间：
2021
影响因子：
0.9
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Shinno;Y.;& Fujia;T.
在这项研究中，我们的目标是描述一种可以在小学数学课堂上产生的证明方式，并探讨影响这些过程的因素，并导致证明方式的变化。假设证明作为一个社会嵌入式活动，我们概念化它作为“建设”和“充实”之间的相互作用的基础上，在数学教育的一个完善的理论框架：commogistan框架。一个有形的证明任务的设计，基于操作性证明的想法，并在英国的一个五年级教室实施。我们分析了在证明过程中与话语特征（词语使用、视觉中介、叙事和常规）相关的结构和实体化。结果表明，建设和充实之间的相互作用，逐步发展，而不是在一个简单的方式，在以前构建的叙事重建或充实在一个更一般的情况下。这一发现对于理解小学生在证明中作为一种交际手段时，可能影响其改变例证使用和证明方式的因素具有一定的相关性。本研究对中学证明活动的延续性具有一定的启示意义，有助于推进小学证明活动的研究。
In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between ‘construction’ and ‘substantiation’ based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.