在以证明为基础的课程中,数学家如何描述和尝试培养对概念和定义的理解

IF 1.9 Q2 EDUCATION & EDUCATIONAL RESEARCH
Rachel Rupnow, Timothy Fukawa-Connelly
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引用次数: 0

摘要

长期以来,数学教育研究一直关注学生对概念的理解,包括强调被视为有问题的概念和寻找培养更理想概念的方法。然而,对数学家如何描述对概念和定义的理解或推广有益于学生的活动的研究却很有限。根据对 13 位数学家的访谈,我们对理解概念和定义的含义进行了专题描述,强调了数学家认为有助于学生学习的活动,并研究了他们推广这些活动的原因。研究结果包括对理解概念含义的数学基础描述,以及对接近和支持学习的一般性描述。研究的意义包括:需要关注 "理解 "在上下文中的预期含义,以及这如何影响培养理解能力的适当活动,并仔细研究现有研究文献中关于概念理解的看似统一的概念的主张。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
How mathematicians characterize and attempt to develop understanding of concepts and definitions in proof-based courses
Mathematics education research has long focused on students’ conceptual understanding, including highlighting conceptions viewed as problematic and looking for ways to develop more desirable conceptions. Nevertheless, limited research has examined how mathematicians characterize understanding of concepts and definitions or promote activities beneficial for students. Based on interviews with 13 mathematicians, we present thematic characterizations of what it means to understand a concept and definition, highlight activities mathematicians believe assist students’ learning, and examine their reasons for promoting these activities. Results include mathematically grounded descriptions of what it means to understand a concept but general descriptions of approaching and supporting learning. Implications include a need for attending to intended meanings for “understanding” in context and how this impacts appropriate activities for developing understanding, as well as a careful examination of the extant research literature’s claims about seemingly unified notions of conceptual understanding.
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来源期刊
Frontiers in Education
Frontiers in Education Social Sciences-Education
CiteScore
2.90
自引率
8.70%
发文量
887
审稿时长
14 weeks
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