On learning fundamental concepts of group theory
On learning fundamental concepts of group theory
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关于学习群论的基本概念
DOI：
10.1007/bf01273732
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发表时间：
1994
影响因子：
3.2
通讯作者：
Rina Zazkis
中科院分区：
文献类型：
--
作者：
E. Dubinsky;J. Dautermann;U. Leron;Rina Zazkis
本文报道的研究探讨了学生对群论知识的性质，以及个人如何发展对这一领域某些主题的理解。作为一个长期的研究和发展项目的一部分，在学习和教学本科数学，这份报告是一系列的论文之一，抽象代数的组成部分，该项目。这里讨论的意见收集在为期六周的夏季研讨会，24名高中教师参加了抽象代数课程作为他们工作的一部分。通过比较书面样本，和学生访谈与我们自己的理论分析，我们试图描述这些人似乎是接近的概念，组，子群，陪集，常态，和商群的方式。我们在这里推断的一般学习模式说明了一个行动-过程-对象-图式框架，用于解决这些特定的群体理论问题。我们在这里只做一些相当普遍的意见，学习这些特定的主题，“理解”的复杂性，以及错误和误解的作用，根据行动过程图式框架。作为进一步探索的研究问题，我们希望这些观察能为我们和其他研究者的持续调查提供信息。最后，我们简要讨论了我们的考虑所产生的一些教学建议。然而，我们推迟，充分考虑教学策略及其对学习这些主题的影响，到将来的某个时候，更广泛的研究可以提供一个更坚实的基础，为设计的具体的课程。
The research reported in this paper explores the nature of student knowledge about group theory, and how an individual may develop an understanding of certain topics in this domain. As part of a long-term research and development project in learning and teaching undergraduate mathematics, this report is one of a series of papers on the abstract algebra component of that project.The observations discussed here were collected during a six-week summer workshop where 24 high school teachers took a course in Abstract Algebra as part of their work. By comparing written samples, and student interviews with our own theoretical analysis, we attempt to describe ways in which these individuals seemed to be approaching the concepts of group, subgroup, coset, normality, and quotient group. The general pattern of learning that we infer here illustrates an action-process-object-schema framework for addressing these specific group theory issues. We make here only some quite general observations about learning these specific topics, the complex nature of “understanding”, and the role of errors and misconceptions in light of an action-process-schema framework. Seen as research questions for further exploration, we expect these observations to inform our continuing investigations and those of other researchers.We end the paper with a brief discussion of some pedagogical suggestions arising out of our considerations. We defer, however, a full consideration of instructional strategies and their effects on learning these topics to some future time when more extensive research can provide a more solid foundation for the design of specific pedagogies.