| APOS理论视角下无穷概念认知分析 |
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| 引用本文： | 曹荣荣.APOS理论视角下无穷概念认知分析[J].数学教育学报,2010(1). |
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| 作者姓名： | 曹荣荣 |
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| 作者单位： | 华东师范大学数学系;青岛大学数学科学学院; |
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| 摘 要： | 无穷概念一直是学生学习的一个困难.APOS理论是一种建构主义的数学学习理论,包含操作、过程、对象和图式4个阶段.内化和凝聚是APOS理论的两个重要的心理机制.教师对无理数的认识要从历史视角下关注数的发展,从发生教学法角度上进行无理数教学设计,让学生从概念发展的过程阶段转化到对象阶段.
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| 关 键 词： | 实无穷和潜无穷 高等数学思维 APOS理论 无理数 |
APOS-based Cognitive Analysis on the Concept of Infinity |
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| CAO Rong-rong.APOS-based Cognitive Analysis on the Concept of Infinity[J].Journal of Mathematics Education,2010(1). |
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| Authors: | CAO Rong-rong |
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| Institution: | CAO Rong-rong1,2 (1. Mathematics Department,East China Normal University,Shanghai 200241,China,2. College of Math Science,Qingdao University,Sh,ong Qingdao 266071,China) |
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| Abstract: | The issues involving the infinity had been a source of student difficulty. This paper applied APOS theory to propose an analysis about how undergraduate students think about the concept of infinity, which would help not only students to overcome the cognitive conflict and construct the infinity schema, but teachers develop pedagogical strategies based on these analyses. Finally we gave some suggests about the teaching strategies of irrational numbers in middle school. |
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| Keywords: | actual and potential infinity advanced mathematical thinking APOS theory irrational numbers |
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