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Classroom Model for Resolving Misconceptions of Children in School Mathematics Learning

化解儿童学校数学学习误区的课堂模式

基本信息

批准号：
06680228
负责人：
KAMADA Tsugio
金额：
$ 1.28万
依托单位：
Akita University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

Although mathematical constructs of children often bear inconvenient conceptions or misconceptions that affect negatively their conceptual and procedual understanding in mathematics learning, effective teaching models for resolving their misconceptions have not been addressed. The object of the study is,(1) to reveal misconceptions of children in test problems of school mathematics,(2) to identify some of the underlying factors of misconceptions and make up classroom model of mathematics for resolving misconceptions.We developed test problems to reveal misconceptions of students of sixth, seventh, and eighth grade children and examined responses to the problems. Analyzing test results and protocols, we classified misconceptions into some categories of conceptual and procedural knowledge in mathematics : (1) compartmentalization, (2) oversimplification, (3) self-restriction, and so on.These misconceptions exist in children's inner psychological schemes, but are inconsistent with logical system of mathematics. Identifying factors of misconceptions obtained in the research, we make up a classroom model of teaching mathematics for resolving misconceptions in mathematics.It is intended to bring children with misconceptions to the realizations that their ideas are inconvenient and inadequate, and in need of modification. For this intention, two tasks named Critical Task and Assimilation Task were developed. The former consisted of both items with misconceptions and correct responses, and the latter with new scheme which might be formed through critical task for checking its availability. The use of multiple analogies and multiple mental representations with computer graphic seems effective teaching strategies for resolving misconceptions as well as the tasks. Classroom model developed in the study is effective in building connections between conceptual and procedual knowledge in school mathematics.

尽管儿童的数学概念经常带有不方便的概念或错误概念，对他们在数学学习中的概念和程序理解产生负面影响，但解决他们的错误概念的有效教学模式还没有得到解决。本研究的目的是：(1)揭示儿童在学校数学试题中的错误概念；(2)找出产生错误概念的一些潜在因素，并构建解决错误概念的数学课堂模型。我们开发了反映六、七、八年级学生错误概念的试题，并考察了问题的反应。通过对测验结果和测验方案的分析，我们将数学中的概念错误知识分为几类：(1)划分，(2)过于简单化，(3)自我限制等。这些错误概念存在于儿童的内在心理图式中，但与数学逻辑系统不一致。通过识别研究中获得的错误概念的因素，我们构建了一个数学课堂教学模式，以解决数学概念中的错误，旨在使有错误概念的儿童认识到他们的概念不方便、不充分，需要修改。为了达到这一目的，我们开发了两个任务，分别称为关键任务和同化任务。前者包括有误解和正确回答的项目，后者有可能通过关键任务形成的新方案来检查其可用性。运用计算机图形进行多种类比和多种心理表征，似乎是解决错误概念和任务的有效教学策略。本研究开发的课堂模型能有效地在学校数学的概念性知识和程序性知识之间建立联系。