权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Semiotic and cognitive research on social interaction in the process of mathematical generalization

数学概括过程中社会互动的符号学和认知研究

基本信息

批准号：
16530602
负责人：
YAMAGUCHI Takeshi
金额：
$ 2.3万
依托单位：
Fukuoka University of Education
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Regarding to the first research, we introduced "synectics" by Gordon, W. to clarify the substantial difference between extensional and intensional generalization from the angle of cognition although DOrfler distinguished them logically. The definition of those terms has the following predicates. The former is to make the familiar strange in addition to its logical sense of enlargement of the extent of a set. It gives us the new point for integration of various pieces of old knowledge by making the familiar strange as a consequence. On the other hand, the latter is to make the strange familiar in addition to its logical sense of elaboration of the properties of objects. We proposed "separation model" which has both extensional generalization and intensional generalization as the alternative of two cognitive processes just after "symbols as object" in Dorfler's generalization model.Regarding to the second research, we focused on difficulties of division with fractions. The cause of this difference could be explained as qualitative difference of generalization after "symbols as objects" in terms of separation model. We designed an alternative teaching of division with fractions for extensional generalization, which could induce the transition from arithmetic to mathematics. The teaching experiment based on it was practiced for the sixth graders in this research. It showed us not only the effectiveness of an alternative teaching but also the cognitive process in the separation model.The third research was to elaborate a theory of Wittmann's "Teaching Units (TU)" in terms of our separation model. We complemented TU diachronically by incorporating his theory into separation model. The fourth research was to consider current teaching way of "subtraction with negative numbers" critically in terms of our separation model to develop a teaching material for transition from arithmetic to algebra.

关于第一个研究，我们引入了Gordon，W。虽然多夫勒在逻辑上对外延概括和内涵概括进行了区分，但从认知的角度阐明了外延概括和内涵概括的本质区别。这些术语的定义有以下谓词。前者是使熟悉的事物陌生化，除了其逻辑意义上的扩大化外，还扩大了一个集合的范围。它为我们整合各种旧知识提供了新的切入点，从而使熟悉的东西变得陌生。另一方面，后者是使陌生人熟悉，除了其逻辑意义上的阐述对象的属性。在Dorfler的泛化模型中，我们提出了“分离模型”，即既有外延泛化，又有内涵泛化，作为继“符号作为对象”之后的两个认知过程的选择。造成这种差异的原因，可以从分离模式的角度解释为“符号作为对象”后泛化的质的差异。我们设计了一种可供选择的带分数除法的外延推广教学，它可以引导算术向数学的过渡。本研究在此基础上对六年级学生进行了教学实验。研究三是以我们的分离模式为基础，阐述了Wittmann的“教学单位”理论。我们通过将他的理论融入分离模型，对TU进行了历时性的补充。第四项研究则是以本研究所提出的分离模式，批判性地思考目前“负数减法”的教学方式，以发展算术转代数的教材。