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Development of teaching unit of proportional reasoning from the perspective of learning process of individual pupils in the mathematics classroom

从数学课堂小学生学习过程看比例推理教学单元的开发

基本信息

批准号：
12680178
负责人：
HINO Keiko
金额：
$ 1.66万
依托单位：
Nara 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：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12680178/
关键词：
Proportional reasoning Qualitative research Internalization of mathematical notations

项目摘要

The purpose of this study was to capture the quality and mechanism of change in pupils' proportional reasoning through classroom teaching in upper elementary grade level. The change was examined both in the long and short spans. During one school year, three written tests were conducted in three 5^<th>-grade classes of different elementary schools. Pupils' approaches for proportional problems became multiplication/division based ; their use of addition/subtraction became less and less. One of the classes where pupils developed more sensible and divergent strategies than the other two was examined further in micro level. Here, the focus was put on the interactions between the change and mathematical notations that were introduced and treated in class. Two research questions were set ; (i) What were the mathematical notations that were relevant to pupils' change in proportional reasoning? and (ii) In what ways did such mathematical notations emerge, and in what processes did they exert such relevance through classroom teaching? For this purpose, a framework of "internalization of mathematical notations" was used, which characterizes person's evolving use of notations as three phases : "use as a label," "forming criteria for use" and "purposeful use." It was adopted to analyze the cases of five focused pupils under the teaching of "Quantity Per Unit." Based on the results obtained by the study, implications were made for teaching, together with the development of teaching units of "Quantity Per Unit" and ''Proportion." Tasks for the future were also clarified.

本研究旨在探讨国小高年级学生比例推理能力的变化性质与机制。这种变化在长跨度和短跨度中都得到了检验。在一个学年中，在不同小学的三个五年级班进行了三次书面测试<th>。小学生解决比例问题的方法变得以乘除法为主，他们越来越少使用加减法。在微观层面上，进一步研究了其中一个班级，学生比其他两个班级发展了更明智和更发散的策略。在这里，重点放在变化和数学符号之间的相互作用，在课堂上介绍和治疗。两个研究问题：（一）什么是相关的数学符号，小学生的比例推理的变化？以及（ii）这些数学符号是以什么方式出现的，它们在课堂教学中发挥了什么作用？为此，使用了一个“数学符号内化”的框架，它将人们对符号的使用分为三个阶段：“作为标签使用”，“形成使用标准”和“有目的地使用”。本研究采用个案研究的方法，对五名重点学生在“量”字教学下的学习情况进行分析。根据研究结果，提出了对教学的启示，并提出了“每单位数量”和“比例”教学单位的发展。“还明确了今后的任务。