The longitudinal analyses of change processis in understanding fraction concepts

变化过程的纵向分析是为了理解分数概念

• 批准号: 62510061
• 负责人: YOSHIDA Hajime
• 金额: $ 0.9万
• 依托单位: Miyazaki 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: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62510061/
• 关键词: fraction concepts; incorrect strategies; cognitive task analysis; spefic domenin of know ledge; 知識の領域固有性; 全体としての1の概念; 概念の変化過程

This research found some intetresting results on understanding processes of fraction concepts.1. Changing processes of magnitude for the fraction concepts. A framework to advance our research was (1)per-test two or three months before begining the fraction unit, (2)individual interviews to children with some incorrect strategies, (3)three or four weeks teaching of the fraction in public elemenatary schools, and (4)pre-test immediately after finishing the unit. Children possessed correct informal knowledge on the fraction concepts before receiving formal instruction in their school. However, after learning the fraction concepts, children who understood the concepts correctly dropped from 92 % in the pre-test of the third grade to 76 % in the post-test. This wea very interesting results. Children interrupted their informal correct knowledge vy taking formal instruction.2. Cocept of 1 as a whole in fraction. Children had great difficulty for understanding the concept of one as a whole in fractin. Across the six tests, about 40 % of children showed always incorrect strategies on this concepts. However, we do not yet analyze relation between incorrect strategies on magnitude of the fraction and on concept as a whole.3. Drawing pictures. To make children draw the magnitude of the fractions reflected fairly well situation of knowledge for fraction concepts in children. Almost all children with Rule B drew the figrues whose magnitude per unit was always same. However, such figures seemed to be correct for the fraction problems with same denominators.

本研究在分数概念的理解过程中发现了一些有趣的结果。分数概念的大小变化过程。推进我们研究的一个框架是：(1)在开始分数单元前的两三个月进行每次测试，(2)对使用一些错误策略的儿童进行个别访谈，(3)在公立小学进行三到四周的分数教学，以及(4)在完成单元后立即进行预测试。儿童在学校接受正式教学之前，就已经掌握了正确的分数概念的非正式知识。然而，在学习分数概念后，正确理解概念的儿童从三年级前测的92%下降到后测的76%。这是一个非常有趣的结果。孩子们通过接受正式的指导而中断了他们非正式的正确知识。1作为分数的整体概念。在分数法中，孩子们很难理解一作为一个整体的概念。在六次测试中，大约40%的孩子在这些概念上总是表现出错误的策略。然而，我们还没有分析错误策略在分数大小和整体概念之间的关系。画画。使幼儿画出分数的大小，较好地反映了幼儿对分数概念的认识情况。几乎所有遵循规则B的孩子所画的图形，其单位大小总是相同的。然而，这些数字似乎对相同分母的分数问题是正确的。