Theoretical and Corroborative Research on the Conceptual Change in Mathematics Education.

在这项研究中，我在调查的基础上调查了分数、面积和有问题的问题，以揭示学生对它们的理解情况，并通过实验课来克服每一门学科产生的困惑。对三、四年级学生关于分数表示量的理解的历时考察表明，他们在分数表示上的困惑是在完成三年级分数单位的学习后才发现的。此外，他们对RQF任务的反应会根据任务中问题的表征和图表的不同而变化。根据这些结果，我实施了实验课，被试是四年级学生。结果，第一节课处理分数在数线上的位置的班级对第二节课处理的RQF的理解几乎没有混乱。研究结果表明，数线模型能有效提高学生的RQF值。对四年级学生进行了面积与周长分离的实验课。前测和后测的结果表明，课程目标的完成程度还不够。然而，在每节课结束时进行的调查表明，学生在网格上绘制各种图形并在几何图形板上构建图形的数学活动促进了学生对课程中使用的任务的兴趣。对问题问题的初步探讨表明，试卷上描述的问题情境和指导会影响学生对问题问题的反应。这些结果表明，在概念的引言部分，如何设置问题情境以及学生在该情境中的行为在很大程度上影响了他们随后的学习。

In this research, I investigated fraction, area, and problematic problems based on the inquiry to reveal how students understood them and on experimental lessons to conquest confusion generated by each subject matter.1. The diachronic inquiry on the third and fourth graders' understanding about the representation of quantities by fractions (RQF) revealed that their confusion on RQF was observed just after finishing their learning of the unit of Fraction treated in the third grade. Moreover, their responses to the task of RQF changed according to the representation of problems and diagrams adopted in the task. Based on these results, I implemented experimental lessons of which subjects were the fourth graders. As a result, a class in which the location of fractions on the number line was treated in the first lesson showed little confusion on their understanding of RQF treated in the second lesson. It suggested the effectiveness of the number line model to enhance students' RQF.2. Experimental lessons on the separation of area from perimeter were implemented for the fourth graders. The results of pre- and posttest showed insufficient accomplishment of the aim of the lessons. However, inquiry administered at the end of each lesson indicated that students' mathematical activities to draw various figures on a grid and to construct them on a geoboard promoted students' interest in the tasks employed in the lessons.3. Preliminary inquiry on problematic problems suggested that problem situations and instruction described on a test sheet influenced students' responses to the problematic problems.These results suggest that, at the introductory part of a concept in particular, how to set a problem situation and how students act in the situation affect their subsequent learning to a considerable degree.