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

在这项研究中，我调查了基于探究的分数、区域和问题，以揭示学生是如何理解它们的，并通过实验课来克服每个主题产生的困惑。对三、四年级学生分数表示理解的历时性调查显示，他们在分数表示上的困惑是在刚学习完三年级的分数单位后才出现的。此外，他们对RQF任务的反应根据任务中采用的问题和图表的表示而变化。基于这些结果，我实施了以四年级学生为对象的实验课。因此，在第一节课中处理分数在数轴上的位置的班级中，他们对第二节课中处理的RQF的理解几乎没有混淆。结果表明，数轴模型对提高学生的rqf是有效的。对四年级学生实施了区域与周长分离的实验课。前测和后测的结果表明，课程的目的没有达到。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数字并在地理板上构建这些数字的数学活动提高了学生对课程任务的兴趣。对问题问题的初步调查表明，问题情境和试卷上描述的指导会影响学生对问题问题的反应。这些结果表明，特别是在概念的介绍部分，如何设置问题情境以及学生在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.