Curriculum Development in Elementary Mathematics Education in terms of Design Research.

目的和研究问题我们研究的目的是用设计研究来开发课程。我们特别关注从二年级到四年级的比例推理。本研究探讨了以下三个研究问题：1.调查数学课堂中比例推理的学习过程；2.制定二年级至四年级比例推理课程指南；3.开展数学课堂设计研究。结果与方法编制了二年级至四年级比例推理课程指南。在课程开发过程中，我们在小学进行了三次设计研究，分析了学生的学习过程和师生互动。第一次是六年级的设计研究。我们制定了活动顺序，帮助学生学习比例推理。活动序列包含比例、线性和平方、相似性等概念。重点是了解六年级学生的比例概念。二是二年级的设计研究。我们开发了测量的活动序列，以促进天真比例推理的发展。重点介绍了朴素比例推理的学习过程。第三个设计研究关注学生对整数比例推理的学习过程，以及构建复合单元的活动顺序的发展。

Purpose and research questionsOur purpose of research is to develop curriculum with design research. Particularly we focus on proportional reasoning from the second grade to fourth grade. We approached the following three research questions.1.To investigate learning process of proportional reasoning in the mathematics classroom2.To develop the guideline of curriculum for proportional reasoning from the second grade to fourth grade3.To conduct and develop design-research in the mathematics classroomResults & MethodsWe developed the guideline of curriculum for proportional reasoning from the second grade to the forth grade. In the guideline, we emphasize four aspects, construction of composite units, basic proportional reasoning, representation of students, and mathematical expressions.In the curriculum developing process, we conducted three design-research in the elementary school and analysed students' learing process and interaction between teachers and students.The first one is design-research in the sixth grade. We developed the sequence of activities to contribute students learning of proportional reasoning. The sequence of activity contains the concept of proportion, linear and square, and similarity. The focus is to understand students' concepts of proportion in the sixth grade. The second one is design-research in the second grade. We developed the sequence of activities for measuring to contribute the development of naive proportional reasoning. The focus is learning process of naive proportional reasoning. The third design research focuses on students' learning process of proportional reasoning in integer and on development of sequence of activities to construct composite unit.