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

目的和研究问题我们的研究目的是用设计研究来开发课程。我们特别关注二年级到四年级的比例推理。我们处理了以下三个研究问题。探讨数学课堂中比例推理的学习过程。制定二年级至四年级比例推理课程指南。在数学课堂中开展设计研究。结果与方法我们制定了二年级至四年级的比例推理课程指导方针。在指导方针中，我们强调了四个方面：复合单元的构建、基本比例推理、学生的代表性和数学表达式。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。第一个是六年级的设计研究。我们开发了一系列的活动来帮助学生学习比例推理。活动的顺序包含了比例、线性和方形以及相似性的概念。重点是了解六年级学生的比例概念。第二个是二年级的设计研究。我们开发了测量活动的顺序，以促进幼稚比例推理的发展。重点是朴素比例推理的学习过程。第三个设计研究的重点是学生在整数中比例推理的学习过程，以及构建复合单元的活动序列的发展。

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.