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

研究目的与研究问题本研究的目的是以设计研究开发课程。特别是我们专注于从二年级到四年级的比例推理。我们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.在数学课堂中进行和开展设计研究结果与方法我们制定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，第二次是六年级的设计研究，第三次是六年级的设计研究，第四次是六年级的设计研究，第五次是六年级的设计研究，第六次是六年级的设计研究，第六次是六年级的设计研究，第七次是六年级的设计研究，第七次是六年级的设计研究，第八次是六年级的设计研究，第九次是六年级的设计研究，第九次是六年级的设计研究，第九次是六年级的设计研究，第八次是六年级的设计研究，第九次是六年级的设计研究，第九次是六年级的设计研究。我们开发了一系列的活动，以帮助学生学习比例推理。活动序列包含比例、线性和平方以及相似性的概念。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。我们开发了测量活动的序列，以促进朴素比例推理的发展。重点研究了朴素比例推理的学习过程。第三个设计研究则着重于学生学习整数比例推理的过程，以及建构组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.