Curriculum Development of Mathematical Proof to Cultivate Democratic Dispositions in Junior High Schcool Mathematics

研究的目的是开发新的数学证明课程，培养学生的民主气质，并验证教学与学习的有效性。主要研究结果如下：●建立理论框架，开发培养民主倾向的数学证明新课程通过连接数学教育中理解定义的层次（0级：图形属性，1级：数字定义，2级：定义的绝对属性，3级：定义的相对属性）与理解社会规范作为民主倾向的层次(0级：前规范，1级：规范，2级：规范的绝对属性（第三层次：规范的相对属性）可以建立数学证明新课程开发的理论框架。●在已确立的框架下开发课程并验证其有效性。在已确立的框架下，可以开发连接数学教育单元“平面几何”与德育单元“社会规范”的新课程。对公办初中八年级学生实施了该课程，并对其有效性和局限性进行了分析。

The aims of research are to develop new curriculum of mathematical proof to cultivate democratic dispositions, and to verify the validity of teaching and learning along with the curriculum. Main results of research are followings.● Establishing theoretical framework to develop new curriculum of mathematical proof which cultivates democratic dispositionsThrough connecting the levels of understanding definition in mathematics education (Level 0: Figural properties, Level 1: definition of figures, Level 2: absolute attributes of definitions, Level 3: relative attributes of definitions) with the levels of understanding social norms as democratic dispositions (Level 0: pre-norms, Level I: norms, Level II: absolute attributes of norms, Level III: Relative attributes of norms) theoretical framework to develop new curriculum of mathematical proof could be established.● Developing curriculum with the established framework and verifying the validity of it Along with the established framework new curriculum connecting the unit "plane geometry" in mathematics education with the unit "social norms" in moral education could be developed. For 8th graders of public junior high school the curriculum was put into practice, and the effectiveness and limitation could be identified。