Development of Materials for Mathematical Activities in Cooperation between University and High school , and Teacher Education

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Recently, the importance of mathematical-activities has been increasing. We started to develop the materials for mathematical-activities in cooperations between an universities and a high-school, and we studied on mathematical-activities in high school mathematics from both side of Mathematical educations and Mathematics.As the contents of mathematical-activities, the application-oriented mathematics, in which the functional value is emphasized, tends to be taken up. However, we propose the "structure-oriented mathematical-activity" that can induce the learner's proactive and dynamic considerations, and in which, the learner can value the contents and the considerations for themselves, not for their functional values.In this study, we propose the model of such mathematical-activities, which is also a miniature of the researching activities of real mathematicians. Also we develop examples of materials for such activities and verify its effects and meanings in practices.