高等学校数学科における例を用いる活動に焦点を当てた授業構成に関する研究 ―授業構成モデルの構築とその実証的検討―

抄録

　　 The purpose of this research is to propose the methodology to design and conduct a mathematics lesson through students’ activities with examples. In this paper, I made the lesson design model to enhance and use their activities with examples and then, conducted a series of experiment lessons based on it about a logarithm function in high school mathematics to analyze empirically.

　　 In principle, the model consists of three stages of students’ activities - operation, reflection, and application -  and a concrete teaching way to change them effectively.  Students form their own typical example at each stage  and change the stage by making use of it.  The teaching way with the model is necessary for a teacher to have the students’ activity stage increase.

　　 I designed a series of lessons based on the model and conducted it.  And then, I analyzed it qualitatively what typical examples students had and how students’ activities changed.  As a result, I argued that students had their own typical examples and changed their activities by using them.  Students had their own typical examples that the inequality is the example of inequality including exponent, because students calculated directly inequality 2^x > (6.37 × 10⁸)² in the class of first time. In the class of the eighth time, students solved the same problem using common logarithm and they had their own typical examples that the problem or inequality is the example that they solve the problem using common logarithm.  In the class of the ninth time, students changed the activities that they utilize a typical example of the eighth time as for it and consider the structure of other problems.

　　 I suggest that when students change the activities, they change the formation of their own typical examples, too.  Therefore, the result implies that students change the examples while being activities by learning of mathematics lessons and I could demonstrate the effectiveness of the model.