高等学校数学科における生徒の主体的な学びを促す授業に関する研究 ― 数学Ａ「整数の性質」の授業における亜教授学的状況の検討 ―

抄録

　　 The purpose of this paper is to clarify conditions to realize the lesson for students’ active learning in the high school mathematics subject of ‘Properties of Integers’. From the viewpoint of the theory of didactical situations  (TDS), this study regards the lesson for students’ active learning as the lesson in which adidactical situations realize. 

　　 In this paper, the purpose was achieved through the following 3 steps.  First, some milieu was designed from the viewpoint of adidactical situation and fundamental situation in TDS, and the lesson was planned.  Then, a priori analysis on the planned lesson was performed based on TDS.  Secondly, the author myself practiced the lesson and performed a posteriori analysis of the lesson.  Thirdly, comparing the result of the a posteriori analysis with the one of the a priori analysis, it is considered what kind of differences were in the result of both and what made the differences.

　　 The result of the consideration showed that the following points can contribute to realize adidactical situation for the lesson on ‘Properties of Integers’:

・ Setting the situations where students cannot examine all the cases by division in order to reflect the  result and process by division;

・The new additional milieu promotes the emerge of mathematical knowledge.