Improuvement of teaching geometrical reasoning in junior hight school

理解几何推理的意义对于理解图形在几何证明中的作用是必要的，理解图形在几何证明中的作用也是理解几何推理的意义所必需的。我们选择从理解图形在几何证明中的作用，即Fischbein的图形概念开始，开始学习几何推理。我们的学习方案有两个案例，使用几何构造器(Iijima公司的计算机软件)，以及使用空间图形和构造题。作为我们教学实践结果的一个例子，学生能写出矩形是梯形的正确理由的比率在前测中为2%，在后测中为47%。北海道、德佑、爱知和大阪的388名三年级学生对同一问题的正确答对率为17%。因此，我们认为我们的教案是有效的。

Understanding the meaning of geometrical reasoning is neccesary to understand the role of figures in geometrical proof, and understanding the role of figures in geometrical proof is also neccesary to understand the meaning of geometrical reasoning. We choice to start to understand the role of figures in geometrical proof, namely Fischbein's figural concepts, in order to initiate to learning the geometrical reasoning.Our learning plan has two cases, using 'Geometric Constructor' (a computer soft maken by Iijima), and, using spatial figures and construct problems.We practice each teaching plan for junior high school 2nd students. As one example of results of our teaching practice, the rate of students, who can wright a correct reason why a rectangle is a trapezoid, is 2% in the pretest and is 47% in the posttest. The right answer rate of the same qestion by 3rd grade students, who were 388 in Hokkaido, Tokyou, Aichi and Osaka, was 17%. Therefore, we think our teaching plan is effective.