コンピュータを活用した数学の問題作り(VI) : 問題の作成過程の分析を通して

抄録

The purpose of a series of our studies is to discuss more effective method of mathematical problem posing by using computer. We have reported in the previous studies such mathematical activities by university students who were the prospective teachers. In study (I), we practiced the problem posing by using computer after solving original problem, and through study (II) to study (V) we examined various ways for the effective problem posing. The features of our methods are to give students enough time to create problems, and to provide situations in which students make conjectures on results and get the numerical calculation by using computer. In this paper, we report the practice of problem posing by using computer after solving original problem which has some good characteristic to guide the developmental problem posing. In addition to the above features, we requested students to make the good-quality problem. We require the students to describe how they contrived their own problems from the original problem or other sources and how they devised the problem with mathematical inquiry by using computer, and we analyze such procedures using the posed problems by them. Results of analysis indicate that such activities enable students to extend mathematical inquiry. As in the previous studies, the practice shows some tendency that students who tackled making problem by using computer get some deep understanding for the mathematical properties related to the problems. Students solved problems to each other, and the solver and the student who posed a problem commented on problems each other. As a result, there was communication between students. We observed more positive learning attitude of students than the usual classes. It is asserted that the opportunity in a class to discuss problems posed by using computer is very important in such activity, in particular for the prospective teachers.