The purpose of a series of our studies is to discuss effective methods of mathematical problem posing by using computer. We have reported in the previous studies such mathematical activities by university students who are prospective teachers. In study (I), we studied the first practice of the problem posing by using computer after solving original problem, and through study (Ⅱ) to study (Ⅴ) we examined various ways of the effective problem posing.
In study (Ⅵ), we pursued the study on the problem posing process by students, and requested students to make good-quality problems. 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 study the practice of problem posing by using computer after solving original problem which has some good characteristic to guide the developmental problem posing, and investigate the problem posing process in detail through interviews to students. As in study (Ⅵ), 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 and interviews from the posed problems by them. The results 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.
