コンピュータを活用した数学の問題作り （Ⅷ） ―大学におけるグループ活動を通して―

抄録

　　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.  In study (Ⅶ), we investigated the problem posing process in detail through interviews to students.  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.  In addition to the above features, we employ the method to divide the problem posing into two stages.  That is, we provided situations in which students made problems after solving original problem by using computers at the first stage and made a mathematical inquiry about their problems by group activities at the second stage.  From the activities, we investigate the problem posing process in detail through interviews to students.  As in study (Ⅶ), 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 group activities, 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, the solver and the student who posed a problem commented on problems each other, and they did the developmental problem posing by group activities.