比例的推論におけるユニット化の進展を目指した算数科授業づくり ―小学校第３学年「形づくり」の学習を通して―

抄録

　　In this study, using the results of a pre-test that included mathematics problems that required the use of proportional reasoning, we designed and implemented a lesson on “Composing the Shapes“ in the third grade of elementary school, aiming at the development of proportional reasoning (especially the development of unitizing). It was based on Lamon’s (1994) framework for the development of unitizing (Table 1). Then, we examined the development of children’s unitizing in the lesson by means of a post-test consisting of questions related to the content of the lesson.

　　As a result, it was inferred that children with many correct answers in the pre-test were able to develop a viewpoint related to “Relating” process through class practice. On the other hand, for the children who did not have many correct answers in the pre-test, it was inferred that some of the children had effective results from the class practice, while others did not. As an example of children who did not see the effectiveness of the lesson, we found that they were not conscious of the unitizing in their post-class reflections. Furthermore, it was inferred that even the children who tried to solve the problem using only the “strategy g” in the pr-test were encouraged to view the uniting and unitizing of units as a result of the lesson.

　　However, there were some children who were able to sympathize with the value of unitization by being exposed to the ideas of other children who had developed their own ideas about unitizing in the class. Of course, these results were found in the children who were the subjects of this paper, and we do not claim that they can be immediately generalized. In the future, we would like to further improve the lesson design and develop classes that promote the development of children’s unitizing.