Abstract
The purpose of this study is to collect the fundamental data on the children's probability concept which provide information for teachers and other developers of curriculum. In this paper, the author adopted a roulette as a continuous event and investigated the Common Cognitive Path (CCP) in the sixth grade children's probability judgments. As a result, the following CCP were found through the analysis of the reaction to the problem which compare likelihood of coming up black on the roulette boards divided into white sectors and black sectors. (1) The ratio of the area of the black sectors to the white sectors is different → The ratio of the area of the black sectors to the white sectors is the same (2) The size of the roulette boards is the same → The size of the roulette boards is different (3) The roulette boards are divided into a black sector and a white sector → The roulette boards are divided into two or more black sectors and white sectors. Then the author proposed the methods and techniques of instruction based on the CCP, and also constructed the rubric to evaluate grounds for children's probability judgments. As a result of instruction based on the CCP, the ratio of children who judge likelihood objectively based on the idea of the ratio of the area of the black sectors to the white sectors increased. This shows the achievement of criteria on the rubric assessment. This study shows the necessity and the possibility of the curriculum development based on the realities of the probability concept of children in the elementary education stage, and it also gives the suggestions for the curriculum development that connects with the curriculum of probability in secondary education in Japan.
