A Probability Curriculum Development for Formation of Interpretation of Probability

Abstract

　　The purpose of this study is to develop probability curriculum for formation of interpretation of probability. To accomplish a purpose, we set lower purpose (a) and (b).

　(a) To Indicate theoretically what process should be used to form a learner’s interpretation of probability.

　(b) To consider as case what kind of teaching materials can support its formation.

　　Firstly, lower purpose (a) was considered based on “Psychogenese et histoire des sciences” (Piaget & Garcia, 1996). As a reason for this is that historical development of interpretation of probability and formation process of interpretation of probability can be considered as mutually negotiable. Secondly, for lower purpose (b), we considered the teaching materials that could become problem situations that could not be solved by existing interpretation of probability based on studies on formation of probability conception. As a reason for this is that interpretation of probability are an aspect of the probability concept.

　　The results were as follows.

　・ We constructed formation process of interpretation of probability. It takes the following steps. The first is “Intuitive subjectivist interpretation of probability” which is formed in daily life before learning probability, the second is “Frequentist interpretation of probability”, the third is “Subjectivist interpretation of probability”, and the fourth is “Common understanding viewpoint between frequentist and subjectivist interpretation of probability”.

　　・ We have developed teaching materials that can be problem situations to which existing interpretation of probability cannot be applied as teaching materials that can support formation of interpretation of probability.

　　・ We discussed the relationship between formation of interpretation of probability and formation of mathematical aspect of probability, and developed probability curriculum for formation of interpretation of probability.