The study focused on probability education in elementary schools and used Siegler’s rule-assessment approach to elucidate learners’ expected value judgments. The experiment analyzed the relationship between ease of encoding two variables, namely, probability (P) and random variable (V), from the following perspectives. The first pertains to grade differences, that is, compared to 5th graders, 6th graders found it easier to encode two variables with one type of problem. The second refers to differences in quantity. The second aspect is related to the difference in the amount that defined the probability. It was easier for 5th graders to encode the two variables P and V with discrete variable tasks than with the continuous variable tasks. The third perspective is related to the difference in the number of trials. The study demonstrated that in both grades 5 and 6, two variables were easier to encode in 10-trial problems than in one-trial problems. Finally, the fourth perspective examined the qualitative aspect of expected value judgment, and it was shown that there is difficulty in shifting from qualitative reasoning to quantitative reasoning. These results suggest that it is effective to focus on frequency as a teaching strategy for probability and expected value in the upper grades of elementary school.

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The purpose of this study is to examine causal attributions of success and failure in actual academic performance, with a special focus on strategy attribution. Furthermore, this study will explore how students attribute their academic success or failure and then regulate their learning strategies for future learning. One hundred fifty-four Japanese high school students (97 males, 54 females, and 2 unknown) from the same school participated in the study. Open-ended questions were used to obtain students’ causal attributions for their results on periodic examinations about contemporary society or geography, and the strategies that they develop as they prepare for future examinations. The results were as follows. First, participants were most likely to attribute their examination results to their learning strategies. Second, participants were more likely to attribute their success to study strategies and their failure to effort and examination strategies. Finally, future strategies that were based on causal attribution for failure were more likely to be “Indirect Strategies” that were aimed at managing the students’ environment.

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The purpose of this study was to examine the effectiveness of a lesson plan based on two principles, the transition from intuitive judgment of salt concentration to quantitative judgment based on a proportion, and were abstracted from concrete definitions to general ones. The effectiveness of the lesson plan was evaluated based on the post-evaluation tasks, the follow-up tasks, and the learners' observations during the lessons. Analysis of 25 fifth graders showed that on the post-evaluation tasks, the rate of correct responses exceeded 80%. However, in the follow-up tasks conducted four months after the end of the class, the formulas were scarcely applied, and when solving the problem using proportions, many learners were confused between the ratio and the comparison amount. Analysis of the lesson process showed that the “size per unit amount” in the lesson was not sufficiently distinguished from the ratio, which might have caused confusion.

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