Children’s Judgements of Expected Value in Grades Five Through Six of Elementary Schools

Abstract

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.