Students' Understanding Of Expected-Value

This paper investigated high school students' understanding of the concept of expected-value. Mainly, Grade 12 students, who had learned the concept, their comprehension of the concept and their consciousness of using the concept in solving practical problems, were studied. Further, the cognitive development of students' understanding of the concept was also described through the observation how the students from Grades 8,10 and 12 made their decisions in games.Two questionnaires were given to 961 high school students, and some of them were interviewed. Finally, the following conclusions were obtained:1. Grade 12 students' understanding the concept of expected-value was comparatively poor. They had difficulties and errors in the process of explaining meaning, using formula, and integrating all possible values. Their main misconceptions were: (1) to take the expected-value as the value they expect to most; (2) to take the expected-value as the value which is most likely to happen; (3) to take the expected-value as the average of all the possible values.2. Students revealed their intuitions of the conception of expected-value in games, although most of them had no formal experience in learning the concept. It seemed that some of the students tended to consider both factors, i.e. probabilities and values. Some of the students made comparative decision in their own ways. The main ways they used were: (1) to make decision only by one of the two factors, which they paid more attention to; (2) to make decision by both of the two factors, by comparing the differences; (3) to make decision by both of the two factors, by comparing the proportions.3. Grade 12 students performed better in making judgments in games. It seemed that teaching could improve their performance. However, the students' consciousness of using expected-value in solving practical problems were weak.In the end, some practical suggestions were proposed to curriculum developers and school teachers based on the findings of this study. This paper appeals teachers should pay enough attention on student's misconceptions, and help them in overcoming, so that to improve their comprehension.