Previous studies have proposed many teaching methods to rectify learners’ misconceptions, wherein the type of examples used and the order of presenting examples and scientific concepts are important. However, for deeper understanding, it is also important to encourage learners to re-explain an instructed concept. This study demonstrates effects of learners’ re-explaining on conceptual change. A total of 106 university students were instructed on an air pressure rule. Although air exerts pressure, many people have the misconception that a vacuum draws substances into it. After instruction, two conditions were compared: (a) students’ re-explaining the air pressure rule (N=52) and (b) students’ copying the important points summarized by the teacher (N=54). The result revealed that the students who re-explained the air pressure rule were able to apply it to solve a new problem. Therefore, learners’ re-explaining an instructed concept is effective for conceptual change.

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In a prior study (Magara, 2009), it was demonstrated that many fifth and sixth graders could not understand that the area of triangle A was twice as large as triangle B when the bases of the 2 triangles were equal, and triangle A was twice the height of triangle B. This fact implies that they couldn’t operate the variable in the formula when a problem didn’t contain numerical value. In this study, we presented seventh and eighth graders (N=67 and N=31, respectively) not only with geometric math problems but also algebraic ones that don’t contain numerical values. Only half of them could solve these problems by operating the variables. Next, we tried to teach eighth graders how to use a formula by operating the variables in the formula. In this attempt, we contrived to show the process of operating the variables intuitively. As a result, most of the participants became able to operate variables successfully.

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A questionnaire composed of 10 paired adjectives ranked on a 7 point-scale was given at a Japanese university to confirm the ‘emotional aspect’ of familiarity and measure images of 20 unit titles of a textbook. After hearing three passages twice each, respondents first answered 6 or 16 TF questions (2, 5, 5 min), then answered a 7 point-scale questionnaire about their prior knowledge of the three topics. In particular a factor of emotional aspect found in the factor analysis named ‘closeness’ was ranked as a sub concept of familiarity. The highest title, the lowest one, and the third one were adopted as ‘the most familiar-’, ‘the least familiar-’ and ‘for-training title’. The results showed statistically siginificant superiority of the most familiar title over the least familiar one. A significant main effect of title familiarity on the scores of the subjects’ first TOEIC Half test score level (then academic achievement), no interaction between title familiarity and the subjects’ first TOEIC Half test score level, and no correlation between TF score for the most familiar title and prior knowledge.

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The variation judgment problem of sample proportion is a task that requires us to compare the size of one sample with that of another sample. This problem can be solved by applying the law of large numbers. Although two sample sizes were different, the misjudgment that two variables were the same was often made. The tendency not to consider sample size and apply the law of large numbers was called “Insensitivity to sample size”. The author hypothesized that the factor of the misjudgment lied in the fact that the learners could not operate the law of large numbers to apply the variation judgment problem. In this research, university students carried out the operational simulation to change the law of large numbers to its reverse proposition. In the result, many subjects changed to proper judgments. In addition, the respondents cited the law of large numbers greatly increased. It was suggested that the operational simulation facilitated learners to verify the variation judgment of sample proportion

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