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An analytic study of children's problem solving process with Tower of Hanoi

Abstract

The purpose of this study is to analyze the metacognitive process of elementary school students in their ability to carry out the Tower of Hanoi experiment. Hundred twenty subjects were selected from 2nd, 4th, and 6th grades of an elementary school in Seoul. Five classes from each grade were chosen. Eight students, 4 boys and 4 girls, from each class were selected by their teachers for their average achievement in school. All 120 students were observed but only 114 cases were analyzed. Five tasks with the tower of Hanoi were provided for the experiment. The children were given a wooden board with three poles and three different-sized discs. The disc size increased from top to bottom. The children were asked to move the discs one at a time with the restriction that a smaller disc had to be on top of a larger one. Their task was to move the disc in the same order on another pole as it was on the first pole. In order to assess the metacognitive abilities, observations were made on the success rate of the task, the duration of each trial, the number of disc movements, the duration of pre-planning, self-monitoring, and representation. Performances of the children were video taped and analyzed by a check list of 9 items. The result indicated that the second graders were significantly inferior to their older counterparts in all catagories. The fourth and the sixth graders did not differ significantly in all catagories except in success rate and representation ability. The only unexpected result was the second graders taking longer time to plan before starting the tasks. In all cases, the general trend seemed to be improvement over first three trials which required simple repetition of the 1st trial. But less success in all categories for the last two trials which reacquired representation and application abilities. For those children with lower levels of metacognition, it is important to give them enough time to understand the underlying principles by active repetition. Only then can we help them develop the ability to apply these principles to different situations.

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