Effects of Substantiation of the Results of Mental Operations on Understanding the Ratio of the Areas of Two Similar Figures
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- SHINDO TOSHIHIKO
- UNIVERSITY OF YAMANASHI
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- MAGARA KEIICHI
- WASEDA UNIVERSITY
Bibliographic Information
- Other Title
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- 面積比の理解に及ぼす操作結果の実体化の効果
- メンセキヒ ノ リカイ ニ オヨボス ソウサ ケッカ ノ ジッタイカ ノ コウカ
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Abstract
Prior research demonstrated that students, even at the university undergraduate level, thought that when the length of the sides of a rectangle was enlarged k times, the rectangle’s area was also enlarged k times. It was hypothesized that this “illusion of linearity” was the result of inappropriate mental operation of the formula for the area of a rectangle. The aim of Experiment 1 was to increase learners’ understanding of the following rule: “If length×k, then area×k2”. Participants (159 undergraduates) were divided into 3 groups. As a demonstration of incorrect linearity, materials were prepared to substantiate the participants’ incorrect mental operation. Group A was presented with 2 rectangular photos of a face, one of which was the original photograph, the other, the same photograph enlarged 3 times by enlarging only the width of the original, so that the enlarged version was an oblong version of the original. Group B was presented with 2 rectangles that were the same shape as the photographs used in Group A. Group C was presented no such materials. The performance of the students in Group A was best on the post-test. Experiments 2 (233 undergraduates) and 3 (109 undergraduates) demonstrated that the oblong was effective in changing the students’ understanding only when it gave them a sense of incongruity in contrast to actual objects.
Journal
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- The Japanese Journal of Educational Psychology
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The Japanese Journal of Educational Psychology 59 (3), 320-329, 2011
The Japanese Association of Educational Psychology
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Details 詳細情報について
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- CRID
- 1390282679760386048
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- NII Article ID
- 130002151060
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- NII Book ID
- AN00345837
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- ISSN
- 21863075
- 00215015
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- NDL BIB ID
- 023339567
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed