Effects of Substantiation of the Results of Mental Operations on Understanding the Ratio of the Areas of Two Similar Figures

• SHINDO TOSHIHIKO

  UNIVERSITY OF YAMANASHI

• MAGARA KEIICHI

  WASEDA UNIVERSITY

Bibliographic Information

Other Title

• 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

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

• The Japanese Journal of Educational Psychology

  The Japanese Journal of Educational Psychology 59 (3), 320-329, 2011

  The Japanese Association of Educational Psychology

Keywords

• substantiating the results of mental operations
• illusion of linearity
• undergraduates

Details

• CRID: 1390282679760386048
• NII Article ID: 130002151060
• NII Book ID: AN00345837
• DOI: 10.5926/jjep.59.320
• ISSN: 21863075
• ISSN: 00215015
• NDL BIB ID: 023339567
• Web Site: http://id.ndl.go.jp/bib/023339567
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I023339567
• Web Site: https://www.jstage.jst.go.jp/article/jjep/59/3/59_3_320/_pdf
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed