算数文章題場面における演算関係の統合的スキーマ : 二重三角図とその授業実践

An Integrated Schema of Operational Relationships between Quantities in Arithmetic Word Problems: Classroom Practice of Double Triangle Diagram

平嶋 宗

林田 雄樹

電子情報通信学会技術研究報告. ET, 教育工学

IEICE Technical Report. Educational technology

本稿では，算数文章題に対する統合的スキーマである二重三角図の授業利用について報告する．比例場面を扱う二重三角図は，二つの存在量に対して対となる二つの関係量，包含除，等分除，値が小さくなる掛け算，値が大きくなる割り算，を互いに関連・制約する必然のものとして可視化できる．この二重三角図を用いた授業を５年生の３月の授業で実施したところ（１クラス２３名，２時限），（１）児童の８９％が対となる関係量を含んだ二重三角図を問題文に対して正しく書けた，（２）児童の７９％が二重三角図によって可視化される６つの演算関係に対応する６つの式を立式できた，（３）関係量保存性課題のスコアが事前事後で有意に向上し，効果量は大であった，といった結果が得られた．

This paper reports on the use of double triangle diagrams in the classroom, which have been proposed as an integrated schema for arithmetic word problems. The double triangle diagram, which deals with proportional situations, can visualize two paired relational quantities, inclusive division, equal division, multiplication to reduce the value, and division to increase the value, as necessarily related and constrained to each other. When we conducted a class using this double triangle diagram in a 5th grade class in March (23 students, 2 lessons), (1) 89% of the students were able to correctly draw a double-triangle diagram including the paired relational quantities to the problem text, (2) 79% of the students were able to write 6 expressions including in the problem, and (3) significant improvement was observed in the pre- and post-tests using the problems of conservation of relational quantities, and the effect size was large.

算数文章題

二重三角スキーマ

比例場面

対となる関係量

小学５年生

Mathematic/Arithmetic Word Problem

Integrated Schema

Multiplication/Division

Proportional Relation

日本語

電子情報通信学会

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