How Can We Help Junior High School Students to Use a Formula When They Solve Math Problems that Don't Contain Numerical Values

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  • 数字がなくても公式を使えるようにするにはどうすればよいか
  • 数字がなくても公式を使えるようにするにはどうすればよいか : 中学生への操作的思考の援助
  • スウジ ガ ナクテモ コウシキ オ ツカエル ヨウニ スル ニワ ドウ スレバ ヨイ カ : チュウガクセイ エ ノ ソウサテキ シコウ ノ エンジョ
  • －中学生への操作的試行の援助－

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Abstract

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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