Classification of Efficient Calculation Problems and the Effect of Instruction Using an Abstract Strategy

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  • 工夫速算問題の分類と抽象的方略を用いた教授の効果
  • クフウ ソクサン モンダイ ノ ブンルイ ト チュウショウテキ ホウリャク オ モチイタ キョウジュ ノ コウカ

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Abstract

There are calculation problems such as 1+2+3+97+98+99 which can be solved rapidly and easily by using certain techniques. We call these problems "efficient calculation problems" and it has been pointed out that many students do not always solve them efficiently. To address this problem among students, the current study developed a new teaching method. The first study sought to examine underlying subcategories of efficient calculation problems. Multidimensional scaling and cluster analysis to a similarity matrix obtained from expert judgments were conducted, and the results showed that 20 efficient calculation problems were classified into 8 categories. The second study examined the effect of intervention. 59 eighth graders and 52 fifth graders received an abstract strategy "think carefully about the whole expression" and were taught solution. The results indicated that the eighth graders solved similar problems efficiently after the intervention, while the fifth graders could not. The results also suggested that the effect of the intervention was greater among students with sufficient basic calculation skills.

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