繰り下がりのある減法の思考の考察(1)

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  • クリサガリ ノ アル ゲンポウ ノ シコウ ノ コウサツ 1
  • The Investigation of Thinking concerning Subtraction with Regrouping (1)

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The purpose of this study is as follows : (1) the analyzing of difference between the main two rules in subtraction with regrouping ; 1. regrouping minuend rule : (Genka rule)12－8＝(10－8)＋2 2. regrouping subtrahend rule : (Gengen rule)12－3＝12－2－1 (2) the investigation of the relation of the follwing three elements ; 1. subtraction skill 2. subtraction rules 3. scholastic ability First, we described the theory of subtraction with regrouping from the viewpoints of mathematics, psychology, and teaching method. According to this theory, we investigated the variation of the relation with age. Subjects were three elementary school-, four junior high school-, four high school-, one university-students, 694 in all. This investigation made clear the following facts ; (1) They used six subtraction rules : regrouping minuend, regrouping subtrahend, additive subtraction, subtraction with intuition, abacus, and using multiple. In most cases, they used the regrouping minuend rule. (2) After they have learned the regrouping minuend rule, they learn the regrouping subtrahend rule and others. Lastly in high school, they can use any of subtraction rules intuitively. (3) The subtraction skill makes progress as age increases. (4) The child who has high scholastic ability has high subtraction skill, but not vice versa. (5) There are some relations between the type of subtraction with regrouping and subtraction rules. Lastly we suggested the desirable sequence of learning the subtraction with regrouping.

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