Teachers' Inappropriate Conception of the Decimal Number Multiplication and a Trial of Teaching the Meaning of Multiplication to Teachers College Students

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  • 「小数のかけ算」に関する教師の不十分な意味理解と教員養成系学生への援助
  • ショウスウ ノ カケザン ニ カンスル キョウシ ノ フジュウブンナ イミ リカイ ト キョウイン ヨウセイケイ ガクセイ エノ エンジョ

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Abstract

Many teachers and researchers have reported that it is difficult for elementary school students to understand the meaning of the multiplication of decimal numbers. They explained that such difficulty might be caused by the students' notion that the meaning of multiplication was the cumulation of same number. We hypothesize that teachers' inappropriate understanding of multiplication concepts causes the students' difficulty. In study 1, we investigated how elementary school teachers conceptualize the meaning of multiplication of decimal numbers. Two problems were given to them. One was to write a story problem, where a correct answer would be obtained by calculating 3.2×4.6. The other was to explain the meaning of the multiplication 2.7×3.6 to a student who was perplexed by the nonsense notion of repeatedly adding 2.7 three point six times. Approximately seventy percent of teachers provided appropriate answers on the first problem, while only sixteen percent did on the second problem. In study 2, we tried to teach teachers college students the meaning of multiplication and obtained very good results. They were discussed from the standpoint of teaching principles adopted.

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