# 小学校児童による有理数の乗法における乗数効果の分析An Analysis of the Multiplier Effect in the Multiplication of Rational Numbers

## 抄録

The purpose of this study is to identify the multiplier effect in elementary school students from 4th to 6th grades who had already learned multiplication, and to investigate how to overcome it. For this purpose, we set the two viewpoints of i) the consciousness about the size relation of multiplier, multiplier, and product, and ii) the relation with results of ×0 and ×1, and a questionnaire investigation for students is carried out in order to inquire the feature and tendency of their understanding. According to the questionnaire for 638 students in four elementary schools, it checked that multiplier effect was especially seen in the 4th and 5th grade students. Moreover, in order to explore the cause, the consciousness of students who show the multiplier effect was followed up by using the selection problem and case method. These results showed that (1) the students who show multiplier effect especially tends to take notice of the size relation between multiplier and multiplier. (2) leanings of ×0 and ×1 could not prevent the belief "becoming large whenever it multiply", and these suggested that the consistent consideration of supports in teaching of integer, rational numbers, proportion and ratio was required.

The purpose of this study is to identify the multiplier effect in elementary school students from 4th to 6th grades who had already learned multiplication, and to investigate how to overcome it. For this purpose, we set the two viewpoints of i) the consciousness about the size relation of multiplier, multiplier, and product, and ii) the relation with results of ×0 and ×1, and a questionnaire investigation for students is carried out in order to inquire the feature and tendency of their understanding. According to the questionnaire for 638 students in four elementary schools, it checked that multiplier effect was especially seen in the 4th and 5th grade students. Moreover, in order to explore the cause, the consciousness of students who show the multiplier effect was followed up by using the selection problem and case method. These results showed that (1) the students who show multiplier effect especially tends to take notice of the size relation between multiplier and multiplier. (2) leanings of ×0 and ×1 could not prevent the belief "becoming large whenever it multiply", and these suggested that the consistent consideration of supports in teaching of integer, rational numbers, proportion and ratio was required.

## 収録刊行物

• 鳴門教育大学研究紀要

鳴門教育大学研究紀要 22, 206-215, 2007

鳴門教育大学

## 各種コード

• NII論文ID(NAID)
110006184927
• NII書誌ID(NCID)
AA12124651
• 本文言語コード
JPN
• 資料種別
Departmental Bulletin Paper
• 雑誌種別
大学紀要
• ISSN
18807194
• NDL 記事登録ID
025034710
• NDL 請求記号
YH247-458
• データ提供元
NDL  NII-ELS  IR

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