Project/Area Number  10680261 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
教科教育

Research Institution  Shinshu University 
Principal Investigator 
AMAIWA Shizuko Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (60060688)

Project Period (FY) 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  Calculation / Conceptual understanding / Instruction method / Checkinganswer method / 計算の工夫 / 計算過程 / 計算エラー 
Research Abstract 
The purpose of this research was not only to clarify the relation of third to fifthgraders' conceptual knowledge among four rules of arithmetical calculation (addition, subtraction, multiplication and division) but also to examine the effect of instruction which made children think about the meaning of four calculations. The following 5 points emerged from the research. 1. Meaningful correlation was observed among the understanding of checkinganswer methods of subtraction, multiplication and division. 2. Significant correlation was found between the solution level of "invention of calculation" task and checkinganswer method of calculations. Unfamiliar "invention of calculation" task required the children to solve multiplication by using addition and to solve division by using subtraction. 3. As the result of ANOVA, we observed some improvement in the response to "where did the borrowed number go?" with subtraction, and "invention of multiplication" according to the children's age. 4. Understanding of the meaning of subtraction such as "how many numbers did you borrow from upper rank number?", "where did the borrowed number go?", and "what number was the gone number?" was deeply related with "checkinganswer method" and "invention of calculation". It was shown that clear understanding of the meaning of subtraction lie at the base of conceptual understanding of multiplication and division afterwards. 5. The instruction that made children think about the meaning of calculations brought good results in the test given soon after the investigation. But the test given in a year later showed the effect of instruction came to decline. It suggested that repeated experience to consider the meaning of calculation in school education is necessary for acquisition of precise conceptual understanding of calculations.
