• 한국수학사학회지
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• 제28권5호
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• pp.207-231
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• 2015

We discuss several issues relating to the meaning of the terms and phrases in the first half of Chapter One fang tian 方田章 of ${\ll}$Jiuzhang suanshu九章算術${\gg}$. I understood those issues more clearly in the course of the translation of ${\ll}$Kujang sulhae 九章術解${\gg}$. Those are '今有' in the beginning of each problem, '積' and '冪' in the method of square field 方田術, '齊' in the method of reduction to a common denominator 齊同術, '經' and '有分者通之重有分者同而通之' in the method of dividing fraction 經分術, '實如法而一' in the calculation using the rods, '兩邪' in the method of trapezium field with a perpendicular side 邪田術. We may find out the value of ${\ll}$Kujang sulhae 九章術解${\gg}$ through our discussion.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권3호
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• pp.329-355
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• 2014

The purpose of this study is to understand the difference of cognitive structure depending on the level of the 6th graders' problem-solving abilities about the division of fraction and to propose a method for improving the 6th graders' understanding about the division of fraction through the word association test. The following is the findings from this study. 1)The lower level students' is, the lower the step that the chunk appeared in cognitive structure is. 2)The basic level students' association frequency between any two concepts was less than the excellent level students and the ordinary level students' it. 3)The basic level students' connection number between concepts was far less than the excellent level students and the ordinary level students' it. 4)The connection between natural number and unit fractions, subtraction of fraction and division of fraction, division of fraction and reduction to common denominator, and division of fraction and common multiple that expected in this study did not appear in the three groups.

• East Asian mathematical journal
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• 제40권2호
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• pp.183-207
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• 2024

This study is a case study that considered fractional senses and fraction operation abilities for 107 gifted students in elementary school classes. In order to find out the fractional sense, in the first question comparing the sizes of fractions 2/3 and 4/5, the students showed a variety of strategies, but the utilization rate of strategies excluding reduction to a common denominator did not exceed 50%. The second question can be solved by using the first question. It is a problem of finding two fractions by selecting four from six numbers 1, 3, 4, 5, 6, and 7 to create two fractions of which sum does not exceed 1. The percentage of correct answers to this question was about 27% (29 out of 107). Only 5 out of 29 students found answers using the first question, and the rest of the students sought answers through trial and error in various calculations. It shows that the item arrangement method from a deductive perspective has no significant effect on elementary school students. The percentage of correct answers was about 27% in the questions to find out the fraction operation ability-the question of drawing a 4/3 bar using a given 3/8-sized bar and 30.7% (23 out of 75) of the students who had wrong answers showed insufficient splitting operation. In addition, it has been shown that the operation of partitioning and iterating to form numerical senses and fractional concepts related to the fractions of the students has no significant impact.

• 한국초등수학교육학회지
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• 제7권1호
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• pp.45-64
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• 2003

1차부터 7차까지의 초등학교 수학 교과서에 나타난 약수와 배수의 지도 방법을 교수학적 변환론의 관점에서 비교-분석하였다. 1, 2차 교과서에서는 약수와 배수를 별도의 단원으로 구성하지 않고, 분수의 덧셈과 뺄셈, 곱셈을 주요 내용으로 하는 단원에서 분수의 통분과 약분 지도 내용 속에 포함시켜 약수와 배수를 지도하고 있다. 3, 4차 교과서에서는 새 수학 운동의 영향을 받아 약수와 배수가 분수의 내용과 독립되어 하나의 단원으로 설정되었고, 수 영역에 집합의 개념을 도입하여 수체제를 확립하면서 집합의 내용과 함께 다루어졌다. 5, 6, 7차 교과서에서는 약수와 배수가 분수 내용뿐만 아니라 집합의 내용과도 분리되어 지도되기 시작하였고, 특히, 7차 교과서에서는 학습자의 활동 자체를 통한 이해가 매우 강조되고 있다. 약수와 배수에 대한 지도 방법은 교과서 개편을 거듭하는 동안 수학적 체계를 갖추 기 위해 학습 요소의 정돈이 이루어졌고, 교수학적 변환 역시 교과서가 개편됨에 따라 점차 체계적인 형태를 갖추게 되었다.