• School Mathematics
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• v.11 no.3
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• pp.463-477
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• 2009

Decimal Fraction with a significant meaning is being treated for long periods, from elementary school to high school. It is necessary to consider in a course of guidance about various aspects of decimal Fraction first of all in order that student understand well about the concert of it. If you overlook guidance of various means of decimal Fraction, Previously learned number system is limited understand of Decimal Fraction concept or meaning of Decimal Fraction limited to the one is difficult to calculate the Decimal Fraction, even can weaken understand of Real Number. Accordingly, in this study, we would like to separate meanings of the Decimal Fraction, focusing on the role and function of the Decimal Fraction in various situations used the Decimal Fraction. Based on this, we analyzed and criticized how to introduce the Decimal Fraction in elementary school textbooks according to the 7th curriculum.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.55-66
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• 2005

In our school mathmatics, the irrational numbers and the real numbers are defined and instructed on the basis of decimal fractions. In relation to this fact, we identified the essences of the real number and the irrational number defined by the decimal fractions through the historical analysis. It is revealed that the formation of real numbers means the numerical measurements of all magnitudes and the formation of irrational numbers means the numerical measurements of incommensurable magnitudes. Finally, we suggest instructional plan for the meaninful understanding of the real number concept.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.1-25
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• 2008

The purpose of this study was to identify pre-service teachers' Pedagogical Content Knowledge (PCK) about decimal calculation. A written questionnaire was developed dealing with decimal calculation. A total of 152 pre-service teachers from 3 universities were selected for this study; they had taken an elementary mathematics teaching method course and had no teaching experience. The results were as follows: First, with regard to the method of decimal calculation, most pre-service teachers were familiar with algorithms introduced in the textbook. But with regard to the meaning of decimal calculations, they had difficulties in understanding decimal multiplication or decimal division with decimal number. Second, pre-service teachers recognized reasons of errors as well as errors patterns that student might make. But this recognition was limited mainly to errors related to natural number calculation. Third, pre-service teachers frequently commented about decimals algorithms, picture models, the meanings of decimal calculations, and connections to natural number calculations. Many of them represented the meanings of decimal calculations through picture models as to help students' understanding, while they just mentioned algorithms or treated decimal calculation as natural number calculations with decimal point.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.445-458
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• 2012

Current textbooks may provide students and teachers with three improper notions related to the quotient and the remainder in division for decimal numbers as in the following. First, only the calculated results in (natural numbers)${\div}$(natural numbers) is the quotient. Second, when the quotient and the remainder are obtained in division for decimal numbers, the quotient is natural number and the remainder is unique. Third, only when the quotient cannot be divided exactly, the quotient can be rounded off. These can affect students and teachers on their notions of division for decimal numbers, so improvements are needed for to break it. For these improvements, the following measures are required. First, in the curriculum guidebook, the meaning of the quotient and the remainder in division for decimal numbers should be presented clearly, for preventing the possibility of the construction of such improper notions. Second, examples, problems, and the like should be presented in the textbooks enough to break such improper notions. Third, the didactical intention should be presented clearly with respect to the quotient and the remainder in division for decimal numbers in teacher's manual.