• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.285-298
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• 2008

According to the 7th curriculum, irrational numbers should be introduced using infinite decimals in 9th grade. To do so, the relation between rational numbers and decimals should be explained in 8th grade. Preceding studies remarked that middle school students could understand the relation between rational numbers and decimals through the division appropriately. From the point of view with the arithmetic handling activity, I analyzed that the integers and terminating decimals was explained as decimals with repeating 0s or 9s. And, I reviewed the equivalent relations between irrational numbers and non-repeating decimals, rational numbers and repeating decimals. Furthermore, I suggested an alternative method of introducing irrational numbers.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.1-17
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• 2004

According to the 7-th curriculum, irrational number should be introduced using repeating decimals in 8-th grade mathematics. To do so, the relation between rational numbers and repeating decimals such that a number is rational number if and only if it can be represented by a repeating decimal, should be examined closely Since this relation lacks clarity in some text books, irrational numbers have only slight relation with repeating decimals in those books. Furthermore, some text books introduce irrational numbers showing that $\sqrt{2}$ is not rational number, which is out of 7-th curriculum. On the other hand, if we use numeral 0 as a repetend, many results related to repeating decimals can be represented concisely. In particular, the treatments of order relation with repeating decimals in 8-th grade text books must be reconsidered.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.237-246
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• 2007

According to 7-th curriculum, irrational number should be introduced using non-repeating infinite decimals. A rational number is defined by a number determined by the ratio of some integer p to some non-zero integer q in 7-th grade. In 8-th grade, A number is rational number if and only if it can be expressed as finite decimal or repeating decimal. A irrational number is defined by non-repeating infinite decimal in 9-th grade. There are misconceptions about a non-repeating infinite decimal. Although 1.4532954$\cdots$ is neither a rational number nor a irrational number, many high school students determine 1.4532954$\cdots$ is a irrational number and 0.101001001$\cdots$ is a rational number. The cause of misconceptions is the definition of a irrational number defined by non-repeating infinite decimals. It is a cause of misconception about a irrational number that a irrational number is defined by a non-repeating infinite decimals and the method of using symbol dots in infinite decimal is not defined in text books.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.375-396
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• 2022

In this paper, to provide an idea for the 2022 revised mathematics curriculum by restructuring the content of the 2015 mathematics curriculum, the content elements of recurring decimals of textbooks, which showed differences in the curriculum of Korea and Japan, were analyzed. As a result of this study, in Korea, before the introduction of the concept of irrational numbers, repeating decimals were defined in the second year of middle school, and the relationship between repeating decimals and rational numbers was dealt with. In Japan, after studying irrational numbers in the third year of middle school, the terminology of repeating decimals is briefly dealt with. Then, when learning the concept of limit in the high school <Mathematics III> subject, the relationship between rational numbers and repeating decimals is dealt with. Based on the results of the study, in relation to the optimization of the amount of learning in the 2022 curriculum revision, implications for the introduction period of the circular decimal number, alternatives to the level of its content, and the teaching and learning methods were proposed.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.1-10
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• 2012

In Chinese mathematics, there have been two numeral systems, namely one in spoken language for recording and the other by counting rods for computations. They concerned with problems dealing with practical applications, numbers in them are concrete numbers except in the process of basic operations. Thus they could hardly develop a pure theory of numbers. In Song dynasty, 0 and TianYuanShu were introduced, where the coefficients were denoted by counting rods. We show that in this process, counting rods took over the role of the numeral system in spoken language and hence counting rod numeral system plays the role of that for abstract numbers together with the tool for calculations. Decimal fractions were also understood as denominate numbers but using the notions by counting rods, decimals were also admitted as abstract numbers. Noting that abacus replaced counting rods and TianYuanShu were lost in Ming dynasty, abstract numbers disappeared in Chinese mathematics. Investigating JianJie YiMing SuanFa(簡捷易明算法) written by Shen ShiGui(沈士桂) around 1704, we conclude that Shen noticed repeating decimals and their operations, and also used various rounding methods.