• Education of Primary School Mathematics
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• v.25 no.3
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• pp.251-278
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• 2022

The purpose of this study is to obtain implications for mathematical education by analyzing how the multiplication and division of decimal numbers are presented in the elementary mathematics textbooks in Korea, Japan, Singapore, and Finland. Compared to the fact that students often have misconceptions about multiplication and division of decimal numbers, there have been not many comparative studies in recent elementary mathematics textbooks. For this study, we selected elementary mathematics textbooks those are widely used in Japan, Singapore, and Finland along with Korean elementary mathematics textbooks. We chose the textbooks because the students in the selected countries have scored high in international achievement studies such as TIMSS and PISA. The analysis was examined in terms of elementary mathematics curriculum related to multiplication and division of decimal numbers, introduction and content, real-life situations, use of visual models, and formalization methods of algorithms. As a result of the study, the mathematics curricula related to multiplication and division of decimal numbers includes estimation in Korea and Finland, while Japan and Singapore emphasize real-life connections more, and Finland completes the operations in secondary schools. The introduction and content are intensively provided in a short period of time or distributed in various grades and semesters. The real-life situations are presented in a simple sentence format in all countries, and the use of visual models or formalization of algorithms is linked to the operations of natural numbers in unit conversions. Suggestions were made for textbook development and teacher training programs.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.41-52
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• 2009

Dutch mathematician Simon Stevin published De Thiende(The Tenth) in 1583. In that book Stevin suggested new numerical notation which could express all numbers. That new notation was decimal fraction system. In this article I will argue that Stevin invented new decimal fraction system with two main purposes. The explicit purpose was to invent a new system which could be used easily by practical mathematicians. The implicit purpose which cannot be found in De Thiende alone but in his other writings was to break the Aristotelian tradition which separated geometry and arithmetic which dealt continuous magnitude and discrete numbers respectively.

• Journal of the Korean BIBLIA Society for library and Information Science
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• v.19 no.2
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• pp.129-146
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• 2008

Notes in library classification systems are inevitable tools for creating and building of classification numbers. The purposes of this study are to make better notes in Korean Decimal Classification(KDC) by analyzing and comparing notes in other library classification system and to assign the most appropriate classification numbers based upon the better notes. In order to achieve these purposes, analyzing notes in Dewey Decimal Classification(DDC) and KDC was carried. And the comparison of notes used in 000 Computer science, information, general works in DDC and KDC was done. Based upon these analysis, additional notes and their various forms were suggested.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.6 s.312
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• pp.10-16
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• 2006

This paper proposed a carry lookahead (CLA) circuitry design. It was based on dynamic circuit aiming at delay reduction in an addition of BCD coded decimal numbers. The performance of these decimal adders is analyzed demonstrating their speed improvement. Timing simulation on the proposed decimal addition circuit employing $0.18{\mu}m$ CMOS technology yielded the worst-case delay of 0.83 ns at 16-digit. The proposed scheme showed a speed improvement compared to several schemes for decimal addition.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.5
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• pp.241-249
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• 2003

Carry lookahead(CLA) circuitry of decimal adders is proposed aiming at delay reduction. The truncation error in calculation of monetary interests may accumulate yielding a substantial amount of errors. Binary Coded Decimal(BCD) additions. for example, eliminate the truncation error in a fractional representation of decimal numbers. The proposed BCD carry lookahead scheme is aiming at the speed improvements without any truncation errors in the addition of decimal fractions. The delay estimation of the BCD CLA is demonstrated with improved performance in addition. Further reduction in delay can be achieved introducing non-weighted number system such as the excess-3 code.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.5
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• pp.6-11
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• 1975

반복형 그래이 부호 중 14진 및 16진 부호용 디지트 절차(digit sequence 또는 DS)의 여러가지 특성에 관하여 논하였으며 그것들을 통일적으로 기적할 수 있는 PDS는 각각 31종 및 11종이 있다는 것을 명백히 하였다. 그리고 이 PDS들에 회전변환과 순렬변환을 실시하여 얻을 수 있는 DS의 총수와 각종 특수 DS의 성질에 관하여도 논하였으며 대칭형 DS를 이용한 14진 및 16진 GC Counter를 설계하여 그것들의 동작을 실험에 의하여 확인하였다. Investigations on some characteristics of Tetra-Decimal and Hexa-Decimal recycling Gray co de (GC)-digit sequence(DS) are carried out, and, 31 and 11 kinds of prime digit sequence(PDS) are proposed respectively. From these PDS, by means of rotational conversion and permutational conversion, the numbers of all DS are obtained, and also the characteristics of some special DS are studied. Tetra Decimal and Hexa-decimal GC counters are designed using symmetrical DS, and, their operations are experimentally verified.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.11
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• pp.491-494
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• 2006

In the adder design, reduction of the delay of the carry propagation or ripple is the most important consideration. Previously, it was introduced that, if a redundant number system is adopted, the carry propagation is completely eliminated, with which addition can be done in a constant time, without regarding to the count of the digits of numbers involved in addition. In this paper, a RBCD(Redundant Binary Coded Decimal) is adopted to code 0 to 11, and an efficient and economic carry-free BCD adder is designed.

• The Mathematical Education
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• v.56 no.2
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• pp.131-145
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• 2017

The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an 'Object'. For this reason, this research explored how mathematics textbooks affected to students' understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using 'non repeating decimal', 'numbers cannot be represented as a quotient', 'numbers with the radical sign', 'number line' representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.159-172
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• 2016

This study examines the approach of introduction of the real numbers through the infinite decimal, which is suggested by Lee Ji-Hyun(2014; 2015) in the aspect of the overcoming the double discontinuity, and analyses Li(2011), which is the mathematical background of the foregoing Lee's. Also, this study compares these construction methods given by Lee and Li with the traditional method using the nested intervals. As a result of analysis, this study shows that Lee Ji-Hyun(2014; 2015) and Li(2011) face the risk of the circulation logic in making the infinite decimal corresponding each point on the geometrical line, and need the steps not using the 'limit to a real number' in order to compensate the mathematical and educational defect. Accordingly, this study raises the opinion that the traditional method of defining the infinite decimal as a sequence by using the geometrical nested intervals axiom would be a appropriate supplementation.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.475-496
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• 2018

Although the multiplication of decimal fractions is expected to be easy for students to understand because of the similarity to natural numbers multiplication in computing methods, students show many errors in the multiplication of decimal fractions. This is a result of the instruction focused more on skill mastery than conceptual understanding. This study is a basic study for effectively developing a unit of multiplication of decimal fractions. For this purpose, we analyzed the curriculums' performance standards, significance in teaching-learning and evaluation, contents and methods for teaching multiplication of decimal fractions from the 7th curriculum to the revised curriculum of 2015 and the textbooks' activities and lessons. Further, we analyzed preceding studies and introductory books to suggest effective directions for developing teaching unit. As a result of the analysis, three implications were obtained: First, a meaningful instruction for estimation is needed. Second, it is necessary to present a visual model suitable for understanding the meaning of decimal multiplication. Third, the process of formalizing an algorithms for multiplying decimal fractions needs to be diversified.