• Education of Primary School Mathematics
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• v.26 no.3
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• pp.125-140
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• 2023

In elementary school mathematics, the addition and subtraction of fractions are difficult for students to understand but very important concepts. This study aims to examine the teaching methods and visual aids utilized in the context of common denominator fraction addition and subtraction. The analysis focuses on evaluating the lesson flow and the utilization of visual representations in one national textbook and ten certified textbooks aligned with the current 2015 revised curriculum. The results show that each textbook is composed of chapter sequences and topics that reflect the curriculum faithfully, with each textbook considering its own order and content. Additionally, each textbook uses a different variety and number of visual representations, presumably intended to aid in learning the operations of fractions through the consistency or diversity of the visual representations. Identifying the characteristics of each textbook can lead to more effective instruction in fraction operations.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.241-262
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• 2010

This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.285-304
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• 2009

The operations of fractions are the main contents of number and operations in the elementary mathematics curriculum. They are also difficult for students to understand conceptually. Nevertheless, there has been little study on the addition and subtraction of fractions. Given this, this paper explored the connection between the national mathematics curriculum and its concomitant textbooks, the adequacy of when to teach, and the method of constructing each unit to teach addition and subtraction of fractions. This paper then analyzed elementary mathematics textbooks and workbooks by three parts aligned with the general instructional flow: 'introduction', 'activity', and, 'exercise'. First, it was analyzed with regard to the introduction part whether the word problems of textbooks might reflect on students' daily lives as intended, how different meanings of operations would be expected to be taught, and how the subsequent activities were connected with the original word problems. Second, the main analysis of activity part of the textbooks dealt with how to use concrete or iconic models to promote students' conceptual understanding of operations and how to formalize the calculation methods and principles with regard to addition and subtraction of fractions. Third, the analysis of the part of exercise in the textbooks and workbooks was conducted with regard to problem types and meanings of operations. It is expected that the issues and suggestions stemming from this analysis of current textbooks and workbooks are informative in developing new instructional materials aligned to the recently revised mathematics curriculum.

• Communications of Mathematical Education
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• v.36 no.2
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• pp.229-252
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• 2022

This study analyzed the introduction of addition and subtraction, including the composition and decomposition of numbers in the Korean, Singaporean, American, and Japanese elementary mathematics textbooks. The analytic foci of this study included visual models and their connections with the given problem contexts, the introduction of addition/subtraction or addition/subtraction sentences and their connections with the visual models, and additional activities for students to develop a relational understanding of the equal sign. The results of the analysis demonstrated diverse connections, mainly because the problem contexts, visual models, and the introduction of addition/subtraction or addition/subtraction sentences were implemented differently for each textbook. There were differences among the textbooks in what order of problem contexts were presented. Regarding the use of visual models, two textbooks tended to use one model consistently, whereas the other textbooks used various models depending on the problem contexts. There were subtle but significant differences in introducing addition/subtraction or addition/subtraction sentences. For a relational understanding of the equal sign, all textbooks included activities emphasizing that both sides of the equal sign are equal. Based on the results of this study, this paper closes with several implications related to the problem contexts to introduce addition/subtraction and addition/subtraction sentences as well as the use of visual models, which can serve as a basis for a new unit for the subsequent textbook.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.599-617
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• 2011

This study is aimed at finding some drawbacks of current elementary mathematics textbooks and to give suggestions for ongoing new textbooks according to 2009 revised curriculums, by comparing and analyzing Korean textbooks and chinese textbooks of People's Education Press. The areas are confined to number concepts, addition and subtraction for comparative analyzing. The results are followings: Korea textbooks have more verbal expressions, designated instructive activities for students to do, similar algorithm applied for enlarging mathematical concepts, bigger number concepts and number usage of operations, and monotonous number sense activities. Therefore Korean textbooks, compared to China's, is more weaker in areas such as encouraging student's interest, in challenging mathematics, and in forming fundamental mathematical concept.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.185-205
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• 2013

In this study, to begin with, it was discussed to gather vocabularies which are expected to be vocabularies related to four fundamental rules of arithmetic and classify them according to kinds and groups, to demarcate vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics which are associated with addition, subtraction, multiplication, and division directly. Next, the basic vocabularies related to four fundamental rules of arithmetic were discussed. At this time, regarding vocabularies related addition, subtraction, multiplication, and division as coming from the verb add, subtract, multiply, divide respectively, vocabularies that contains the stem of each verb were considered as the basic vocabularies related to four fundamental rules of arithmetics. Following it, vocabularies which assist the operation and indicate the result of the operation were included, then, vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics were demarcated and presented according to the following criteria. First, a newly coined verb or derivative using the noun form of a certain verb as a root should not be used. Second, such vocabularies of which examples do not exist or rarely exist in textbooks/workbooks should not be used, even though they are registered in mathematics glossary book published by ministry of education or Korean dictionary published by the national institute of Korean language. Third, vocabularies which are not replaceable and vocabularies which have some didactical reasons for using them should be used.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.16-18
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• 2002

고속 회로 합성에 있어서, Wallace 트리 스타일은 연산을 위한 가장 효율적인 수행 방식의 하나로 인식 되어졌다. 그러나, 이러한 방법은 빠른 곱셈기의 수행이나 여러가지 연산수행 에 있어, 입력 시그널을 고려하지 않은 일반적인 구조로 수행되어졌다. 본 논문은 연산기에 있어서 이러한 제한점을 극복하는 문제를 다룬다. 우리는 캐리-세이브 방법을 덧셈, 뺄셈, 곱셈 이 혼합되어 있는 일반적인 연산 회로에 적용한다. 그 결과 효율적인 회로를 생성하며, 시그널 들의 임의의 시그널 스위칭 변화에 대해 회로의 전력 소모를 최적화 한다. 우리는 이러한 최적화 방법을 여러 디지털 필터에 적용시켜 보았고 이는 기존의 비트 단위가 아닌 캐리-세이브 수행방법보다 상당한 양의 전력 소모의 향상을 보였다.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1998.12a
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• pp.405-420
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• 1998

본 논문에서는 타원곡선 암호시스템의 효율적인 소프트웨어 구현 방법을 제안하였다. 타원곡선과 유한체 F$_{p^{m}}$ 의 선택 방법을 제안하고, 선택한 타원곡선에서 생성자 G를 찾는 방법을 제시하였다. 타원곡선 위의 점에 대한 상수배 (scala multiplication)를 효율적으로 구현하기 위해서 덧셈/뺄셈 사슬을 사용한 윈도우 방식을 채택하여 타원곡선에서의 KCDSA(EC-KCDSA)를 구현하고 수행 성능과 수치 예를 보였다.

• The Journal of the Acoustical Society of Korea
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• v.5 no.3
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• pp.5-12
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• 1986

음성 신호 처리분야에서 고속이며 정확히 기본 주파수를 추출하는 방법은 중요하며, 이를 위한 많은 연구가 제안되어 왔다. 이러한 방법들은 보통 성도의 방해를 제거한 후에 기본 주파수를 검출하기 때문에 지금까지는 처리과정이 복잡하다. 우리는 그러한 과정을 간단히 처리할 수 ldt는 inverse rate type filtering 법을 제안하였다. 제안된 방법은 유한 길이의 정수 계산이고 덧셈과 뺄셈으로 처리될 수 있기 때문에 범용 마이크로 컴퓨터에 의해서도 실시간 처리를 할 수 있게 된다.

• Communications of Mathematical Education
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• v.11
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• pp.27-46
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• 2001

본 논문은 과거 신라시대에 사용하여 경주 안압지에서 출토되었던 6, 8면체 주사위를 오늘날 우리 교육과정에서 활용할 수 있는 방안을 모색하였다. 첫째, 6, 8 면체는 6개의 사각면과 8개의 삼각면으로 구성되어있는데 이를 6진법과 8진법에 이용하여 그 개념과 자리수를 익히고 덧셈, 뺄셈에 활용되는 방법을 연구하였고, 둘째, 14면체의 면의 모양과 면의 개수가 갖는 성질을 이용하여 문자와 식의 개념을 도입하고 이 개념을 확장시켜 다항식의 연산을 적용하여 보았으며, 셋째, 동 ${\cdot}$ 서양의 철학에서 살펴본 수의 의미로서 주사위가 지닌 의미를 재해석해보았다.