• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• School Mathematics
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• v.8 no.2
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• pp.139-160
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• 2006

It seems that North Korea has been trying to reorganize its educational system as well as its economic system on a large scale since July 1, 2002. There has been a decrease in quantity of math textbooks by about 30% decrease. Until the 1990's, geometry and algebra had been kept apart from each other in North Korea, but they are put together now. Moreover many changes have been made in both contents and methods of teaching. For example, an area model is used in North Korea to teach operation of fraction, which makes the learning period shorter. This idea will provide us with many implication when we need to ready for decreasing the quantities in the future. Moreover teaching methods of division algorithms need to be reconsidered since the visual algorithm of division could help save the thinking in problem solving.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.1-17
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• 2019

In this study, prospective teachers were involved in arranging the teaching sequence of multiplication and division of fractions and decimal numbers based on their experience and knowledge of school mathematics. As a result, these activities provided an opportunity to demonstrate the prospective teachers' perception. Prospective teachers were able to learn the knowledge they needed by identifying the differences between their perceptions and curriculum. In other words, prospective teachers were able to understand the mathematical relationships inherent in the teaching sequence of multiplication and division of fractions and decimal numbers and the importance and difficulty of identifying students' prior knowledge and the effects of productive failures as teaching methods.

• School Mathematics
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• v.11 no.4
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• pp.685-706
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• 2009

This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

• Journal of The Korean Association of Information Education
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• v.4 no.1
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• pp.32-39
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• 2000

The traditional programs developed by the existing CAI technique have the fixed curricular, which make it difficult to deliver various study materials that fit the learners of various levels. In addition, a lack of the flexibility prevents from helping to make their methodology in studying uniform open minded. In order to solve these problems, we have designed and implemented a learner interface that can exclude the limits in the learners active study in solving the fractional operation. In addition to the user interface, this study includes a diagnosis module that can intellectually extract the status of learners understanding, ostensible bugs, and the associated misconceptions through the interface. The experimentation based on the learner interface and the diagnosis module shows that this system correctly diagnoses the level of learners' understanding and the errors in learning, which greatly helps the individualized study.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.7 no.11
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• pp.3544-3555
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• 2000

매칭방법은 기하 및 입체 모델링에서 재단 곡면과 이들에 대한 부울 연산에 사용되는 기초적인 연산이다. 그러나 매칭연산은 부드러움을 정확하게 표현하는데 고 차수의 미분계수 제약조건으로 인하여 많은 계산량이 필요할 뿐만 아니라 곡면상의 여러 점을 동시에 선택하여 이동하였을 때, 곡면표현에 사용되는 복잡한 함수식으로 인하여 일반해를 구하기 어려운 단점을 가진다. 본 논문은 분수식에 의하여 RMC(Rotation-Minimizing Curve)을 정의하고 이를 이용하여 자유 형태 곡면간에 변형 매칭 방법을 제안한다. RMC는 매칭곡선과 곡면의 접선벡터, 회전벡터, 곡률의 변화율과 같은 기하학적 기법을 기반으로 한다. 제안한 방법은 입력으로 주어지는 곡면의 기하학적 복잡도와는 무관하게 매칭을 수행할 수 있으며 수행 성능은 계산된 매칭 곡선의 복잡도에 의해서만 좌우된다. 또한 곡선 표현에 사용된 값들을 정의된 매칭 곡선식에 그대로 적용할 수 있었으므로 최적화 응용 문제에 효율적으로 적용할 수 있다.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.483-498
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• 2010

The purpose of this paper is to investigate the dispositions of university students' understanding and reasoning about rational number concept. For this, we surveyed for the subject groups of prospective math teachers(33), engineering major students(35), American engineering and science major students(28). The questionnaire consists of four problems related to understanding of rational number concept and three problems related to rational number operation reasoning. We asked multi-answers for the front four problem and the order of favorite algorithms for the back three problems. As a result, we found that university students don't understand exactly the facets of rational number and prefer the mechanic approaches rather than conceptual one. Furthermore, they reasoned illogically in many situations related to fraction, ratio, proportion, rational number and don't recognize exactly the connection between them, and confuse about rational number concept.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.63-77
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• 2016

SENKs (Students who Emigrated from North Korea to South Korea) are exposed to the general problem of Su-Po-Ja(mathematics give-uppers) as well as their own difficulty in learning mathematics. In this study, we conducted the FGI (focus group interview) in order to examine the recognition on mathematics teaching and learning in South Korea with 6 SENKs and 3 teachers who teach the SENKs. As a result, it was found that SENKs' had difficulties in understanding math because of the differences in math terminology used in South and that in North Korea, the unfamiliar problem situation used in math lesson, and the shortage of time for solving math problem. And the teachers reported that they had difficulties in teaching great deal of basic math, SENKs' weak will to learn math, and SENKs' lack of understanding about problem situation because of the inexperience about culture and society in South Korea.