• Education of Primary School Mathematics
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• v.1 no.1
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• pp.73-83
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• 1997

옛날부터 계산을 잘하는 것이 수학적으로 우수하다고 생각해왔으며, 거의 1900년까지도 교육을 받았다는 것은 계산할 수 있다는 것을 의미하였다. 초등학교의 대부분의 시간은 덧셈, 뺄셈, 곱셈, 나눗셈을 배우는 데 투입되었다. 현재에도 초등학교의 교육과정은 기본 교육에 중점을 두어 3R's(reading, writing, arithmetic)을 강조하고 있으며, 많은 교사나 학부모들은 계산능력에 대해 지대한 관심을 가지고 있다. 1970년대의 '새 수학' 운동으로 계산력이 약화되었다는 비난이 쏟아지자 '기본에 충실하자(Back to basic)'는 운동으로 계산이 강화되기도 하였다.(중략)

• East Asian mathematical journal
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• v.31 no.4
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• pp.505-525
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• 2015

The purpose of this study is to analyze teaching method of addition and subtraction of whole number in Korea and New Zealand lower grade textbook and to get some suggestive points to develop mathematics curriculum and for a qualitative improvement of textbook. To do this, we will analyze focusing on teaching material, type and method of teaching, cases of real teaching and in the case of New Zealand, we will analyze portfolios together to see what kind of things do they deal with related to addition and subtraction. From these analyzing, the results are as follows: First, the guideline of accomplishment of group of year are stated in 2009 revised curriculum in Korea but it is rough. On the other hand, the level of accomplishment from kindergarten to high school are stated divided by eight kinds of thing in New Zealand curriculum. Second, there were common and different points in the aspect of teaching material. The common points are that both of our Korea and New Zealand are using materials related to real life intimately and the diifferent points are to use technology such as calculator and computer. They are more widely used in New Zealand than our Korea. Third, Korea had used routine method mainly but New Zealand had used method to develop creativity of learner such as to write problem corresponding to expression, posing problem corresponding to information, to complete table and find pattern and to write word problem to explain pattern and so on. Fourth, we could see special calculation strategies in the case of teaching addition and subtraction such as concept of double, compensation, various strategy based on counting of number, addition of the same number, magic square, near-double which are not finding in our mathematics textbook. Fifth, in the New Zealand textbook they had used teaching methods inducing curiosity of learner such as finding message and puzzle problem than solving given problem simply.

• Journal of Elementary Mathematics Education in Korea
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• v.4 no.1
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• pp.21-37
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• 2000

Although methods about teaching basic principles and skills of addition and subtraction is long traditional, view points of interpreting those algorithms and ways of introducing those calculating skills are various according to textbooks at each historical stage of elementary mathematics curriculum development in Korea. The 1st and 2nd stage shows didactic transpositions less systemic. In the 3rd and 4th stage, didactic devices, which were influenced by the new math, for help of understanding the principles of addition and subtraction muchly depends on mathematical and logical mechanism rather than psychological and intellectual structure of students who learn those algorithms. Relatively compromising and stable forms appear in the 5th and 6th stages. Didactic transpositions in the 7th stage focus on the formation of mathematical concepts by exploration activities rather than on the presentation of mathematical contents by text. Anyone who wishes to design an elementary mathematics textbooks based upon the constructive view should consider the suggestions derived from such transition.

• Journal of the Korean School Mathematics Society
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• v.17 no.3
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• pp.409-435
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• 2014

This study examines relations between the 5th graders' fraction operation skills and error types on constructed-response items. As results, first, the participants have lower fraction operation skills on 'multiplication of fraction' than 'addition and subtraction of fraction'. Second, the participants have different error types depend on their constructed-response items. Most of error types which group with high ability made was 'leap of solving process', both groups error type with medium ability as well as low ability is 'misunderstanding of questions'. Third, the operation skills on 'addition and subtraction of fraction' have an influence on their operation skills on 'multiplication of fraction', and error types of 'understanding of questions' and 'understanding of solving process' have the most effects on the influence.

• School Mathematics
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• v.11 no.4
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• pp.567-581
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• 2009

Many articles have reported that zero causes children's arithmetic errors. This article was designed to measure the effect of zero on children's arithmetic performances. For this, 222 of 3,4,5,6 graders in elementary school were tested with pencil and paper. The test were categorized into four parts: basic number fact, column subtraction, column multiplication, and column division. These data showed that the negative effect of zero on children's arithmetic was limited to several areas, concretely, multiplication facts with zero, column subtraction with numbers which have two successive zeros, column multiplication with numbers which have zero in a middle position, long division with zeros. But there was no evidence that students could self-control these negative effects of zero as grade went up. It implies that we should keep attention to children's arithmetic performance with zero in some special areas.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.1
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• pp.1-6
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• 2008

There are many possible representations in denoting both positive and negative numbers in the binary number system to be applicable to the complexity of the hardware implementation, arithmetic speed, appropriate application, etc. Among many possibilities, the signed-magnitude representation, which keeps one sign bit and magnitude bits separately, is intuitively appealing for humans, conceptually simple, and easy to negate by flipping the sign bit. However, in the signed-magnitude representation, the actual arithmetic operation to be performed may require magnitude comparison and depend on not only the operation but also the signs of the operands, which is a major disadvantage. In a simple conceptual approach, addition/subtraction of two signed-magnitude numbers, requires comparator circuits, selective pre-complement circuits, and the adder circuits. In this paper circuits to obtain the difference of two numbers are designed without adopting explicit comparator circuits. Then by using the difference circuits, a universal signed-magnitude adder/subtracter is designed for the most general operation on two signed numbers.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.531-546
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• 2017

This study explores the basis for determining priority among the four arithmetical operations in order to provide useful pedagogical content knowledge for teaching the order of operations. The study also discusses the perspective for viewing the order of operations. It presents the following five suggestions based on the results of the discussion. First, teachers should be made to realize that the same result can be obtained on calculation even when subtraction and division are performed first in mixed operations of addition and subtraction and mixed operations of multiplication and division. Second, teachers should understand why the rule of calculating sequentially from the left side of an equation has become customary. Third, teachers should be offered an explanation for the driver of the rule setting that multiplication takes precedence over addition in mixed operations of multiplication and addition. Fourth, the significance of the quantity within parenthesis must be emphasized to teachers. Fifth, teachers must gain an in-depth understanding about the order of operations by getting a description of all the customary and conceptual perspectives on the order of operations when describing the same in the teacher's guide.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.307-332
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• 2022

This action research was carried out to help students learn fractions computation by making and using semi-concrete fraction manipulatives that can be used continuously in math classes. For this purpose, the researcher and students made semi-concrete fraction manipulatives and learned how to use these through reviewing the previously learned fraction contents over 4 class sessions. Afterward, through the 14 classes (7 classes for learning to reduce fractions and to a common denominator, 7 classes for adding and subtracting fractions with different denominators) in which the principle inquiry learning model was applied, students actively engaged in learning activities with fraction manipulatives and explored the principles underneath the manipulations of fraction manipulatives. Students could represent various fractions using fraction manipulatives and solve fraction computation problems using them. The achievement evaluation after class found that the students could connect the semi-concrete fraction manipulatives with fraction representation and symbolic formulas. Moreover, the students showed interest and confidence in mathematics through the classes using fraction manipulatives.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.651-654
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• 2008

In finite field operations based on $GF(2^m)$, additions and subtractions are easily implemented. On the other hand, multiplications and divisions require mathematical elaboration of complex equations. There are two dominant way of approaching the solutions of finite filed operations, normal basis approach and polynomial basis approach, each of which has both benefits and weakness respectively. In this study, we adopted the mathematically feasible polynomial basis approach and suggest the optimization techniques of finite field operations based of mathematical principles.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2002.11a
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• pp.84-87
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• 2002

최근 정보보호의 중요성이 커짐에 따라 암호이론에 대한 관심이 증가되고 있다. 이 중 Galois 체 GF(2$^{m}$ )은 대부분의 암호시스템에서 사용되며, 특히 공개키 기반 암호시스템에서 주로 사용된다. 이들 암호시스템에서는 GF(2$^{m}$ )에서 정의된 연산, 즉 덧셈, 뺄셈, 곱셈 및 곱셈 역원 연산을 기반으로 구축되므로, 이들 연산을 고속으로 계산하는 것이 중요하다. 이들 연산 중에서 곱셈 역원이 가장 time-consuming하다. Fermat의 정리를 기반으로 하고, GF(2$^{m}$ )에서 정규기저를 사용해서 곱셈 역원을 고속으로 계산하기 위해서는 곱셈 횟수를 감소시키는 것이 가장 중요하며, 이와 관련된 방법들이 많이 제안되어 왔다. 이 중 Itoh와 Tsujii가 제안한 방법[2]은 곱셈 횟수를 O(log m)까지 감소시켰다. 본 논문에서는 Itoh와 Tsujii가 제안한 방법을 이용해서, m=2$^n$인 경우에 곱셈 역원을 고속으로 계산하는 방법을 제안한다. 본 논문의 방법은 필요한 곱셈 횟수가 Itoh와 Tsujii가 제안한 방법 보다 적으며, m-1의 분해가 기존의 방법보다 간단하다.