• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.527-540
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• 1998

In the teacher's guide of mathematics textbook for the 1st grade of the middle school, the clear and logical reason why the multiplication of negative number to negative number makes positive number, and $a^{-m}$ with a>0 and m>0, is defined by ${\frac{1}{a^m}}$ is not given. When we define the multiplication or the power by successive addition or successive multiplication of the same number, respectively, we encounter this ambiguity, in the case that the number of successive operations is negative, In this paper, we name this number, negative counting number, and we make the following more logical and intuitive definition, which is "negatively many successive operations is defined by positively many successive inverse operations." According to this new definition, we define the multiplication by the successive addition or the successive subtraction of the same number, when the multiplier is positive or negative respectively, and the power by the successive multiplication or the power is positive or negative, respectively. In addition, using this new definition and following the E.R.S Instruction strategy which revised and complemented the Bruner's E.I.S Instruction strategy, we develope new teaching model available in the 1st grade class of middle school where the concept of integers, three operations of integers are introduced.ntroduced.

• 대한수학교육학회지:학교수학
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• 제1권1호
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• pp.19-37
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• 1999

In this study, we examined some matters related to the learning of variable concept in school mathematics on the basis of the theoretical foundation from the previous studies(e.g. Davis, 1975; Rosnick, 1981; IK chemann, 1981; Wagner, 1983.) and practices on variable concept teaching by evaluating the current state of that. Matters be discussed are as follows; the use of symbol for place holders in elementary mathematics, the dealing with sets those elements are literals and operations of such sets, the teaching of dummy variable, the construction of literal expressions that contains variables, the labeling indeterminates as a constant, the change in the exact meaning of variable according to the function concept, the teaching of a generalization by means of variables. After considering on these matters that are connected with the teaching-learning of variable concept, we suggested the alternative proposal to the current state of variable concept teaching.

• 한국초등수학교육학회지
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• 제14권2호
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• pp.355-376
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• 2010

본 연구는 초등학교 1학년 수학의 수와 연산 영역에서 학생들이 보인 주된 오류 유형을 찾아 분석하고, 오류에 따른 효과적인 지도방법을 알아보았다. 1학년 1개반 학생들에게 교과서수준의 20문항씩 2번 나눠서 실시하여 20%이상의 오류문항을 선별하여 해당학생과 개별 면담과 관찰을 통한 분석하였다. 오류를 많이 보인 내용은 수 영역에서 50개 이상의 수 세기에서 수를 잘못 세는 오류가 50%이상 발생하였고, 연산 영역에서 대부분의 뺄셈에서 발생하였다. 여기서 발생된 오류를 4가지 유형에 따라 분류한 결과, 부정확한 개념과 정의에 대한 오류가 가장 많았다. 이에 따라 초등학교 1학년 학생들은 수와 연산에 대한 기초적인 개념, 정의, 사실, 기능 등을 확실하게 정립할 수 있는 방안의 모색이 필요하였다. 또 오류의 교정방안으로 개별 면담과 구체물을 이용하여 다양한 놀이를 통하여 흥미를 유발하고 적극적인 참여를 유도할 때 오류교정에 효과가 있음을 알 수 있었다.

• 한국경영과학회지
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• 제16권1호
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• pp.113-119
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• 1991

The author is currently assistant professor of Management Science at Korea Advanced Institute of Science and Technology, following a few years as assistant professor of Industrial Engineering at Kyung Hee University, Korea. He received his doctorate from the department of Industrial Engineering and Operations Research, University of California, Berkeley. His research interests are time series and forecasting modelling, Bayesian forecasting and the related software development. He is now teaching time series analysis and econometrics at the graduate level.

• 대한수학교육학회지:학교수학
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• 제8권1호
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• pp.1-25
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• 2006

양수와 음수의 취급이 처음으로 시작되는 제 7-단계 교과서들을 살펴본 결과 양의 부호, 음의 부호가 붙은 수를 읽는 방법과 유리수에 대한 일부 교과서의 정의는 재고해야 하며, 반대의 수 곧 반수를 정의하여 활용하는 것과 양수와 음수의 도입은 대소 관계를 다루는 곳에서 그 정의를 하는 것이 바람직함을 알 수 있었다. 연산에서는 양의 부호와 음의 부호가 붙은 수에 대한 가시적인 표현을 충분히 익히게 하여 초등학교에서의 연산 도입을 구체적이고 가시적으로 처리한 것과 같이 양수, 음수의 연산에도 그 방법을 연계하여 활용 할 수 있도록 하는 것이 바람직하다고 생각되어 화살표(유향선분)를 사용하여 양수 음수를 가시적으로 도입한 후에 이들을 사용하여 초등학교에서의 계산 방법을 양수 음수까지 확장된 수에까지 그대로 적용한 학습 내용을 제시하였다. 그리고 제시한 학습 내용으로 지도를 하여본 결과 이와 같이 연계된 학습내용이 보다 바람직한 것임을 알 수 있었다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.122-122
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• 2000

Polishing work of a free-curved surface die demands simple and repetitive operations but requires a considerable amount of time for high precision. In out previous study, to reduce the polishing time and solve the problem of the shortage of skilled workers, the automatic polishing system was developed. However, in the polishing process of die, workers have to stay still in factory to monitor the polishing process for a long time in the poor environment. Therefore, this study proposes the remote operation and monitoring system of the automatic polishing robot. The developing system offer worker monitoring functions and teleoperating functions, as following: system state check, manual manipulation mode, automatic mode, manual teaching mode, automatic teaching mode, simulation by virtual manufacturing device. And automatic teaching system is developed to easily obtain a teaching data.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권4호
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• pp.541-559
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• 2003

This paper considers learning and teaching of mathematical analysis in teachers college. It concentrates on showing a way how learning and teaching of mathematical analysis should be considered for mathematical teachers training. It is composed of five chapters including Chapter I as an introduction and Chapter Vasa concluding remarks. Chapter II deals with goal and contents of global mathematical analysis. The main Chapter, named Chapter III, demonstrates exhibition of contents, way of operations, and contents of teaching and learning of mathematical real analysis. Chapter IV shows an example of learning and teaching of mathematical real analysis concerning to fixed points and approximate solutions.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권3호
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• pp.275-293
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• 2006

The purpose of this study was to analyze the connection between students' errors and prior knowledge as an attempt to design an efficient teaching method in decimal computation. A survey on decimal computations was conducted in two 6th grade elementary school classrooms. Error patterns on decimal computations were analyzed and clinical interviews were conducted with 8 students according to their error patterns. Main errors resulted from the insufficient understanding of prior knowledge such as place value, connection between decimals and fractions, meaning of operations, and computation principles of fractions. In order to help students overcome such obstacles, a teaching experiment was designed in a manner that strengthens a profound understanding of prior knowledge related to decimal computations, and connects such knowledge to actual decimal calculations. This study showed that well-designed lesson plans with base-ten blocks might decrease students' errors by helping them understand decimals and connect their prior knowledge to decimal operations.

• 대한수학교육학회지:수학교육학연구
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• 제18권1호
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• pp.51-62
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• 2008

7차 교육과정에서 복소수 단원은 복소수의 사칙연산만을 다루고 있다. 문자식 계산과 다를 바 없이 지도되는 실정이다. 본 논문은 복소수의 대수가 평면 기하학의 닮음변환과 맺고 있는 본질적인 관계를 수학적으로 분석하고, 이러한 본질적인 관계를 학교수학에 접목하기 위한 방법을 찾기 위해 역사적 분석을 하였다. 그 결과 Viete의 직각삼각형 연산을 바탕으로 기하학적 측면에서 복소수의 지도 가능성을 찾았다. 이러한 분석을 바탕으로, 학교수학에서 복소수의 기하학적 해석의 지도가능성을 고찰하였다.

• East Asian mathematical journal
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• 제30권4호
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• pp.509-526
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• 2014

The mathematics has moved toward the independence from unit. However, is this tendency also kept up in teaching and learning mathematics? This study starts from this question. We have illuminated this question in respects of a character of unit operation, an essential probability of unit operation and a didactical application of unit. As results, addition and subtraction are operations on identical objects and the result of operation does not also get out of operation's object. On the other hand, multiplication and division are operations on both identical objects and different objects. And the result of operation can generate new unit. We proposed a hypothesis which multiplication and division are transcendental operations from this analysis. The unit operation is not possible essentially. It seems only like unit operation is possible superficially by operational definition on unit. We could discuss on a didactical application of unit from above analysis. And we could deduct implications that the direction of developing mathematic does not necessarily match with the direction of teaching and learning mathematics.