• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.375-389
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• 2017

The purpose of this study is to analyze the difference and inter-connectivity between the definition of continuity in school mathematics and the definition of academic mathematics in four perspectives. These difference and inter-connectivity have not analyzed in previous papers. According to this study, the definition of 'continuity and discontinuity at one point' in school mathematics depends on the limit processing but in academic mathematics it depends on the topology of the domain. The target function of the continuous function in school mathematics is a function whose domain is limited to an interval or a union of intervals, but the target function of the continuous function in academic mathematics is all functions. Based on these results, the following two opinions are given in relation to the concept of continuity in school mathematics. First, since the notion of local continuity in school mathematics is based on limit processing, the contents of 2009-revised textbooks that deal with discontinuity at special point not belonging to the domain is appropriate. Here the discontinuity appears as types of infinite discontinuity, removable discontinuity, and step discontinuity. Second, the definition of a general continuous function is proposed to "if there is no discontinuity point in the domain of a function y = f(x), we call the function f a continuous function." This definition allows the discontinuity at special point in non-domain, but is consistent with the definition in academic mathematics.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.307-307
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• 2021

개념적 강우-유출모형에서 토양수분과 관련된 물리적 거동은 간략화 된 형태로 강우 및 온도자료를 활용하여 중간변량(state variable)으로 간접적으로 고려되고 있다. 특히 강우-유출모형에 초기함수 조건은 선행함수조건을 고려하여 수문지질학적 평가를 통하여 결정되어야 하나, 일반적으로 가정되거나 모형에서 간략화 된 분석과정을 통해 추정되고 있다. 본 연구에서는 토양의 Water Balance 모형 기반의 개념적 토양수분 추정모형을 활용하였다. 토양수분의 시간적 변동성을 평가하는데 있어서 연속적으로 측정된 In-situ 토양수분 자료를 이용하여 모형의 적합성을 평가하였다. Green-Ampt 방법과 중력식 침투방법과 온도를 활용한 증발산 추정기법을 연계한 토양함수 평가 모형을 개발하였다. In-situ 토양수분 자료와 유역의 강수량 및 온도자료를 이용한 관련 매개변수를 Bayesian 기법을 통해 추정하였으며 매개변수의 민감도를 평가하여 제시하였다. 최종적으로 제안된 모형의 활용측면에서 강우-유출모형의 초기함수 조건으로써의 역할을 평가하였다. 구체적으로 첨두유량 및 유출고와 초기함수조건과의 관계를 제시하고 강우-유출모형에서 활용방안을 제시하고자 한다.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.196-202
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• 1997

[6]에서 Zhang과 Zheng은 부울함수의 암호학적인 전역상관계수의 특성을 계산하기 위해서 GAC(Global Avalanche Characteristic)이라는 새로운 개념을 제시하였다. 그들은 GAC의 값들에 대한 측적을 위해서 2개의 단위를 제시했고 2개의 단위의 상한과 하한에 대해서 계산했다. 그러나 그들은 균등함수의 GAC의 하한은 향후의 연구과제로 남겨놓았다. 본 논문에서는 균등함수의 GAC의 하한에 대해서 계산했고, 연접의 방법에 의한 좋은 GAC 의 특성을 가지는 함수의 생성방법을 제시하였다.

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.331-348
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• 2012

With a gradual increase in research on teaching and learning calculus, there have been various studies about students' thinking about the derivative. This paper reviews the results of the existing empirical studies published in Korean and English. These studies mainly have shown that how students think about the derivative is related to their understanding of the related concepts and the representations of the derivative. There are also recent studies that emphasize the importance of how students learn the derivative including different applications of the derivative in different disciplines. However, the current literature rarely addressed how students think about the derivative in terms of the language differences, e.g., in Korean and English. The different terms for the derivative at a point and the derivative of a function, which shows the relation between concepts, may be closely related to students' thinking of the derivative as a function. Future study on this topic may expand our understanding on the role language-specific terms play in students' learning of mathematical concepts.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.435-457
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• 2013

The purpose of this paper is to discover effective teaching and learning methods for improving low level mathematic matriculants', who passed the early decision program, problem solving abilities by analyzing their error patterns in the special lecture for basic mathematics in P University. In this paper, we examine the matriculants' understanding and errors on the fundamental concepts of function, and continuity and differentiability of function based on the pre-examination. We also measure the their academic achievement in the special lecture for basic mathematics, and analyze the differences of error patterns between pre-test and post-test result on the concepts of continuity and differentiability of function.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.267-281
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• 2013

In this paper, we explore the possibility that ladder diagram games can be used for the introduction of the function and composite function. A ladder diagram with at most one rung is a bijection. Thus a ladder diagram with r rungs is the composition of r one-to-one correspondence. In this paper, we use ladder diagrams to give simple proofs of some fundamental facts about one-to-one correspondence. Also, we suggest Story-telling for introduction of function in middle school and high school. The ladder diagram approach to one-to-one correspondence not only grabs our students' attention, but also facilitates their understanding of the concept of functions.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.371-374
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• 2009

In this paper, we introduce the concepts of effects and observable as generalizations of event and random variable, respectively. Also, we introduce the concept of $\sigma$-morphism and we investigate some results on $\sigma$-morphism as a probability measure on the set of effects.

• Proceedings of The KACE
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• 2018.08a
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• pp.25-27
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• 2018

교구에 대한 적절한 조작 및 탐구 활동은 수학의 개념과 원리를 이해하는 데 도움을 준다. 본 연구에서는 중학교 수학 교과 과정에 부합하는 함수의 개념과 성질에 대한 이해를 도울 수 있는 안드로이드 기반의 앱을 개발하였다. 개발한 앱은 앱인벤터(App Inventor) 2를 기반으로 사용자가 구체적인 함수 그래프를 그리도록 요구하는 것이 아니라 대략적인 개형을 이해하도록 하여 학습 부담 경감을 도모한다. 즉, 계산 능력 배양을 목표로 하지 않는 교수학습 상황에서 스팀 기반으로 공학적 도구를 이용하여 2015 개정 수학과 교수학습방법에서 요구되는 정보처리 능력 및 문제해결 능력을 함양시킬 수 있도록 학습 도구를 개발하였다.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.121-139
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• 2006

This study identified the problems of teaching quadratic functions using a translation and a vertex form by completing squares of which method make teaching contents not to be interconnected and tend to interfere students' conceptual understanding. This seems to generated from which the current mathematics curriculum is not organized to deliver the related contents of quadratic functions from polynomial expressions students have already known. To resolve it this study investigates the properties of quadratic functions from a polynomial perspective and discusses classroom implications with a couple of concrete applications.