• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.49-72
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• 2017

Despite the importance and necessity of functional thinking in a primary school there has been lack of research in this area, specifically regarding young children. Given this, this study analyzed how students aged from 7 to 9 would figure out and represent the co-variational relationships in context-driven tasks. Semi-clinical interviews were conducted with a total of 12 students. Interview tasks included three types of functions: (a) y=x, (b) y=x+1, and (c) y=x+x. The results of this study showed that most students were able to figure out co-variational relationships in diverse ways. Some factors such as types of function or characteristics of tasks had an impact on how students recognized the relationships. The students also could represent the relationship in diverse ways such as gesture, picture, natural language, and variables. They usually used natural language, but had a trouble using variables when representing the relation between co-varying quantities. Based on these results, this study provides implications on how to foster functional thinking ability at the elementary school.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.715-717
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• 2004

컴퓨터 상에서 집합, 트리, 그래프 등의 이산 객체(discrete object)는 메모리 주소와 같은 정수 값으로 표현되어 왔다. Succinct 표현(succinct representation)은 이산 객체를 이진화 하여 표현하는 방법으로, 정수 값으로 표현된 이산객체보다 적은 공간에 저장된다. Succinct 표현의 데이터는 이산 객체의 개별적 저장 위치를 파악하기 위해서rank와 select함수가 기본적으로 필요하다. rant와 select함수를 MBRAM 모델 상에서 O(1)시간에 계산하는 알고리즘이 제시되었다. MBRAM 모델은 비트연산을 unit cost로 수행하는 모델이다. 그러나 범용 컴퓨터는 바이트 단위의 기본 명령어를 제공하므로 비트연산을 unit cost에 수행할 수 없다. 본 논문은 범용 컴퓨터에서 효율적으로 rank함수를 구현하는 방법을 제시한다. rank함수의 효율적인 구현은 FM-index 등의 패턴 검색에 유용하다.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.87-98
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• 2017

The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.25-37
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• 2002

모든 과학 및 공학분야에 걸쳐, 신호나 함수를 어떻게 표현하는 것이 바람직한 것인지에 대해서 많은 연구가 이루어져 왔다. 만약 신호나 함수를 적절하게 잘 표현하게 되면, 그것들 속에 내재된 의미있는 물리적 현상을 쉽게 파악할 수도 있고, 최소한의 함수나 데이터로 효과적으로 표현할 수도 있다. 지난 10여년 동안 비약적 발전을 해온 ‘웨이블렛’이라는 것도 신호나 함수를 표현하는 새로운 도구인데, 이것이 각광을 받고 있는 이유는 웨이블렛이 전통적인 표현방법이 제공하지 못하는 특성을 제공하기 때문이다.(중략)

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.141-155
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• 2013

Process to translate into other forms in the form of expression for function is important in the development of functional thinking. Also it should be emphasized on the teaching of the function. This study will identify the translation ability of functional expressions and errors in the process to translate. The purpose of this study is to suggest important implications for the teaching and learning of function. To do this, we lead high school students perform the task to examine the translation ability. Then we compute a percentage of correct answers for each question and analyze the types of errors and their causes.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.205-225
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• 2014

This study analyzed how two sixth graders recognized, generalized, and represented functional relationships in exploring geometric growing patterns. The results showed that at first the students had a tendency to solve the given problem using the picture in it, but later attempted to generalize the functional relationships in exploring subsequent items. The students also represented the patterns with their own methods, which in turn had an impact on the process of generalizing and applying the patterns to a related context. Given these results, this paper includes issues and implications on how to foster functional thinking ability at the elementary school.

• Review of Korea Contents Association
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• v.2 no.1
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• pp.34-42
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• 2004

음함수 곡면은 물체 표면을 직접 정의하지 않고 영역 구분 함수를 통해 물체를 포함하는 공간상의 모든 점들의 관계를 정의함으로써 간접적으로 표현하는 방법이다. 음함수 곡면을 이용한 모델링은 함수나 수식을 이용하여 물체를 표현하기 때문에 표면의 위치를 찾기 위한 계산이 필요하지만, 및 가지의 함수 정의만으로 복잡한 형태의 곡면을 직접 표현할 수 있으며 주어진 모델로부터 서로 다른 품질의 이미지를 제공할 수 있다는 장점을 갖는다.(중략)

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.7
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• pp.1110-1114
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• 2001

The discrete wavelet concept in the k-domain is applied to efficiently represent Green function of integral equations. Application of discrete wavelet concept to Green function in the k-domain can be implemented equivalently by using spatial domain variable-sized windows. The proposed method consists of constant Q-filtering, changing the center of coordinates, and transforming spatially filtered Green functions into those in the k-domain. A mathematical expression of Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

• School Mathematics
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• v.11 no.1
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• pp.131-145
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• 2009

This research was designed to investigate the possibility to teach function concept and graph representation of functions in explicit manner toward at elementary level. Eight class-hours instruction was given to four Grade 5(age 11) students, and dynamic geometry software GSP was partially used in the class. Results indicate that the students could conceptualize the function relation, interpret linear function graphs, recognize the meaning of their slopes, and discuss the relationships among linear graphs and real life situation. Results also indicate that GSP helped students to recognize the relation between dots and the linear graph clearly and that GSP-line graph did decisive role for children to understand the meaning of graph representation of function.

• Communications of Mathematical Education
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• v.16
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• pp.123-137
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• 2003

본 논문의 목적은 삼각함수의 학습에 테크놀로지가 기여할 수 있는 방법적인 측면과 인지적인 효과를 명시하는 것이다. 테크놀로지가 삼각함수의 학습에 기여할 수 있는 네 가지 방법론적인 면을 '수학과 학생들의 실제 경험의 연결', '수학적 대상과 수학적 관계의 구체화', '수학의 다양한 표현 체계의 연결', '사고력 중심의 수학교육 추구'의 관점에서 논한다. 이 네 가지 방법론적인 측면 중 '수학적 대상과 수학적관계의 구체화'와 '수학의 다양한 표현 체계의 연결'을 중심으로 삼각함수의 학습법을 예시하면서 이 두 가지 방법이 어떻게 인지적으로 기여하는지를 보여준다.