• 한국수학교육학회지시리즈A:수학교육
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• 제56권1호
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• pp.81-100
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• 2017

The concept of variable is a big idea to develop algebraic thinking. Variable has multiple meanings such as the unknown, a tool for generalization, and the relationship between varying quantities. In this study we analyzed in what ways the meanings of variable were presented in the current elementary mathematics textbooks and workbooks. The results showed that the most frequent meaning of variable was 'the unknown', 'a tool for generalization', and 'the relationship between varying quantities' in order. A close look at the results revealed that the same symbol was often used in representing different values of variable as the unknown. In taking variable as a tool for generalization, questions to provoke generalization were sometimes included not in the textbooks but in the teachers' manuals. The main focus in dealing with variable as the relationship between varying quantities was on finding out the dependent values compared to the independent ones. Building on these results, this study is expected to suggest implications for how to deal with variable concept in elementary mathematics instructional materials.

• 음성과학
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• 제15권2호
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• pp.145-156
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• 2008

The purpose of this study was to investigate the reason why puberphonia patients revisit hospitals after completion of its treatment and the effect of visual voice therapy on voice improvement. The subject the study included are two puberphonia patients who had been diagnosed by laryngologists. The patients who were diagnosed as puberphonia by the laryngologist and treated by the a speech pathologist, completed their treatment and revisited hospital. The study used laryngoscopy, acoustic and aerodynamic analysis before and after voice treatment to investigate what change happens and why generalization of treatment effect did not occur naturally in the daily life. Their voices of pre-therapy and post-therapy were analyzed on the aspects of acoustics, aerodynamics and laryngeal endoscopy. As a result, it was found that fundamental frequency(Fo) was significantly lowered in respect of acoustic change and maximum phonation time(MPT) was increased to some extent in respect of aerodynamic change. In addition, there was a laryngoscopic change and commissure glottic chink disappeared generally in the phonation. The reason why the generalization did not occur naturally in one’s daily routine was mainly due to the fact that high-pitched voicing was used for a long time. Other than that reason, negative reaction or attitude of surrounding people and lack of confidence were to blame for failure of generalization.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제23권2호
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• pp.399-428
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• 2009

2007년 개정교육과정은 대수의 도입 시기를 초등으로 앞당기고 있다. 최근의 연구결과들로부터 볼 때 초등수학 수준에서 대수를 도입할 때 패턴의 일반화를 이용하는 것은 타당한 과정으로 판단된다. 초등학교 6학년 학생들이 패턴의 일반화과정 학습에서 대수를 도입하는 것이 가능한지 그리고 어떤 효과가 있는지, 초등학교 6학년 학생들의 패턴의 일반화 과정은 어떠한지에 대한 연구가 보완되어야 할 필요가 있다. 본 연구는 초등학교 5학년들에게 패턴을 일반화하여 대수를 도입하고 지도하고 그 과정에서 나타나는 일반화 과정의 특징과 학생들이 겪는 어려움을 분석하였다. 이를 통하여 패턴의 일반화를 지도하거나 패턴에 기초한 대수 교육과정을 개발할 때 시사점을 얻고 교수학습 자료 개발에 대한 정보를 제공하고자 한다.

• 한국정보과학회논문지:소프트웨어및응용
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• 제31권5호
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• pp.537-542
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• 2004

다층 퍼셉트론(Multi-Layer Perceptron, MLP) 구조는 그의 비선형 적합능력으로 인하여 매우 다양한 실제 문제에 적용되고 있다. 그러나 일반화된 MLP 구조의 적합능력은 은닉노드의 개수. 초기 가중 값 그리고 학습 회수 또는 학습 오차와 같은 구조인자(factor)들에 크게 영향을 받는다. 만약 이들 구조인자가 부적절하게 선택되면 일반화된 MLP 구조의 적합능력이 매우 왜곡될 수 있다. 따라서 MLP구조에 영향을 주는 인자들의 결합 영향을 살펴보는 것은 중요한 문제이다. 이 논문에서는 제어상자(controller box)를 통한 학습결과와 더불어 MLP구조를 일반화할 때 영향을 줄 수 있는 신경망의 일반적인 구조인자 들을 실증적으로 살펴보고 이들의 상대효과를 비교한다.

• 대한수학교육학회지:학교수학
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• 제5권3호
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• pp.343-360
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• 2003

초등수학에서 중등수학으로의 이행에서 대수는 중요한 역할을 한다. 그리고 학교수학에서 어떻게 대수를 도입하는가 하는 문제는 중등수학 전반에서 그 성공여부를 결정짓는 중요한 요소가 된다. 일반적으로 학교대수는 대수 기호를 형식적으로 도입하는 전통적인 접근법을 따르고 있다. 이것은 대수를 일반화된 산술이라는 관점에서 보는 것으로, 여기서 문제는 이러한 접근법에서 학생들이 많은 어려움을 경험한다는데 있다. 따라서 이 글은 이러한 어려움을 해결하기 위한 하나의 대안으로 형식적인 대수 지도 방법을 대신하여 패턴과 일반화 측면을 강조하여 대수를 지도하는 방법에 대해 살펴보고자 한다. 이것은 대수를 도입하는 다양한 관점 곧, 문제해결과 모델링, 일반화된 산술을 비롯하여 함수를 포함하며, 동시에 대수에 내재된 패턴을 통해 대수학습에서 핵심으로 다루어지는 일반화라는 사고 양식을 이끌어내기 위한 것이다. 이를 위해 이 글은 먼저 대수와 패턴, 일반화 사이의 관계를 살펴보고, 그리고 패턴과 일반화를 강조한 대수 접근법이 대수 수업의 실제에서 어떻게 제시될 수 있는가에 대해 살펴볼 것이다.

• 한국멀티미디어학회논문지
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• 제24권12호
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• pp.1624-1631
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• 2021

With the continued development of image processing technology, we live in a time when it is difficult to visually discriminate processed (or tampered) images from real images. However, as the risk of fake images being misused for crime increases, the importance of image forensic science for identifying fake images is emerging. Currently, various deep learning-based identifiers have been studied, but there are still many problems to be used in real situations. Due to the inherent characteristics of deep learning that strongly relies on given training data, it is very vulnerable to evaluating data that has never been viewed. Therefore, we try to find a way to improve generalization ability of deep learning-based fake image identifiers. First, images with various contents were added to the training dataset to resolve the over-fitting problem that the identifier can only classify real and fake images with specific contents but fails for those with other contents. Next, color spaces other than RGB were exploited. That is, fake image identification was attempted on color spaces not considered when creating fake images, such as HSV and YCbCr. Finally, dropout, which is commonly used for generalization of neural networks, was used. Through experimental results, it has been confirmed that the color space conversion to HSV is the best solution and its combination with the approach of increasing the training dataset significantly can greatly improve the accuracy and generalization ability of deep learning-based identifiers in identifying fake images that have never been seen before.

• East Asian mathematical journal
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• 제40권2호
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• 대한수학회논문집
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• 제29권3호
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• pp.429-437
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• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.563-572
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• 2008

In this paper, we discuss about a generalization of the Key Distribution Pattern which was proposed by C. Mitchell and F. Piper[6]. It is allowing secure communication between every n-pair of users($n\leq2$) in a large network for reducing storage requirements. We further suggest a generalization of K. Quinn's bounds in [9] for the number of subkeys in such general Key Distribution Patterns.

• 대한수학회지
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• 제39권6호
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• pp.881-898
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• 2002

Our aim in this paper is to introduce a generalization of some notions in homological algebra. We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and $\mu$-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.