• The Journal of Korean Institute of Communications and Information Sciences
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• v.7 no.1
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• pp.25-28
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• 1982

A method for finding the symbolic reliability expressision of a conbinational logic circuit is presented. The evaluation of the probabilities of the outputs can be symbolically evaluated by the Boolean operation named sharp operation, provided that every input of such a circuit can be treated as random variables with values set(0, 1) and the output of a circuit can be represented by a Boolean sum of produt expression.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.53-66
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• 2008

The concepts of ratio and proportion are familiar with students but have difficulties in use. The purpose of this paper is to identify the meanings of the concepts of ratio and proportion through investigating the historical development process of the meanings and representations of them. The early meanings of ratio and proportion were arithmetical meanings, however, geometrical meanings had taken the place of them because of the discovery of incommensurability. After the development of algebraic representation, the meanings of ratio and proportion have been growing into algebraic meanings including arithmetical and geometrical meanings. Through the historical development process of ratio and proportion, it is observable that the meanings of mathematical concepts affect development of symbols, and the development of symbols also affect the meanings of mathematical concepts.

• School Mathematics
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• v.10 no.2
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• pp.297-317
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• 2008

This study was designed to gain insight to adopt CAS into secondary level algebra education in Korea. Most inactive usage of calculators in math and most negative effects of calculators on their achievements of Korean students were shown in International studies such as TIMSS-R. A comparative study was carried out with consideration of mathematical backgrounds and technological environments. 8 Korean students and 26 US students in Grade 11 were participated in this study. Subjects' Problem solving process and their strategies of CAS usage in classical Box-problem with CAS were analyzed. CAS helped modeling by providing symbolic manipulation commands and graphs with students' mathematical knowledge. Results indicates that CAS requires shifts focus in algebraic contents: recognition of decimal & algebraic presentations of numbers; linking various presentations, etc. The extent of instrumentation effects on the selection of problem solving strategies among Korea and US students. Instrumentation

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.223-237
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• 2004

본 연구는 중학교 1학년을 대상으로 일차방정식의 풀이 과정에서 나타나는 오류를 분석하고 그래핑 계산기를 활용하여 오류의 교정 과정을 제시하였다. 오류의 유형을 개념적 이해 미흡 오류, 등식의 성질에 대한 오류, 이항에 대한 오류, 계산 착오로 인한 오류, 기호화에 의한 오류로 분류하였으며, 이 중에서 등식의 성질에 대한 오류와 개념적 이해 미흡으로 인한 오류를 많이 범하고 있었다. 학생들이 TI-92를 활용하여 일차방정식의 해를 구할 때, Home Mode에서 Solve 기능을 이용하여 단순히 결과만을 보는 것 보다 Symbolic Math Guide를 이용하여 풀이 과정을 선택하여 대수적 알고리즘을 형성하면서 해를 구하는 것을 선호하였다. 그리고 학생들의 정의적 및 기능적 측면을 고려해야 할 필요성을 느끼게 되었다.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.229-246
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• 2002

In this paper, we start with the question "what is algebraic thinking\ulcorner". The problem is that the algebraic thinking is not exactly defined. We consider algebraic thinking from the various perspectives. But in the discussion relating to the definition of algebraic thinking, we verify that there is the algebraic notations in the core of algebraic thinking. So we device algebraic notations into the six categories, and investigate these examples from the school mathematics. In order to investigate this relation of algebraic thinking and algebraic notations, we present 'the algebraic thinking process analysis model' from Frege' idea. In this model, there are three components of algebraic notations which interplays; sense, expression, denotapion. Thus many difficulties of algebraic thinking can be explained by this model. We suppose that the difficulty in the algebraic thinking may be caused by the discord of these three components. And through the transformation of conceptual frame, we can explain the dynamics of algebraic thinking. Also, we present examples which show these difficulties and dynamics of algebraic thinking. As a result of these analysis, we conclude that algebraic thinking can be explained through the semiotic aspects of algebraic notations.

• Communications of Mathematical Education
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• v.10
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• pp.505-517
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• 2000

수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

• The KIPS Transactions:PartA
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• v.14A no.6
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• pp.383-390
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• 2007

This paper describes the e-learning system for science and engineering mathematics using computer algebra system and Bayesian inference network. The best feature of this system is using one of the most recent mathematical dynamic web content authoring model which is called client independent dynamic web content authoring model and using the Bayesian inference network for diagnosing student's learning. The authoring module using computer algebra system provides teacher-user with easy way to make dynamic mathematical web contents. The diagnosis module using Bayesian inference network helps students know the weaker parts of their learning, in this way our system determines appropriate next learning sequences in order to provide supplementary learning feedback.

• Korean Journal of Logic
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• v.6 no.2
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• pp.49-67
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• 2003

조합논리는 기본적으로 정해진 해석이 없는 순수한 형태만을 가지고 추상적으로 연산하는 관점에 관한 논리로서, 논리학을 기호학적 관점에서 볼 수 있는 토대를 제공해 준다. 조합논리의 특징은 연산자가 피연산자도 될 수 있다는 사실에 있으며 그래서 동일한 연산자가 그 자신의 피연산자도 될 수 있다. 이 논문에서 우리는 기본연산자들의 직관적 개념과 형식적 개념을 소개하고 연산자 대수에 내해 검토하고 나서 조합논리와 $\lambda$-연산의 번역가능성에 다해 알아보겠다. 조합논리에 유형의 개념을 추가하면 자연언어 분석에서 아주 효율적인데 기본유형인 대상자 명제 이외의 어떤 요소라도 함수자로 나타낼 수 있는데 이들은 조합자의 특수한 경우로서 파생유형들이다.