• 대한화학회지
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• 제45권4호
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• pp.370-376
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• 2001

본 연구에서는 서술형 검사를 이용하여 고등학생의 문제 해결 전략 수행 능력을 측정하고, 논리적 사고력과 전략 수행 능력 사이의 관계를 조사하였다. 서울시에 소재한 두 고등학교에서 4학급(N=187)을 선정한 후, 전략 수행 능력 검사와 논리적 사고력 검사를 실시하였다. 전략 수행 능력의 채점틀은 7개 하위 범주-문제의 조건 파악, 관련 법칙 회상, 하위 목표 설정, 물리량 유도, 수리적 수행, 논리적 전개, 검토-로 구성하였다. 채점에 대한 신뢰도는 분석자간 일치도 .92로 확인하였다. 연구 결과, 학생들의 조건 파악 능력과 수리적 수행 능력은 비교적 높으나, 하위 목표 설정 능력과 검토 능력은 저조한 것으로 조사되었다. 전략 수행 능력 검사의 전체 점수 및 하위 범주별 점수는 논리적 사고력과 유의미한 상관을 나타내었다.

• 한국학교수학회논문집
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• 제16권4호
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• pp.927-941
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• 2013

본 연구에서는 고등학교 학생들이 삼각형에 대한 코사인 법칙으로부터 사각형과 n각형에 대한 코사인 법칙을 유추적 사고를 통하여 발견하는 과정을 조사하였으며 삼각형에 대한 코사인 법칙에 대한 충분한 이해가 일반화된 법칙을 발견하고 증명하는데 어느 정도 영향을 미치는지를 분석하였다. 이와 같이 귀납적 추론이나 유추적 사고 활동을 통해 학생 스스로 지식을 발견하고, 스스로 발견한 수학적 지식을 논리적 추론이나 연역적 증명을 통해 정당화하는 경험을 쌓을 수 있을 때, 학생들은 이 지식을 자신의 것으로 내면화할 수 있게 되고, 다양한 상황에 자유롭게 활용할 수 있는 능력을 가질 수 있을 것이다.

• East Asian mathematical journal
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• 제37권2호
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• pp.149-167
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• 2021

The six core competencies included in the mathematics curriculum revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the reasoning is very important for students' enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of investigation and fact guess, justification, the logical performance of mathematical content and process, reflection of reasoning process, And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the reasoning competency were shown in each textbook.

• 한국수학교육학회지시리즈A:수학교육
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• 제24권2호
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• pp.105-116
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• 1986

For any thought and knowledge, its growth and development has close relation with the society where it is developed and grow. As Feuerbach says, the birth of spirit needs an existence of two human beings, i. e. the social background, as well as the birth of body does. But, at the educational viewpoint, the spread and the growth of such a thought or knowledge that influence favorably the development of a society must be also considered. We would discuss the goal and the function of mathematics education in relation with the prosperity of a technological civilization. But, the goal and the function are not unrelated with the spiritual culture which is basis of the technological civilization. Most societies of today can be called open democratic societies or societies which are at least standing such. The concept of rationality in such societies is a methodological principle which completes the democratic society. At the same time, it is asserted as an educational value concept which explains comprehensively the standpoint and the attitude of one who is educated in such a society. Especially, we can considered the cultivation of a mathematical thinking or a logical thinking in the goal of mathematics education as a concept which is included in such an educational value concept. The use of the concept of rationality depends on various viewpoints and criterions. We can analyze the concept of rationality at two aspects, one is the aspect of human behavior and the other is that of human belief or knowledge. Generally speaking, the rationality in human behavior means a problem solving power or a reasoning power as an instrument, i. e. the human economical cast of mind. But, the conceptual condition like this cannot include value concept. On the other hand, the rationality in human knowledge is related with the problem of rationality in human belief. For any statement which represents a certain sort of knowledge, its universal validity cannot be assured. The statements of value judgment which represent the philosophical knowledge cannot but relate to the argument on the rationality in human belief, because their finality do not easily turn out to be true or false. The positive statements in science also relate to the argument on the rationality in human belief, because there are no necessary relations between the proposition which states the all-pervasive rule and the proposition which is induced from the results of observation. Especially, the logical statement in logic or mathematics resolves itself into a question of the rationality in human belief after all, because all the logical proposition have their logical propriety in a certain deductive system which must start from some axioms, and the selection and construction of an axiomatic system cannot but depend on the belief of a man himself. Thus, we can conclude that a question of the rationality in knowledge or belief is a question of the rationality both in the content of belief or knowledge and in the process where one holds his own belief. And the rationality of both the content and the process is namely an deal form of a human ability and attitude in one's rational behavior. Considering the advancement of mathematical knowledge, we can say that mathematics is a good example which reflects such a human rationality, i. e. the human ability and attitude. By this property of mathematics itself, mathematics is deeply rooted as a good. subject which as needed in moulding the ability and attitude of a rational person who contributes to the development of the open democratic society he belongs to. But, it is needed to analyze the practicing and pursuing the rationality especially in mathematics education. Mathematics teacher must aim the rationality of process where the mathematical belief is maintained. In fact, there is no problem in the rationality of content as long the mathematics teacher does not draw mathematical conclusions without bases. But, in the mathematical activities he presents in his class, mathematics teacher must be able to show hem together with what even his own belief on the efficiency and propriety of mathematical activites can be altered and advanced by a new thinking or new experiences.

• East Asian mathematical journal
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• 제32권4호
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• pp.589-608
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• 2016

The purpose of this study was to develop an effective Calculus Supplement Learning Program for university students who are from liberal arts and investigate how the program affects their achievement and attitude in mathematics. we analyzed their answer sheets and interview reports with qualitative methods. After adapting the program, students recognized that mathematical concepts and definitions were very important to study a college calculus. Also they picked up how to learn mathematics in college. Finally, we found that students could develop their abilities of proof, problem solving, and logical thinking through the program.

• East Asian mathematical journal
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• 제23권3호
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• pp.313-326
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• 2007

The purpose of education of propositional logic is to understand the basic structure of the mathematics and to improve the logical thinking in normal life. But in the seventh curriculum, some basic terms, for examples $\wedge$ and $\vee$, are not introduced, the proposition $p{\\rightarrow}q$ is not defined properly, and use the wrong term $\Rightarrow$ so that it is difficult to understand the propositional logic. In this paper, we present a suitable content for the propositional logic in high-school mathematical class. We also present a proper definition of the proposition $p{x}{\Rightarrow}q{x}$ without using the notation $\rightarrow$. We finally give proper definitions of necessary conditions, sufficient conditions, and necessary and sufficient conditions.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권2호
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• pp.317-333
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• 2001

The equations of figures given by rectangular coordinates are used to look into the properties of them, which are very restricted in examining them in the school mathematics. Therefore, it is quite natural to consider the figures in terms of parameters without restriction to coordinates and also, it is possible for the students to analyze them. Thus, the visualization of figures is important for students in mathematics education. In particular, the teaching-learning methods using computers make loose the difficulties of geometry education, and from the viewpoint that various abstract figures can be visualized and that can be obtained by means of this visualization the learning of figures can be accomplished through the direct experience or control. This study is intended to present concretely the aim and its utility to visualize figures represented as parameters with Mathematics. In this paper, we introduce a new teaching-learning method of figures represented by parameters using Mathematica so that the learners establish themselves their knowledge obtained through their search, investigation, supposition and they accomplish the positive transition to advanced learning. So the leasers extend their ability of sensuous intuition to their ability of logical reasoning through their logical intuition. Consequently they can develop the ability of thinking mathematically, so many natural phenomena and physical ones.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권1호
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• pp.83-98
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• 2015

By analysing the examination papers for geometry, we classified the errors occured in the proofs for geometric problems into 5 main types - logical invalidity, lack of inferential ability or knowledge, ambiguity on communication, incorrect description, and misunderstanding the question - and each types were classified into 2 or 5 subtypes. Based on the types of errors, answers of each problem was analysed in detail. The errors were classified, causes were described, and teaching plans to prevent the error were suggested case by case. To improve the students' ability to express the proof of geometric problems, followings are needed on school education. First, proof learning should be customized for each types of errors in school mathematics. Second, logical thinking process must be emphasized in the class of mathematics. Third, to prevent and correct the errors found in the proofs for geometric problems, further research on the types of such errors are needed.

• 한국초등수학교육학회지
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• 제15권1호
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• pp.95-120
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• 2011

논술에서 요구되는 능력, 즉 논술 능력은 기본적으로 이해력, 논리적이고 창의적인 사고력, 표현력과 같은 고등사고능력이다. 그러나 이러한 논술 능력은 단기간에 신장되지 않는다. 더욱이 수학은 계열성이 강한 학문으로 이러한 능력의 신장을 위해서는 초등학교 저학년 때부터 차근차근 단계에 맞게 준비해야하는 것은 어찌 보면 당연한 일이다. 그러나 현재 초등 수리 논술에 대한 용어의 정의가 없어 사교육 시장을 중심으로 무분별하게 초등 수리 논술이라는 용어가 사용되고 있다. 초등학교는 1학년부터 6학년까지 다양한 발달단계의 학생들이 모여 있는 곳이다. 초등 논술이 입시논술과 그 성격과 지도방향이 다르듯 초등 수리 논술 또한 그 성격과 지도 방향이 달라야 한다. 논술 능력은 단기간에 완성되는 것이 아니므로 어릴 때부터 꾸준한 연습이 필요하며, 더욱 중요한 것은 흥미를 잃지 않도록 하는 것이다. 따라서 초등 수리 논술의 올바른 개념을 정립하고, 성격과 지도방향을 설정하여 후속연구를 활발히 해야 할 필요성이 있다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제28권4호
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• pp.529-552
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• 2014

본 연구에서는 수학에서 추론의 중요성과 그 역할에 의미를 두고, 고등학교 수학 내용(문제)의 분석을 통해 학생들이 제공받는 추론의 유형이 얼마나 높은 수준, 즉 다양한 것인지에 대해 살펴보고자 한다. 현재, '수학 II' 교과목은 2009 개정에 따른 교과목들 중에서 '수학 I' 교과목을 이수한 후 선택하는 것(신이섭, 2011)으로, 중등 수학에서 가장 심도 있는 학습 내용을 다룬다고 볼 수 있다. 이러한 점에 감안하여 본 연구에서는 '수학 II' 교과목의 내용을 중심으로 Johnson, et al.(2010)의 여섯 가지 추론 유형을 재구성하여 이를 바탕으로 현행 9종의 모든 교과서에 수록된 추론 문제의 정도(비율) 및 유형을 파악하고자 한다. 이로써, 학생들에게 어느 정도의 추론 활동의 기회가 제공되고 있는지 살펴보고, 수학 수업에서의 추론 능력 신장의 긍정적 가능성을 가늠해 보고자 한다.