• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.1-21
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• 2004

중국의 수학교육에서는 두 가지 기본, 즉 기본지식과 기본기술을 주창하는 전통이 있다. 이러한 전통의 직접적인 결과는, 중국 학생들이 국제수학시험(예를 들어 1989년도의 IAEP)에서 뛰어난 성적을 거둘 수 있는 능력을 갖추거나 국제수학올림피아드(IMO)에서 빼어난 성적을 거두는 것으로 나타난다. 우리는 이 강연에서, 중국 교사들이 "두 가지 기본"을 왜 그리고 어떻게 가르치는가와, 그들의 "두 가지 기본"을 학생의 창의성과 어떻게 결합시키는가를 보일 것이다. 개방형 문제해결 기법은 그러한 목적을 달성하기위한 한 가지 방법이다. 이 강연에서 생각할 주제들은 다음과 같다. 문화적 배경; 계산속도; "연습이 완전함을 만든다"라는 가설; 교실에서의 효율성; "두 가지 기본"과 개인적 성장 사이의 균형. 특히, 중국의 수학 교육자는 개방형 문제해결 기법과 "두 가지 기본" 초석 사이의 연결성에 더 많은 주의를 기울이고 있다.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.793-806
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• 2010

In this paper we study meaning and methods of analyzing problems related with equation of high school mathematics. By analyzing problem we can get two types of informations. Based on these informations we suggest some problem solving methods. Especially we try to extract second type information using analysis through synthesis. This second type information can help us to find new non-routine problem solving method.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.31-54
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• 2008

The discovery method is known to be the most effective in improving students' mathematical thinking. Recently, the long-term slow thinking(LST) is suggested as a possible method to implement the discovery method into the real classroom. In this concept, we examined whether students can solve such a problem, as appears to be beyond their ability, by themselves(LST) or not. 10 middle school students of the ninth grade were selected for the study, who had no previous experience on the infinite concept of calculus of the high school course. They had tried to solve a problem about the calculus by their LST for three days. Two of students solved the problem by themselves and seven of students solved it with help of hints. This result shows that if students are given the opportunity of LST for rather difficult mathematical problem with appropriate guidance of a teacher, they might solve it by themselves. That is, LST could be a possible method for implementation of the discovery method.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.247-265
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• 2009

In the 21C information-based society, there is an increasing demand for emphasizing communication in mathematics education. Therefore the purpose of this study was to research how properties of communication among small group members varied by mathematical problem types. 8 fourth-graders with different academic achievements in a classroom were divided into two heterogenous small groups, four children in each group, in order to carry out a descriptive and interpretive case study. 4 types of problems were developed in the concepts and the operations of fractions and decimals. Each group solved four types of problems five times, the process of which was recorded and copied by a camcorder for analysis, among with personal and group activity journals and the researcher's observations. The following results have been drawn from this study. First, students showed simple mathematical communication in conceptual or procedural problems which require the low level of cognitive demand. However, they made high participation in mathematical communication for atypical problems. Second, even participation by group members was found for all of types of problems. However, there was active communication in the form of error revision and complementation in atypical problems. Third, natural or receptive agreement types with the mathematical agreement process were mainly found for conceptual or procedural problems. But there were various types of agreement, including receptive, disputable, and refined agreement in atypical problems.

• Communications of Mathematical Education
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• v.9
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• pp.153-164
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• 1999

작도 문제는 역사적으로 아주 오래된 문제 중의 하나일 뿐만 아니라, 현재 우리 나라 기하 교육에 있어 매우 중요한 역할을 하고 있다. 즉, 평면 기하의 중심 정리들 중의 하나인 삼각형의 합동 조건들을 도입하기 위한 기초로 주어진 조건들(세 선분, 두 선분과 이들 사이의 끼인각, 한 선분과 그 양 끝에 놓인 두 각)에 상응하는 삼각형의 작도가 행해진다. 그러나, 현행 수학 교과서나 수학 교수법을 살펴보면, 작도 문제 해결 방법 및 지도에 대한 연구가 미미한 실정이다. 본 연구에서는 작도 문제의 특성, 작도 문제의 해결 방법 및 지도에 관한 접근을 모색할 것이다. 이를 통해, 학습자들이 다양한 탐색 활동 속에서 작도 문제를 탐구할 수 있는 이론적, 실제적 근거를 제시하고, 수학 심화 학습에 작도 문제를 이용할 수 있는 가능성을 제시할 것이다.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• Korean Journal of Logic
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• v.18 no.1
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• pp.39-64
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• 2015

The most difficult problem for mathematical Platonism is the epistemological problem raised by Paul Benacerraf and Hartley Field. Recently, Mark Balaguer argued that his version of mathematical Platonism, Full Blooded Plantonism (FBP), can solve the epistemological problem. In this paper, I show that there are serious problems with Balaguer's argument. First, I analyse Balaguer's argument and reveal a formal defect in his argument. Then I raise an objection based on an analogical argument. Finally, I disarm some potential moves from Balaguer.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.285-301
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• 2013

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009

The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

• School Mathematics
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• v.16 no.1
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• pp.111-133
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• 2014

This study aims to explore mathematical belief system and core belief factors to be found. The mathematical belief system becomes an auto regulation device for students' using mathematical knowledge in mathematical situations and provides them with the context to perceive and understand mathematics. They have individual mathematical beliefs for each of mathematics subject, mathematical problem solving, mathematical teaching and learning and self-concept, and these beliefs of students construct mathematical belief system according to mutual relationships among the mathematical beliefs. Using correlation analysis and multiple regression, mathematical belief system was structuralized and core belief factors were found. Mathematical belief system is structuralized and, as a result the core belief factors that are psychological centrality of high school students' mathematical belief system are found to be persistence, challenge, confidence and enjoyment. These core belief factors are formed on the basis of personal experiences and they are personal primitive beliefs that cannot be changed with ease and cannot be shared with other people but they are related with many other beliefs influencing them.