• School Mathematics
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• v.15 no.1
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• pp.201-219
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• 2013

The purpose of this study was to analyse the belief about mathematics teaching of elementary preservice teachers and mathematics teachers. This study involved 100 respondents from the preservice teachers and 114 respondents from the mathematics teachers. The instruments used in this study consist 15 items of mathematical knowledges and 19 items of mathematical activities. The finding showed that preservice teachers emphasized the conceptual knowledge, whereas mathematics teachers emphasized the procedural knowledge in the mathematical knowledges. And preservice teachers emphasized the knowledge representation, knowledge generation, knowledge deliberation, knowledge communication, whereas mathematics teachers emphasized the use of knowledge(syntax) in the mathematical activities. Finally, even though two groups showed the significant difference in some items, preservice teachers and mathematics teachers emphasized the various mathematical knowledges and mathematical activities.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.345-359
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• 2011

In this research, we designed an educational activities of exploring mathematics programs in a course of mathematics education in teacher's college. We divided future mathematics teachers into 8 groups and suggested 8 mathematics programs to them. Each group explored one mathematics program. We asked to future mathematics teachers exploring some cases that use effectively a mathematics program in the teaching of school mathematics. In the process of an exploring, we designed some activities of teaching and learning. We provided opportunities of long-term exploration, group learning, presentations, exercises, reflections to mathematics teachers. As a result, future mathematics teachers acquired basic knowledge on the usage of mathematics programs in school mathematics textbook. In addition, their capabilities that are needed to explore mathematics programs have been enhanced. Also they had learned the teacher's positive attitude through the activities of teaching and learning.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.381-393
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• 2007

The study focuses on what to consider and do for the improvement of math education of Korean Universities by comparing freshmen and seniors of department of math education in their beliefs in mathematics and math. education. The major comparing topics in the beliefs are composed of perception of mathematics as a science, learning methods of mathematics, teaching methods of mathematics, and roles and qualifications of math. teachers. The results of the study show that junior students tend to be more positive in their beliefs, especially in math education area than that of mathematics, compared to the freshmen. It implies that how important the role of topics covered in math education during college years is for changing the future teachers' beliefs in math and math education more positively. The supposed influencing contents of the curriculum of math. education are composed of learning reflection method based on problem-based learning, understanding mathematics as originated from the real world, mathematical pedagogy, text analysis, practice in classroom, and understanding various concepts in math. education area.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.57-65
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• 2011

The conceptions of definition and proof radically change in the transition from secondary to tertiary mathematics. Specifically this paper analyses the historical development of the axiomatic method from Greek to modern mathematics. To understand Greek and modern axiomatic method, it is important to know the different characteristics of the primitive terms, constant and variable. Especially this matter of primitive terms explains the change of conceptions of definition, proof and mathematics. This historical analysis is useful for introducing the meaning of formal definition and proof.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.87-96
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• 2011

Hans Freudenthal made important contributions to algebraic topology and geometry. He also made significant contributions in history of mathematics and mathematics education. In the 1970s, his intervention prevented the Netherlands from the movement of "new math". He had a very important role as a founder of realistic mathematics education and became famous internationally by that. Because he raised the profile of ICMI strongly, Bass used the expression 'Freudenthal Era' for the period that Freudenthal was the president of ICMI. Now many mathematics educator agree to use the Freudenthal Era when they mention about the history of ICMI. In this paper, we present on the life of Freudenthal and his contributions for mathematics education, especially ICMI.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.61-70
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• 2007

Combinatorics, often called the 21 st century mathematics, has turned out a very important subject for the present information era. Modern combinatorics has started from some mathematical works, for example, Pascal's triangle and the binomial coefficients, and Euler's problems on the partitions of integers and Konigsberg's bridge problem, and so on. In this paper, we investigate the origin of combinatorics by looking over some interesting ancient combinatorial problems and some important problems which have started various subfields of combinatorics. We also discuss a little on the role of combinatorics in mathematics and mathematics education.

• School Mathematics
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• v.13 no.4
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• pp.563-580
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• 2011

This study is centered on the application of metaphor theory to math education from the cognitive-linguistic view. This study, at first, introduced what metaphor is, and looked into it from the math-educational view. Furthermore, on the basis of that, this study examined the significance of metaphor to math education, and dealt with its relevance to math education, focusing on the functions that metaphor has. This study says that metaphor has the function of explanation, elaboration and representation. In addition, this study examplifies that using metaphor can be an effective math learning strategy for mathematical concept explanation, mathematical connection and mathematical representation learning.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.553-571
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• 2014

Mathematical process is an issue in current mathematics education. In this paper discuss how to assess the mathematical process using essay type questions. For this we first suggest the concept of Mathematical Process Oriented Question which is an essay type question and possible to assess mathematical processes, that is, the mathematical communication, reasoning, and problem solving as well as mathematics knowledge. And we develop a framework for developing the mathematical process oriented question and rubric, examples of assessment standards and those questions containing rubric for assessing mathematical processes. The results of this paper can serve as basic data and examples for follow up research about mathematical process assessment.

• Communications of Mathematical Education
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• v.16
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• pp.163-164
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• 2003

최근 수학교육에서는 네덜란드의 수학교육이론인 현실적 수학교육(Realistic Mathematics Education: 이하 RME) 이론에 대한 관심이 증대되고 있다. RME 이론의 관점에서 학생들은 만들어져 있는 수학을 수용하는 사람이 아니라 스스로 모든 종류의 수학적 도구와 통찰을 개발하는 활동적 참여자로서 다루어져야 한다. 따라서 수학 학습은 수학화될 수 있는 풍부한 맥락으로부터 시작해야하며, 이러한 수학화를 실제(reality)에 둘 수 있도록 기여할 수 있는 교재로 시작해야 한다. 최근 발간된 'Mathematics In Context(이하 MIC)'는 RME 이론을 반영한 중등학교용 교과서로 맥락 문제가 그 중심이 되고 있으므로 RME 이론의 구체화된 실제를 볼 수 있는 예가 될 수 있다. 지금까지 Freudenthal의 교육철학을 소개하는 문헌 연구를 비롯하여 RME 이론을 기반으로 하는 교수 학습의 효과 분석에 관한 연구가 초등학교를 중심으로 이루어지고 있으나 중등학교 이상의 수준에서 수행된 RME 관련 연구가 부족한 실정이다. 이에 본 연구는 RME 이론이 중등학교 이상에서 수행되는 예를 찾기 위해 MIC 대수 교과서 중 'Comparing Quantities(Kindt, Abels, Meyer, & Pligge, 1998)'를 중심으로 Treffers(1991)의 다섯 가지 교수 학습 원리(구성하기와 구체화하기, 여러 가지 수준과 모델, 반성과 특별한 과제, 사회적 맥락과 상호작용, 구조화와 연결성)가 어떻게 구현되고 있는지 살펴보고자 한다. RME의 수학 학습 이론은 학생들이 맥락과 모델을 사용하면서 다양한 수준의 수학화를 통해서 자신의 수학을 개발할 수 있도록 하는 것이다. MIC 교과서는 맥락 문제와 여러 가지 해결 전략을 제시함으로써 그러한 수학 수업을 할 수 있도록 안내하는 교재가 될 수 있다.

• The Mathematical Education
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• v.32 no.3
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• pp.244-255
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• 1993

본 연구를 수행하게된 동기는 1994년부터 미국에서 S.A.T.를 개정하고, 한국에서는 대학 수학 능력 시험 제도라는 새로운 제도가 도입되는 것에 있다. 대학 학업 적성 평가 제도로서 미국의 S.A.T. 제도에 대한 유효성이 많은 학자들에 의해서 연구되고 있다. 대학 수학 능력 시험과 S.A.T.는 각각 한국과 미국의 대학에서 학업 적성을 측정한다는 면에서 그 목적이 같다. 한국의 대학 수학 능력 시험의 유효성을 연구하기에는 아직 실시되지 않았으므로 너무 이르다고 본다. 대학 수학 능력 시험 제도 확립이 실험 평가에 근거하기 때문에 대학 수학 능력 시험 실험 평가와 S.A.T.를 비교 연구하는 것은 의미가 있다고 본다. 따라서 본 논문에서는 한국의 대학 수학 능력 시험 실험 평가(수리)와 미국의 S.AT.(수학)와의 상관 관계를 연구한다. 본 연구의 조사 대상으로 선발된 집단으로서 광주시의 3개교 6학급의 고등학교 3학년 283명이 참가하였다. 본 논문에서 다음과 같은 문제가 연구되었다. 1. 7차 실험 평가(수리)와 S.A.T.(수학)의 평균 점수에 대한 남녀 차이의 통계학적 유의성 (statistical significance). 2. 7차 실험 평가(수리)와 S.A.T.(수학)의 평균 점수에 대한 자연계 인문계 차이의 통계학적 유의성 (statistical significance). 3. 한국의 대학 수학 능력 시험 실험 평가(수리)와 미국의 S.A.T.(수학)의 상관 관계.