• Journal for History of Mathematics
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• v.17 no.4
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• pp.87-100
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• 2004

There is great enthusiasm among many mathematics educators to seek to understand how mathematical history can be employed to emphasize the usefulness of mathematics and to make it even more useful. This study focused on reviewing the history of mathematics to provide a 'source of insight.' In this study, the reasons for including the history of mathematics in the mathematics curriculum were divided into three domains: cognitive, affective, and sociocultural. Each domain included the followings: mathematical thinking and understanding; development of a positive attitude and increase motivation; and last, humanistic facets and sociocultural experience. At the same time, we need to develope a pedagogical approach that allows educators to use history properly. Furthermore, we must integrate the historical topics into regular curricula including the syllabus historically-informed grounds.

• Communications of Mathematical Education
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• v.12
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• pp.141-153
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• 2001

지금의 수학교육현장은 결과적인 완성된 지식을 교사 주도하에 연역적으로 지도하는 것에 대해 문제가 있는 것으로 지적되어 그에 대한 대안으로 본 논문은 인지갈등을 통한 수학과 학습 모형을 이용한 교수-학습 방법을 제시하고자 한다. 인지 갈등을 유발하여 학습동기를 부여한 후 학생과 교사가 함께 그 갈등을 풀어 나감으로서 동기유발과 수학적 능력을 길러 줄 수 있을 것이다. 특히, 보편화된 컴퓨터 환경은 이러한 수업을 더욱 용이하게 함에 주목하고 또 문제 설정 등 다양한 기법을 통한 수업 모형을 효과적으로 활용할 수 있으며 주제에 따라서는 수학사적 내용을 첨가하여 흥미 있는 수업을 할 수 있다. 이러한 수업방법은 학생들의 흥미와 참여를 유도하게 되어 효과적일 것이다.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.57-72
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• 2007

Recently, dissection puzzles such as pentominoes have been used in mathematics education. But they are not actively applicable as a tool of problem solving or introducing mathematical concepts since researches about the historical background and developments of mathematical applications of such puzzles have not been effectively accomplished. In this article, in order to use pentominoes in mathematical teaming effectively, we first investigate geometric problems related to dissection puzzles and the historic background of development of pentominoes. And then we collect and classify data related to pentomino activities which can be applicable to mathematics classes based on the 7th elementary school national curriculum. Finally, we suggest several basic materials and directions to develop more systematic learning materials about pentominoes.

• Journal for History of Mathematics
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• v.1 no.1
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• pp.86-89
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• 1984

1960년대를 기점으로 하여 일어난 수학 교육현대화 운동은 범세계적인 문화현상으로서 발전하는 방향으로 철저히 진행되어야 했으나 교재내용을 지나치게 비현실적으로 도입함에 따라 교육의 현장에 선교사의 창조적 노력보다는 무비판적인 수학교육이 됨으로써 원래의 수학교육목표와는 달리 진도에만 급급하다. 현실적인 요인으로서 중등학교 진학률의 증가 및 평준화에 대한 원인도 있겠지만 시험에만 연결되는 교육에 이상적인 논리주의 구조주의 적인 수학의 도입도 적지않은 문제 요인으로 되어 있다. 앞으로 교과과정의 개선이 있겠지만, 우선 지도방법에 있어서 새로운 방법론이 시도되어야 할 것이다. 본 논문에선 학생들이 이해할 수 있는 범위내에서 수학사적 자료를 도입하여 수학의 역사 및 수학의 사상적 배경등에 접할 수 있는 기회를 주어 교과내용에 흥미를 유발하고 수업내용을 이해하는데 도움을 주는 방법을 모색하려는 것이다.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.157-196
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• 2015

The purpose of this article is to discuss some of the most commonly repeated misconceptions on the history of mathematics described in the secondary school mathematics textbooks, and recommend that we should include mathematical transculture in the secondary school mathematics. School mathematical history described in the texts reflects the axial age, and deals with mathematical transculture from the ancient Greek into Europe excluding the ancient Egypt, Old Babylonia, and Islamic mathematics. We discuss about them through out the secondary school textbooks and give some alternatives for the historical problems.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.1-8
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• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.19-38
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• 2008

This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.11-32
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• 2005

This paper is a comprehensive study of mathematics education in the Chosun Dynasty. The basis of this work relies on actual historical records from the period. As shown in the records, mathematics education during the Chosun Dynasty remained at the level of basic arithmetics. The arithmeticians of the Chosun Dynasty did not have an understanding of more complex mathematical thought. But the simple arithmetics of the Chosun Dynasty facilitated the building up of a unique merchant 'middle class.' So this paper examines the development of mathematics in the Chosun Dynasty through middle class. Although the Chosun Dynasty arithmetics occupy a significant part of mathematics history, this paper details why their thought did not evaluate more advanced mathematical theories.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.123-146
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• 2006

The topic in this thesis stems from the current education situation that represses learners' freedom by excessive instruction and compulsory institution, in spite of the education helping learners free from inner prejudice as one of its chief aims. In this thesis, to discuss with an educational aspect, I call the learners' freedom in the learning process 'freedom-in-process' and the learners' freedom as the result of learning 'freedom-as-result'. Through this discussion, the conclusions are as follows; First, learners who enjoy freedom-in-process get to obtain freedom-as-result in mathematics education. Second, freedom-in-process and freedom-as-result appear repeatedly in the process of looking for and gaining structures. Freedom-in-process and freedom-as-result are both faces of coin, like seed and fruit which are related mutually and fertilized each other. For this purpose, Mathematics teacher must have awareness of the value of freedom, cherish the freedom, and enjoy it with his students.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.