• Journal for History of Mathematics
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• v.20 no.2
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• pp.33-46
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• 2007

In this Paper the change of trends over historical research of mathematics, that has been developed since 1970, is inquired. Most of all it deals with the controversy concerning so-called 'geometrical algebra'. It covers the contents of Euclid' work II. And the relation of the controversy with the change of direction over historical research of mathematics is examined.

• 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.

• Communications of Mathematical Education
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• v.9
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• pp.327-333
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• 1999

21세기를 바로 앞두고, 우리 나라 수학 교육의 과거와 현재의 실태, 즉 수학교육의 목적, 교수 내용, 교수 방법, 평가 등을 철학적 관점과 심리학적 관점에서 역사적으로 재조명해 보는 것은 새로운 2000년대를 앞두고 의미 있는 일이 될 수 있다. 또한 이를 바탕으로 21세기에 우리 나라 수학 교육이 나아가야 할 방향을 세계적인 추세와 관련하여 제시해 보고자 한다.

• 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.18 no.2
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• pp.55-74
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• 2005

This research studied loaming model for the purpose of renovation of mathematics teaching methods. Especially, this research classified the types of cooperative teaming, the theoretical background for cooperative learning, the need of cooperative learning in school mathematics, and the differences between cooperative teaming and traditional small group learning. This research also suggested special features of cooperative learning and various types of cooperative learning models. The main types of cooperative loaming which this research supported are TAI(Team-Assisted Individualization, JIGSAW cooperative loaming, JIGSAW II cooperative teaming, JIGSAW III cooperative teaming, STAD(Student Team-Achievement division) cooperative learning, and TGT (Teams - Games - Tournament).

• School Mathematics
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• v.11 no.3
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• pp.431-462
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• 2009

Introduction of logarithm in mathematics textbook in the 7th national curriculum of mathematics is the inverse of exponent. This introduction is happened that students don't know the necessity for learning logarithm and the meaning of logarithm. Students also have solved many problems of logarithm by rote. Therefore, we try to present teaching unit for the logarithm according to the historico-genetic principle. We developed the learning-teaching module of unit for the logarithm according to historico-genetic principle, especially reinvention for real contexts based RME. Loaming-teaching module is carried out as the performance assessment. As a results, We find out that this module helps students understand concepts of logarithm meaningfully Also, mathematical errors of logarithm is revised after the application of learning-teaching module.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.233-249
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• 2005

This study discusses on the historico-genetic instruction on fraction. The textbooks of the current curriculum include the variety of contexts of fraction to be intended to connect with the conception of ratio in the grade 6. However mary elementary students have understanding limited to whole-part relation only. This study propose a method on the basis of the process of measurement by an absolute unit. The idea is related to The genesis of fraction in Egypt.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.55-66
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• 2005

In our school mathmatics, the irrational numbers and the real numbers are defined and instructed on the basis of decimal fractions. In relation to this fact, we identified the essences of the real number and the irrational number defined by the decimal fractions through the historical analysis. It is revealed that the formation of real numbers means the numerical measurements of all magnitudes and the formation of irrational numbers means the numerical measurements of incommensurable magnitudes. Finally, we suggest instructional plan for the meaninful understanding of the real number concept.

• Communications of Mathematical Education
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• v.16
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• pp.149-162
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• 2003

수는 도대체 어디서 생겨났을까? 언제쯤부터 어떤 필요에 의해 인간이 사용하기 시작하였을까? 학생들이 이러한 호기심을 한 번쯤 가져본다면 얼마나 좋을까? 그러나 학생들은 십진기수법의 체계에 너무나 잘 길들어져 있기 때문에 그 고마움에 대해서 잘 모른다. 조류즈 이프라는 '신비로운 수의 역사'에서 인간 지성의 환상적 모험이 만들어낸 1, 2, 3, 4, 5, 6, 7, 8, 9, 0에 대하여 불의 사용이나 전기의 발명만큼이나 혁신적인 사건으로 취급하고 있으며 수의 역사는 인간의 보편적인 지성이 이루어 낸 영원히 무너지지 않는 바벨탑으로서, 인종차별까지 극복해낸 위대한 가능성임을 가슴 뿌듯하게 전해 준다. 따라서 본 연구에서는 이러한 인류 역사의 놀라운 소산인 수의 위대함을 깨닫기 위하여 세계 여러 문명들 속에서 숫자가 생겨난 연유, 그 표기 방법 및 그 이후부터의 발달 모습을 학생들이 탐구해 보게 하기 위하여 기수법과 수체계에 대한 지도 방법에 대하여 연구하고자 한다.

• School Mathematics
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• v.10 no.4
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• pp.625-648
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• 2008

We collected the data through the following process. 36 third-grade middle school students are selected, and we conducted ex-ante interviews for researching how they understand the nature of proof. Based on the results of survey, then we chose two students we took a lesson with the Branford's among the 36 samples. After sampling, historic-genetic geometry education, inspected carefully whether the Branford's method helps the students.