• Communications of Mathematical Education
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• v.23 no.2
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• pp.297-312
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• 2009

We study the process of horizontal and vertical mathematization on the polyhedron problems through the history of mathematics, computer experiments, problem posing, and justifications. In particular, we explore the Hamilton cycle problem, coloring problem, and folding net construction on the Archimedean and Catalan polyhedrons. In this paper, we present our mathematical results on the polyhedron problems, and we also present some unsolved problems that we found. We found that the history of mathematics and mathematical experiments are very useful in such R&E exploration as polyhedron problem posing and solving project.

• School Mathematics
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• v.15 no.1
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• pp.159-177
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• 2013

This study is a case study of STEAM education. We have developed teaching and learning materials, suggested teaching method, and analysed the result for exploring the potential and effect of STEAM. The content of this study is based on the history of mathematics. Science (S) is related to the 24 divisions of the year, the height of the sun, the movement of heavenly bodies. Technology (T) is related to the exploration with graphic calculators. Engineering (E) is related to design sundial and research on the design principles. Art (A) is related to literature review about mathematical history, the understanding of the value of the mathematics. Mathematics (M) is related to the trigonometric functions. We have considered that Project-Based Learning is proper teaching and learning for STEAM education, we have designed the STEAM PBL and analysed the results focused on the developing integrative knowledge, mathematical attitude including mathematical value, the competencies of 21 century. The result of this study is as follows. We find that STEAM education activates students' collaboration, communication skills and improves representation and critical thinking skills. Also STEAM education makes positive changes of students' mathematical attitudes including the values of the mathematics.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• Journal for History of Mathematics
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• v.32 no.2
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• pp.61-77
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• 2019

The study was conducted based on the 'method of mathematical exploration through history'. In recent school education, 'Probability and Statistics' education has been emphasized, and as a result, the study has conducted a study on permutations. Permutation is used in a variety of fields, and in this study, we looked at the Derangement. The results of this study are as follows. First, analysis was made at current school mathematics level and academic mathematics level for Derangement. Second, the historical development process of derangement was examined. Third, based on this, the research direction of this study was decided to be 'Derangement number's triangle(Rencontres number's triangle)', and the inquiry for education expansion was carried out. Fourth, we have presented data on concrete educational expansion by discovering various mathematical facts of the Derangement number's triangle. We hope that the results of this study will provide meaningful implications for the application of mathematics and the presentation of new inquiry directions.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.147-166
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• 2007

This study is about the law of cosines. It dealt with its historical origin and the developmental process of the age of Greece, Islam and Modern age. Especially, we tried to find out how the extension of the law of cosines for spherical triangles and tetrahedron from the law of cosines for plane was done. On the basis of this analysis, we investigated how the law of cosines was generated and proved it through the logical demonstration and mathematical induction. This made us find out the mathematical meaning of mathematical concepts.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.187-206
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• 2009

On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation, $\frac{1}{a}$notation, $\sqrt{a}$-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.