• Journal for History of Mathematics
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• v.18 no.2
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• pp.23-30
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• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• Cartoon and Animation Studies
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• s.37
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• pp.393-411
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• 2014

The volume of world market for serious game in year 2015 is expected to be about 9.6 trillion, and the volume of educational serious game market is expected to surpass half of the whole serious game market. In Korea, the development of game for educational purpose has dominated around the education enterprises since late 90s. In 2008, 'Serious Game Forum' was founded led by the Ministry of Culture, Sports, and Tourism with experts from many fields in the society and there were progressing of making policies and plans for potential development of the serious game industry, but the effects were not successful than expected. In 2012, the Ministry of Education, Science, and Technology announced commercialization policy of digital textbook by 2015 and the serious game for educational purpose got attention again. Then, the serious game market became more vigorous with the dispersion of smart devices.13) As a result, the serious games on the smart devices or interlocking between the online and smart devices became an important issue in development rather than the online only serious games. Math field has international competitive power through export in the educational serious game market which takes more than half of the serious game market. Therefore, developing serious game for math education is a good area to raise competitiveness in domestic and international game industries. Moreover, it has no received preferences from students and parents although it has high potential for positive change of individuals and society. The reason is that students recognize it as educational content rather than a game and they avoid it, while parents recognize it as game but not an education. This phenomenon happens because the game elements and educational elements are not properly mixed but focused only on education or emphasized only the fun factors of game when it was developed. Therefore, the purpose of this research is to suggest a direction of developing serious games effectively combining with elementary math for elementary students to get interested in math while playing games. The research will analyze the current elementary math textbooks and find contents which may be combined with the game genre that elementary students enjoy playing these days. This research received advice from serious game developers and math education expert group to reflect the inclination of elementary school students, and respond to the demands from parents and educational institutions, and suggested a direction of developing serious games for effective math education.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.1-20
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• 2006

The administrative service in Chosun Dynasty relating to mathematics was carried out by the middle class(中人) mathematicians selected by the official selection examination(取才). They belong to HoJo(戶曹) department and their ranks are GyeSa(計士), ByulJe(別提), HunDo(訓導 = mathematics teacher), and GyoSu(敎授 = mathematics professor). We call them SanWon(算員). HunDo and GyoSu played very important role although their ranks are low, for they educate SanWon and manage the official selection examination. Using JuHakSeonSaengAn(籌學先生案, List of mathematics teachers) and JuHakIpGyukAn(籌學入格案, List of successful candidates in the official selection examination for mathematics), we investigate HunDo and GyoSu in Chosun Dynasty.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.443-458
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• 2011

There has been a lively discussion on improving Korean students' academic achievement and the imbalance in their recognition of the value of mathematics. In this context, there is a need for a program that enables the majority students who regards mathematics as a subject for the entrance examination to recognize the practicality and historicity of mathematics. Educational books on mathematics in everyday life or the history of mathematics are also expected to serve as an effective tool. In addition, Web 2.0 Map is another means of representing mathematics in everyday life and the history of mathematics in connection with the practical context. The active storytelling process in which mathematics in the practical context in mathematical educational books is represented in Web 2.0 Map is expected to help to understand in depth the practicality and historicity of mathematics. Nevertheless, mathematical educational books and Web 2.0 Map may lead to a considerable variety of outcomes and speeds if carrying out tasks depending on the student's competence and may have practical difficulties in being operated in class. These concerns, however, can be resolved through the creative activity programs adopted in conformance with the 2009 revised curriculum. Therefore, this study intends to develop a program for creating mathematical story maps through mathematical educational books and the Mashup of Web 2.0 Map in accordance with the process of developing activity programs. This study also intends to determine its effectiveness in enabling students to recognize the practical and historical values of mathematics.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.657-673
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• 2015

In this study, we are interested in the teachers' MCK about '$N{\div}0$' and MPCK in relation to the proper ways to teach it. Even though '$N{\div}0$' is not on the current curriculum and textbooks of elementary school mathematics, a few students sometimes ask a question about it because the division of the form '$a{\div}b$' is dealt in whole number including 0. Teacher's obvious understanding and appropriate guidance based on students' levels can avoid students' error and have positive effects on their subsequent learning. Therefore, we developed an interview form to investigate teachers' MCK about '$N{\div}0$' and MPCK of the proper ways to teach it and carried out individual interviews with 30 elementary school teachers. The results of the analysis of these interviews reveal that some teachers do not have proper MCK about '$N{\div}0$' and many of them have no idea on how to teach their students who are asking about '$N{\div}0$'. Based on our discussion of the results, we suggest some didactical implications.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.53-74
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• 2009

Black-out Game(Lightout, Merlin Game, ${\sigma}$+Game) is an interesting game on the chessboard, when you click a button with black or white color, it changes color of itself and other buttons who shares edges. With this rule, we win the game when we have a chessboard with all same color after we click some of the buttons of it. Pretty much of research has been made on founding the winnable strategy for this type of game. In this paper, we first introduce a history of mathematical modeling on this game. Then we develop an algorithm to offer a winnable blackout game of any size. Our tools also show our new algorithm works. Finally, we show how we can use this game in mathematics education.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.31-46
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• 2011

[ ${\ll}$ ]n divisions of figures(${\pi}{\varepsilon}{\rho}{\acute{\iota}}\;{\delta}{\iota}{\alpha}{\iota}{\rho}{\acute{\varepsilon}}{\sigma}{\varepsilon}{\omega}{\nu}\;{\beta}{\iota}{\beta}{\lambda}{\acute{\iota}}o{\nu}$)${\gg}$ is one of the works written by Euclid, but little known to us. In this paper, we introduce this Euclid's book on divisions of figures with its brief history, analyse its contents, and discuss how to use it in mathematics education.

• Journal for History of Mathematics
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• v.27 no.5
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• pp.313-327
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• 2014

Based on the importance and the necessity of the study on history of mathematics and mathemtics education using history of mathematics for finding the cultural identity and values of our traditional mathematics, we refer to two types of teaching and learning methods utilizing 'WonYongSamBangHoGu', the second theme of 'SanSulGwanGyeon' written by Lee Sang Hyuk. First, we present various cases of 'WonYongSamBangHoGu' constructed utilizing kind of mathematics learning software, GeoGebra by high school freshmen belonging to the Education Centers for the Gifted in Seoul Science Park. Second, We modernly reinterpret the questions contained in 'WonYongSamBangHoGu' and show several developed items using it.

• Journal for History of Mathematics
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• v.31 no.3
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• pp.127-150
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• 2018

In spite of important researches and translational works of the Joseon mathematical treatises in the 80's and on, these results were almost out of reach to the school teachers as well as students due to the antiquity of their contents and the terms used. In order to make our traditional mathematics approachable to the middle and high school students, it will be educationally meaningful to reinterpret them tuned at the student's level using modern terminology and symbols. In this study, we reinterpreted 9 problems from Cheukryang Dohae, which is one of the representative mathematical books of Joseon Dynasty. We used the terminology and symbols from the school curriculum. We also reconstructed two of them using modern metrologies adapted to modern situations adding illustrations and photos, so that they are useful at the teaching site.