• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.791-797
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• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.645-668
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• 2014

This study was designed to gain insights into contemporary secondary mathematics curriculum revision in Korea. The two secondary mathematics curriculum reports submitted in the 1920s, the Kilpatrick Reports and 1923 Reports were compared and contrasted as the origin of recent math wars, and their backgrounds, committee members, viewpoints of math and math education and contents were analyzed to understand the perspectives of the two extreeme parts. Kilpatrick Reports was selected at that time, but nevertheless 1923 Report had taken a role of guiding secondary mathematics in US until the New Math era. The direction and process of mathematics curriculum revision were suggested based on the analysis of reports' short- and long-term influences. A close examination of the curriculum revision process in US and in Korea and the implications from the results are also included in the suggestion.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.365-380
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• 1998

Structualist view distinguishes structure(reality) from phenomenon(appearance). Phenomenon is the outside aspect of structure and structure is the inside aspect of phenomenon. From the structualist view, the knowledge could e divided into two parts, the appearance of knowledge(the outside aspect of knowledge)and the structure of knowledge(the inside aspect of knowledge). Structualist view advices teachers to understand knowledge more totally from the inside-outside viewpoint, and not to teach mere the one aspect of knowledge, especially the outside aspect of knowledge, that is, the written expressions in textbook, but to teach the inside and outside aspects fo knowledge totally. In the history of mathematics education, the attempts to teach the structure of knowledge were flourishing in the period of discipline-centered curriculum. 'New Math movement' represents the attempts. The advocators of New Math, however, did not succeed sufficiently to understand the inside-outside view which the term the structure of knowledge represents, and failed to make mathematics teachers to understand the view well. Their attention was put on to introduce the modern mathematics to school math rather than to understand the educational and epistemological perspective which the term the structure of knowledge represents. To teach the structure of knowledge, mathematics teacher should be able to understand mathematical knowledge more totally from the inside-outside viewpoint. Especially, s/he should not regard the outside aspect of mathematical knowledge written in textbook as the totality of knowledge, but inquire into the inside aspect of mathematical knowledge from the outside aspect of mathematical knowledge.

• Journal for History of Mathematics
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• v.28 no.2
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• pp.65-72
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• 2015

The Joseon dynasty (1392-1910) is basically an agricultural country and therefore, the main source of her national revenue is the farmland tax. Thus the farmland tax system becomes the most important state affair. The 4th king Sejong establishes an office for a new law of the tax in 1443 and adopts the farmland tax system in 1444 which is legalized in Gyeongguk Daejeon (1469), the complete code of law of the dynasty. The law was amended in the 19th king Sukjong era. Jo Tae-gu mentioned the new system in his book Juseo Gwan-gyeon (1718) which is also included in Sok Daejeon (1744). Investigating the mathematical structures of the two systems, we show that the systems involve various aspects of mathematics and that the systems are the most precise applications of mathematics in the Joseon dynasty.

• Journal for History of Mathematics
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• v.27 no.1
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• pp.1-12
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• 2014

From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.

• Journal of the Korean School Mathematics Society
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• v.3 no.2
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• pp.155-164
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• 2000

The future society will demand that enables one to solve in many fields by connecting various informations in many fields and then creating his own information. In the coming society, creativeness will be regarded much important. This ability can be developed with materials through group activities experimental class in math classes. This classes using these materials are not teacher-oriented, explanatory classes but student-oriented ones. They offer students opportunities to think by themselves and expand their potential abilities. They are suitable for rising and keeping student's interests. Therefore experimental classes through group activities enable students to think mathematically and make them recognize the importance of mathematical approach by letting them work connecting other subjects or things in real life. They can develop not only expressive, communicative ability and cooperative spirit, but also the ability to transcend the class itself and then reorganize facts in new insights. Besides, math classes with experiments can arouse student's curiosity familiarizing them with mathematics. Moreover, they can expand student's originative and problem-solving abilities.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.177-183
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• 2003

In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [Rings of operators. W. A. Benjamin, Inc., New York, 1968] to abstract the algebra of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p.-rings were introduced by Hattori [A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17 (1960) 147-158] to study the torsion theory. The purpose of this paper is to introduce the near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from ring case, and to extend a results of Armendariz [A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18 (1974), 470-473] and Jøndrup [p.p. rings and finitely generated flat ideals. Proc. Amer. Math. Soc. 28 (1971) 431-435].

• School Mathematics
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• v.14 no.4
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• pp.531-552
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• 2012

In December of 2009, General Guidelines of Curriculum Revised in 2009 was announced and research on corresponding mathematics curriculum revision has been initiated from that period. Finally, in August 2011, Mathematics Curriculum Revised in 2009 was announced. Based on the examination the backgrounds and the basic directions of revision newly reformed mathematics curriculum should be applied in math class effectively and efficiently. According to this purpose, this paper first of all finds out what are the major points or difficulties to be caused by managing 'Mathematics Curriculum Revised in 2009' according to the change of 'General Guidelines of Curriculum Revised in 2009'. They are i) the implementation of grade band system, ii) management of differentiated class, and iii) increasing or decreasing of 20% in math class hour. According to those three points to be changed and reinforced newly in new curriculum, this paper investigates the alternatives and policy of dealing with smoothly and efficiently those issues while solving the difficulties.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.589-623
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• 2015

This study is to find out a way to foster self-directed learning math skills for the low-income youth at child care centers. Taking advantage of EBS materials, we found the youth, low-income youth in particular, were positively influenced to learn mathematics in the way of self-directed and action learning. This program gives a model of the self-directed math learning using the EBS mathematics materials. From the survey of this study, we found see that students started to have a positive attitude for learning and they started to gain new mathematical concept, and improved their problem solving, reasoning, communication and representation skills with these new leaning environments. This study tells us that this type of cooperative learning could help them to have an objective assessment, and gave a positive impact on self-directed learning.

• School Mathematics
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• v.14 no.3
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• pp.315-330
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• 2012

Mathematics educators have tried to teach mathematics to all students who are at any mathematical level by differentiated math instruction from late 1990s in Korea. The common differentiated math instruction separates students into two or three groups according to their mathematical ability and then different activities and tasks are given to each group. This kind of instruction fosters negative attitudes to mathematics to low level students and fix them at low level. So I investigated new mathematics instruction considering able students and low attainers at the same time. This new method is based on using open problems in math class. All students can respond to an open problem in different ways. If teachers could relate all varieties of answers got from students at every level to build good understanding the concept which the problem target at, low attainers could move to their potential developmental levels. This kind of instruction can change low math attainers' negative attitudes to good ones to mathematics and foster their confidence in performing mathematics.