• Journal for History of Mathematics
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• v.21 no.1
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• pp.79-96
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• 2008

In early 21st century, universities in Korea has been asked the new roles according to the changes of educational and social environment. With Korea's NURI and Brain Korea 21 project support, some chosen research oriented universities now should produce "teacher of teachers". We look 100 years back America's mathematics and see many resemblances between the status of US mathematics at that time and the current status of Korean mathematics, and find some answer for that. E. H. Moore had produced many good research mathematicians through his laboratory teaching techniques. R. L. Moore was his third PhD students. He developed his Texas/Moore method. In this article, we analyze what R. L. Moore had done through his American School of Topology and Moore method. We consider the meaning that early University of Texas case gives us in PBL(Problem Based Learning) process.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.865-876
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• 2010

We have examined the modified Moore methods that were applied to college mathematics courses in several researches. We introduce, compare and analyze the concrete teaching methods that the researchers conducted in various modified Moore methods, and propose the appropriate form of modified Moore method most suitable for the present situations of the mathematics and related departments in Korea.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.29-33
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• 2008

• Journal for History of Mathematics
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• v.22 no.3
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• pp.255-272
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• 2009

R. L. Moore's discovery methods are known to have been very effective with certain classes of students. However when the method was attempted by others at the undergraduate level, the results sometimes were disappointing. In this article we study the history of developing modified Moore methods with small group discovery method for the purpose of undergraduate education, and then we discuss some educational point of view in our universities.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.259-282
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• 2010

In this paper, we introduce a modified Moore Method designed for the multivariable calculus course, and discuss about the effective teaching and learning method by observing the changes in the understanding of students' learning and the effects on students' learning in the class implemented by this modified Moore Method. This teaching experiment research was conducted with the 15 students who took the multivariable calculus course offered as a 3 week summer session in 2008 at H University. To guide the students' active preparation, stepwise course materials structured in the form of questions on the important mathematical notions were provided to the students in advance. We observed the process of the students' small-group collaborative learning activities and their presentations in the class, and analysed the students' class journals collected at the end of every lecture and the survey carried out at the end of the course. The analysis of these results show that the students have come to recognize that a deeper understanding of the subjects are possible through their active process of search and discovery, and the discussion among the peers and teaching each other allowed a variety of learning experiences and reflective thinking.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.127-146
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• 2007

From 1876 to 1883, British mathematician James Joseph Sylvester worked as the founding head of Mathematics Department at the Johns Hopkins University which has been known as America's first school of mathematical research. Sylvester established the American Journal of Mathematics, the first sustained mathematics research journal in the United States. It is natural that we think this is the most exciting and important period in American mathematics. But we found out that the International Congress of Mathematicians held at the World's Columbian Exposition in Chicago, August 21-26, 1893 was the real turning point in American's dedication to mathematical research. The University of Chicago was founded in 1890 by the American Baptist Education Society and John D. Rockefeller. The founding head of mathematics department Eliakim Hastings Moore was the one who produced many excellent American mathematics Ph.D's in early stage. Many of Moore's students contributed to build up real American mathematics research power in early 20 century The University also has a well-deserved reputation as the "teacher of teachers". Beginning with Sylvester, we analyze what E.H. Moore had done as a teacher and a head of the new department that produced many mathematical talents such as L.E. Dickson(1896), H. Slaught(1898), O. Veblen(1903), R.L. Moore(1905), G.D. Birkhoff(1907), T.H. Hilderbrants(1910), E.W. Chittenden(1912) who made the history of American mathematics. In this article, we study how Moore's vision, new system and new way of teaching influenced American mathematical society at early stage of the top class mathematical research. and the meaning that early University of Chicago case gave.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• Journal of the Korean Magnetics Society
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• v.6 no.4
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• pp.272-276
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• 1996

1948년 Harvard 대학의 Purcell교수와 Stanford 대학의 Bloch교수가 핵자기 공명(Nuclear Magnetic Resonance : NMR) 현상을 발견한 이래로 NMR은 물질의 분자단위에서 화학적, 물리학적 성질을 밝혀내는 탁월한 방법으로 널리 이용되어 왔다. NMR 현상을 이용한 영상촬영법(Magnetic Resonance Imaging, MRI)은 1970년대초 Lauterber와 Damadian 교수가 처음 영상을 얻을 수 있다는 가능성을 제시한 이후 급속한 발전을 하여 1980년대 초에는 Moore와 Holland에 의해 의학분야에 응용 가능할 정도의 영상이 얻어졌다. 1980년대 중반부터 상용화 되었으며 최근 그 기법도 NMR현상과 연관된 파라미터인 $T_{1}$, $T_{2}$는 물론 혈류의 속도, 자화율, 확산(Diffusion), Perfusion의 영상기법을 비롯해 혈관조영술(MR Angiography), 뇌기능영상(Functional Imaging)등 과거에는 상상도 할 수 없었던 다양한 영상기법 개발되었다. 여기서는 먼저 MRI의 원리를 설명한 후 MRI의 여러 촬영기법들과 그 응용에 관해 설명하겠다.