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강옥기 ( Ok Ki Kang ),김수철 ( Soo Cheol Kim ),이환철 ( Hwan Chul Lee ) 한국수학교육학회 2013 수학교육 Vol.52 No.2
The Ministry of Education Science and Technology represented National Mathematics Education Advance plan in 2012. The plan is focused on reinforcing mathematics education, improving understanding about mathematics, and enhancing self-guided learning. After the National Mathematics Education Advance Plan new middle school mathematics textbooks have been developed and they will be used from 2013. The purpose of this study is to analyse those mathematics textbooks to find how the National Mathematics Education Advance Plan is affecled lo the mathematics This study found some important aspects affected from the Advance Plan to these textbooks and some implications for the future Korean mathematics education.
오채환,강옥기,이상욱,Oh, Chae-Hwan,Kang, Ok-Ki,Ree, Sang-Wook 한국수학사학회 2011 Journal for history of mathematics Vol.24 No.4
20세기 초반에 등장한 수학기초론의 주류 세 학파 (직관주의 논리주의 형식주의)는 상호 대립관계를 보인다. 큰 틀에서 볼 때, 논리주의는 프레게를 계승하는 입장이다. 이와 대립관계의 기초론 중 하나인 직관주의는 구성주의 수학철학의 주축으로 평가된다. 그리고 직관주의가 터를 닦은 구성주의 수학철학을 후속 개진시킨 주역은 의미론적 반실 재론을 주창한 마이클 더밋이다. 따라서 외형상으로는 더밋이 직관주의를 계승하는 후계세대처럼 여겨질 수 있지만 그의 철학적 기반은 분명 프레게이다. 더밋이 논리주의가 아닌 직관주의 계열에 합류한 사실의 속내는 구성주의 내부의 두 입장 (즉, 직관주의와 반실재론) 이 보이는 배중률을 둘러싼 태도의 드러난 일치뿐만 아니라 가려진 차이까지 헤아려질 때 해명될 수 있다고 본다. 본고는 이런 해명을 통해 구성주의 수학철학에 대한 이해도 한층 더할 수 있다는 판단에 따른 제안적 노력이다. Constructionists believe that mathematical knowledge is obtained by a series of purely mental constructions, with all mathematical objects existing only in the mind of the mathematician. But constructivism runs the risk of rejecting the classical laws of logic, especially the principle of bivalence and L. E. M.(Law of the Excluded Middle). This philosophy of mathematics also does not take into account the external world, and when it is taken to extremes it can mean that there is no possibility of communication from one mind to another. Two constructionists, Brouwer and Dummett, are common in rejecting the L. E. M. as a basic law of logic. As indicated by Dummett, those who first realized that rejecting realism entailed rejecting classical logic were the intuitionists of the school of Brouwer. However for Dummett, the debate between realists and antirealists is in fact a debate about semantics - about how language gets its meaning. This difference of initial viewpoints between the two constructionists makes Brouwer the intuitionist and Dummettthe the semantic anti-realist. This paper is confined to show that Dummett's proposal in favor of intuitionism differs from that of Brouwer. Brouwer's intuitionism maintained that the meaning of a mathematical sentence is essentially private and incommunicable. In contrast, Dummett's semantic anti-realism argument stresses the public and communicable character of the meaning of mathematical sentences.
강옥기 성균관대학교 기초과학연구소 1993 論文集 Vol.44 No.1
Korean Ministry of Education developed 6^th mathematics curriculum which will be executed from 1995. But this curriculum is very limited for the coming society which requires high technologies and informations. This study discussed and suggested some tasks to be solved to develop Korean mathematics education. The results are as follows : First, mathematics curriculum should be developed to emphasize problem solving, introduce discrete mathematics, and apply calculators and computers for mathematics instructions. Second, mathematics textbooks should be reformed to have creative features for various individual differences and courses. Regulations for teaching instruments and equipments should be revised for each school should purchase effective instruments and equipments for mathematics instruction. Third, evaluation directions of mathematics education in mathematics classrooms and for college enterance examinations should be changed to assess basic and principal mathematics knowledges, mathematical powers, and positive attitudes toward mathematics. Fourth, teachers' colleges should develop new curriculum focused on training good teachers. For the department of mathematics education, at least 9 units of compulsory and 6 units of optional mathematics education subjects are required.
강옥기 성균관대학교 기초과학연구소 1992 論文集 Vol.43 No.1
Nowadays the Ministry of Education is reforming the 6th curriculum for elementary and secondary schools. Mathematics curriculum is also reformed together with other subjects. This paper aims to suggest some fundamental directions should be considered carefully in reforming mathematics curriculum. To do this work, the researcher has looked over the history of matheamtics curriculum, analyzed some problems of current matheamtics curriculum, and studied the new trends of matheamatics education and curriculum of a few developed countries. The new fundamental directions for mathematics education suggested here are as follows : (1) Reasoning and problem solving should be emphasized. (2) Practical aspects of mathematics should be emphasized. (3) Calculators and computers should be used as tools for mathematics education. (4) Opportunities for individuals study suitable mathematics according to their courses and abilities should be provided. (5) Fundamental mathematics for future societies should be taught. (b) Various and available teaching and evaluation methods should be used in matheamtics classes. Especially, mathematics courses for high school students should be as follows : common mathematics for all high school students, mathematics Ⅰ for the students who completed common mathematics and want to enter colleges, mathematics Ⅱ for the students who completed mathematics Ⅰ and want to enter natural science course of colleges, practical mathematics for the students who want to work in societies after high school diploma, and mathematics Ⅲ for the students who completed mathematics Ⅱ and have high abilities in mathematics. The new directions suggested in this paper are expected to be realized in the 6th mathematics curriculum or in the next curriculum.