• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• East Asian mathematical journal
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• v.26 no.2
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• pp.319-336
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• 2010

There are serious difficulties with management of general mathematics education courses because of enormous gap between freshman's ability of mathematics and lack of problem solving ability. In this paper, we try to find methods so we can reduce the difficulties. By utilizing students survey, management of Mathematics Cafe and setting example classes for Calculus and Linear Algebra we suggest effective management strategies and teaching-learning methods.

• Research in Mathematical Education
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• v.6 no.2
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• pp.123-133
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• 2002

The authors examined a college mathematics professor's change process in teaching practice by analyzing the teacher's reflective journal. Her change engaged cooperative learning method in a college Algebra course and was geared toward the reform-oriented methods. The change processes were revealed as a bumpy road that was full of struggles and challenges to both the teacher and students. The analysis also showed that a reflective journey needed a proper means and support system from a teacher's environment such as institution. This research clearly showed that brining a genuine change in teaching practice toward a broad educational goal was a combined effort among the participants of education.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• International Journal of Computer Science & Network Security
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• v.22 no.5
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• pp.255-265
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• 2022

Educational programs for students with intellectual disabilities have undergone drastic changes in pursuit of the general curriculum. Accordingly, teachers in various fields, including mathematics, strive to find effective methods that enhance learning. The objective of this systematic review is to examine the field of teaching mathematics to students with intellectual disabilities to investigate relevant effective teaching strategies and required teaching skills. To achieve this goal, studies published during the period 2018-2021 were reviewed. Findings indicate the inclusion of nine studies that met the inclusion criteria out of 55 studies. The included studies found that the system of least prompts (SLP) in conjunction with feedback and error correction, and schema-based instruction are generally the most effective strategies in teaching mathematical skills to students with intellectual disabilities. Addition is the most targeted skill, followed by subtraction and algebra problem solving. The least targeted skills are multiplication, recognition of geometric shapes, calculating price after discount, rapid recognition of numbers, and rapid problem solving. The paper provides recommendations and suggests venues of future research.

• Annual Conference of KIPS
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• 2008.11a
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• pp.722-725
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• 2008

복합질환(complex disease)의 원인과 작용 모델을 찾기 위해 여러 가지 통계적인 방법들과 기계 학습(machine learning)의 방법 등이 사용되고 있다. 소수 SNP의 작용모델을 찾는 방법은 많이 알려져 있지만 다수 SNP의 작용 모델을 효과적으로 찾는 방법은 거의 연구되어 있지 않다. 본 연구에서는 원인 SNP들의 작용을 부울 식(boolean expression)으로 나타내고, 유전 알고리즘(genetic algorithm)을 이용하여 예측 정확도가 높은 부울 식을 구성하였으며 실제 자료와 생성된 자료에 대하여 제안한 모델의 성능을 측정하였다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.2
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• pp.151-164
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• 2023

Recently, the development of quantum computers means a great threat to existing public key system based on discrete algebra problems or factorization problems. Accordingly, NIST is currently in the process of contesting and screening PQC(Post Quantum Cryptography) that can be implemented in both the computing environment and the upcoming quantum computing environment. Among them, SIKE is the only Isogeny-based cipher and has the advantage of a shorter public key compared to other PQC with the same safety. However, like conventional cryptographic algorithms, all quantum-resistant ciphers must be safe for existing cryptanlysis. In this paper, we studied power analysis-based cryptographic analysis techniques for SIKE, and notably we analyzed SIKE through wavelet transformation and deep learning-based clustering power analysis. As a result, the analysis success rate was close to 100% even in SIKE with applied masking response techniques that defend the accuracy of existing clustering power analysis techniques to around 50%, and it was confirmed that was the strongest attack on SIKE.

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.27-43
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• 2007

The aim of this paper is to develop a web-based learning system in order to motivate college students in the area of science and engineering to study college calculus. We designed and developed web-based contents, named MathBooster, using Mathematica, webMathematica and phpMath taking advantages of rapid computation and symbolic computation. The features of MathBooster consists of four parts: graphical representation of calculus concepts, textual illustrations of conceptual understanding, example-based step-by-step learning with phpMath, and quizzes with diagnostic feedback. After the MathBooster was practiced with engineering students, the formative evaluation was conducted with survey items composed in four categories: user responses, screen layout, practicing examples and diagnostic feedback in solving quizzes. The overall level of user satisfaction was statistically measured using SPSS. Those results indicate which parts of MathBooster are needed for future enhancement.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.153-176
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• 2010

The purpose of this study is to rethink the importance of manipulative materials and to extract of manipulative materials program and its application methods. Activity, construction, and operation is stressed in the elementary mathematics. For this, various technological tools and manipulative materials is emphasized in mathematics teaching-learning methods. Applications of manipulative materials in the elementary mathematics is gradually increased together with curriculum revisions and textbook developments. As a result, tangram, geo-board etc., many tools ate introduces to school mathematics. This study is executed in this contexts. To achieve this, We introduce Australian 'Maths With Attitude' program. This program is composed of the primary level and secondary level. Each level consists of four domains - Number & Computation, Space & Logic, Chance & Measurement, Pattern & Algebra -, and each domains is made up of 20 tasks(i.e. manipulative materials) and programs. This study takes the focus to 5-6 grades programs in the mid of the primary level. First, We introduce 'Monkeys & Bananas'(Number & Computation) and 'Triangles & Colours' (Pattern & Algebra) tasks, and investigate the examples of lessons using these tasks. Second, We think the probability of these tasks' application and draw examples in the elementary mathematic textbooks. Through this works, We respect teaching-learning methods is rich and various in the elementary mathematics lessons.

• School Mathematics
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• v.6 no.1
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• pp.1-19
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• 2004

Recently, we have been listening such a words, that is, the crisis of public education through the mass communication such as newspaper or broadcasting. This means that we didn't have an enough opportunity to think it over about good education programme which the education of school can be normalized or the design of curriculum in the current problems such as overcrowded class, teacher and poor finance which is not still solved. As we know, it is true that the older generation is familiar with the rote learning which was under the control of behaviorism for about three hundred years. Fortunately, The 7th curriculum which had made public by the ministry of education on 30 Dec. 1997 have changed so many things such as real life based or activity based and so on. But it still leaves something to be desired in reflecting the demand of teachers of field. Taking into account this real situation, I have wondered how they run curriculum and how math learning programme of lower grade is different with ours in New Zealand, etc and so I had tried to find some suggestive points through the comparison of curriculum and text between Korea and New Zealand. But, if we want to compare all the strands of curriculum between two countries, it is too global and so in this paper, we deal with only number and operations(number), measurement, figure(geometry), equation and patter(algebra), probability and statistics(statistics) which are dealt with more comparatively in the lower grade of primary school. Because the main purpose of this paper is a comparison and analysis of the curriculum and math learning program of the lower grade in the primary school between two countries and so we compare global characteristics of education system and curriculum between two countries, at first and then we dealt with the very core part of the content of New Zealand curriculum within the ranges of level 1, 2 and 3 and global characteristics of learning program simultaneously.