• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.389-400
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• 2013

The article makes a discussion to conceptualize a histo-genetic principle in the real historical view point. The classical histo-genetic principle appeared in 19th century was founded by the recapitulation law suggested by biologist Haeckel, but recently it was shown that the theory on it is no longer true. To establish the alternative rationale, several metaphoric characterizations from the history of mathematics are suggested: among them, problem solving, transition of conceptual knowledge to procedural knowledge, generalization, abstraction, circulation from phenomenon to substance, encapsulation to algebraic representation, change of epistemological view, formation of algorithm, conjecture-proof-refutation, swing between theory and application, and so on.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.285-294
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• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• The Journal of the Korea Contents Association
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• v.14 no.12
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• pp.1083-1099
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• 2014

The purpose of this study is to analyze that The arithmetic and algebraic word problem solving skill, strategy preference, and assessment ability of elementary preservice teachers is investigated using a statistical methodology. The research findings are as follows. First, elementary preservice teachers demonstrated logical and delicate problem solving behaviors in arithmetic and algebraic word problem solving. And elementary preservice teachers prefer to create a formula and table strategy in problem solving of the arithmetic question. Second, there was meaningful difference in the math and english elementary preservice teachers' appreciations with significant level of 0.05. And there was not meaningful difference in the 1 and 4 grade elementary preservice teachers' appreciations with significant level of ${\alpha}=0.05$. Results of the study suggest that teachers education course need to improve elementary preservice teachers' word problem solving skill, strategy preference, and assessment ability in the arithmetic and algebraic.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.261-275
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• 2011

We observed the process for solving linear equations of two 5th grade elementary students, who do not have any pre-knowledge about solving linear equation. The way of students' usage of fractional schemes and manipulations are closely observed. The change of their scheme adaptation are carefully analyzed while the coefficients and constants become complicated. The results showed that they used various fractional scheme and manipulations according to the coefficients and constants. Noticeably, they used repeating fractional schemes to establish the equivalence relation between unknowns and the given quantities. After establishing the relationship, equivalent fractions played important role. We expect the results of this study would help shorten the gap between the arithmetic and the algebraic thinking.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.2
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• pp.107-113
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• 2014

The derivation of optimal information from decision table is based on the concept of indiscernibility relation and approximation space in rough set. Because decision table is more likely to be susceptible to the superposition or inconsistency in decision table, the reduction of attributes is a important concept in knowledge representation. While complete subsets of the attribute's domain is considered in algebraic definition, incomplete subsets of the attribute's domain is considered in information-theoretic definition. Therefore there is a marked difference between algebraic and information-theoretic definition. This paper proposes a conditional entropy using rough set as information theoretical measures in order to deduct the optimal information which may contain condition attributes and decision attribute of information system and shows its effectiveness.

• The Mathematical Education
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• v.50 no.2
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.6
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• pp.28-35
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• 1998

Computer simulation technique has been applied on the various engineering fields to reduce cost and development period. On this paper, we introduce a crane analysis program. Using this program, we can predict reaction force of each part or supporting force of truck crane on a personal computer system with out exclusive knowledge of multi-body dynamics. In order to consider the effect of boom flexibility according to each working condition, flexible dynamic theory is applied to the program. Actual crane model is analyzed on special work condition using this program and the results are compared with those of rigid boom model.

• The Mathematical Education
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• v.42 no.5
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• pp.647-672
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• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.

• Journal of the Korean Society of Marine Environment & Safety
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• v.6 no.1
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• pp.23-33
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• 2000

This paper is concerned with finding the global optimal solutions for the redundancy optimization problems in series-parallel systems related with system safety. This study transforms the difficult problem, which is classified as a nonlinear integer problem, into a 0/1 IP(Integer Programming) by using binary integer variables. And the global optimal solution to this problem can be easily obtained by applying GAMS (General Algebraic Modeling System) to the transformed 0/1 IP. From computational results, we notice that GA(Genetic Algorithm) to this problem, which is, to our knowledge, known as a best algorithm, is poor in many cases.