• Journal of the Korean School Mathematics Society
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• v.18 no.2
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• pp.223-240
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• 2015

This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.335-346
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• 2004

PtolemyII is an environment that supports heterogeneous modeling and design of concurrent systems such as embedded system. PtolemyII has several Domains which are physical rules to determine the way of communicating between components. PtolemyII has 11 domains such as PetriNet, Timed Multitasking, SR etc. Components of System can be specified using appropriate domains for their properties. Communicating Sequential Processes(CSP) is implemented as formally designed CSP domain, in PtolemyII. But CCS didn't be implemented as a domain. It is a kind of Process Algebra language which can be used for specifying and verifying concurrent systems formally. Thus, in this paper we implemented CCS domain. And that permitted developers using PtolemyII to use the same modeling pattern used in PtolemyII and to make system specifications in the base of the formal semantics of CCS. This caused the diversity of PtolemyII domains and the power of expression was improved. This paper will explain the structure of CCS domain implemented in PtolemyII and the way of implementing it.

• Journal of Computing Science and Engineering
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• v.11 no.4
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• pp.130-141
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• 2017

Feature selection is one of the most challenging problems of pattern recognition and data mining. In this paper, a feature selection algorithm based on an improved version of binary differential evolution is proposed. The method simultaneously optimizes two feature selection criteria, namely, set approximation accuracy of rough set theory and relational algebra based derived score, in order to select the most relevant feature subset from an entire feature set. Superiority of the proposed method over other state-of-the-art methods is confirmed by experimental results, which is conducted over seven publicly available benchmark datasets of different characteristics such as a low number of objects with a high number of features, and a high number of objects with a low number of features.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.337-342
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• 1995

A semiring is a binary system $(S, +, \times)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $\times$ distributes over +, 0 $\times s s \times 0 = 0$ for all s in S, and $1 \neq 0$. Usually S denotes the system and $\times$ is denoted by juxtaposition. If $(S,\times)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.

• 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.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.137-164
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• 2008

Given the importance of early experience in algebraic thinking, we designed six consecutive lessons in which $4^{th}$ graders were encouraged to recognize patterns in the process of finding the relationships between two quantities and to represent a given problem with various mathematical models. The results showed that students were able to recognize patterns through concrete activities with manipulative materials and employ various mathematical models to represent a given problem situation. While students were able to represent a problem situation with algebraic expressions, they had difficulties in using the equal sign and letters for the unknown value while they attempted to generalize a pattern. This paper concludes with some implications on how to connect algebraic thinking with students' arithmetic or informal thinking in a meaningful way, and how to approach algebra at the elementary school level.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.2
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• pp.177-187
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• 1999

Up to date, in many application fields of GSIS, we usually have used vector-based spatial overlay or grid-based spatial algebra for extraction and analysis of spatial data. But, because these methods are based on traditional crisp set, concept which is used these methods. shows that many kinds of spatial data are partitioned with sharp boundary. That is not agree with spatial distribution pattern of data in the real world. Therefore, it has a error that a region or object is restricted within only one attribution (One-Entity-one-value). In this study, for improving previous methods that deal with spatial data based on crisp set, we are suggested to apply into spatial overlay process the concept of fuzzy set which is good for expressing the boundary vagueness or ambiguity of spatial data. two methods be given. First method is a fuzzy interval partition by fuzzy subsets in case of spatially continuous data, and second method is fuzzy boundary set applied on categorical data. with a case study to get a land suitability map for the development site selection of new town, we compared results between Boolean analysis method and fuzzy spatial overlay method. And as a result, we could find out that suitability map using fuzzy spatial overlay method provide more reasonable information about development site of new town, and is more adequate type in the aspect of presentation.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• School Mathematics
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• v.9 no.2
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• pp.223-240
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• 2007

The purpose of this study was to investigate the degree to which the middle school mathematics curriculum matched the item difficulty levels of representative mathematics items. The items used in this study were developed for the National Assessment of Educational Achievement. Ranks for difficulty values of the 60 multiple-choice item were calculated via both Classical Test Theory and Item Response Theory and correlated with the rank order of the mathematics content and cognitive domains sequence. There are six content domains; number and operation, algebra, measurement, figure, pattern and function, and probability and statistics. The cognitive domains include computation, understanding, reasoning and problem-solving. Results suggest a congruence between cognitive domain's sequence and item difficulty levels of items based on that sequence. This finding indicates that the linear or hierarchical assumptions concerning the sequence appears to be reasonable. The characteristics of items that were exceptions to this trend were addressed.