• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.01a
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• pp.410-420
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• 2001

A primitive conceptualization is defined as the set of all intended situations. A non-primitive conceptualization is defined as the set of all the pairs every of which consists of an intended knowledge system and the set of all the situations admitted by the knowledge system. The reality of a domain is considered as the set of all the situation which have ever taken place in the past, are taking place now and will take place in the future. A conceptualization is defined as precise if the set of intended situations is equal to the domain reality. The representation of various elements of a domain ontology in a model of the ontology is considered. These elements are terms for situation description and situations themselves, terms for knowledge description and knowledge systems themselves, mathematical terms and constructions, auxiliary terms and ontological agreements. It has been shown that any ontology representing a conceptualization has to be non-primitive if either (1) a conceptualization contains intended situations of different structures, or (2) a conceptualization contains concepts designated by terms for knowledge description, or (3) a conceptualization contains concept classes and determines properties of the concepts belonging to these classes, but the concepts themselves are introduced by domain knowledge, or (4) some restrictions on meanings of terms for situation description in a conceptualization depend on the meaning of terms for knowledge description.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.207-219
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• 2007

Students have a hard time with a formal proof, which is one of most important part in mathematics education. They were taught the proof with algebraic visual materials using technology and specialized visual materials. But, they experienced the difficulty in justifying due to the lack of experimental recognition with the representation using technology. The specialized visual materials limited the extension of mathematics thinking of students because it worked only for the case that is fixed. In order to solve this type of problem, we made algebraic visual materials for 9th graders using technology and generalized visual materials so that students experience for themselves to help them to experience experimental justification, thus we recognized that they were improved in enhancing mathematical thinking.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.463-483
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• 2003

In the learning of mathematics, students experience the semiotic activities of representing and interpreting mathematical signs. We called these activities as the representing and interpreting of mathematical signs. On the foundation of Peirce's three elements of the sign, we analysed that students constructed the representamen to interpret the concept of correlation as for the object, "as one is taller, one's size of foot is larger" 4 middle school students who participated the gifted center in Seoul, arranged the statistical data, constructed their own representamen, and then learned the conventional signs as a result of the whole class discussion. In the process, students performed the detailed representing and interpreting of signs, depended on the templates of the known signs, and interpreted the process voluntarily. As the semiotic activities were taken place in this way, it was needed that mathematics teacher guided the representing and interpreting of mathematical signs so that the representation and the meaning of the sign were constructed each other, and that students endeavored to get the negotiation of the interpretants and the representamens, and to reach the conventional representing.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.67-86
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• 2011

This study aimed to examine first graders' recognition and thinking about mathematical patterns. To attain the goal, this paper analyzed 116 students' response with regard to repeating, growing, and changing patterns represented in both picture and number, and also analyzed four students' thinking process of the patterns through interview. It was found that students showed high recognition in repeating, growing, and changing patterns in order. Whereas there was no significant difference between picture and number representation in both repeating and growing patterns, pictures gained a bit higher scores than numbers in changing patterns. Also, according to the result of examining the thinking process by the patterns, students tended to consider the patterns as a bundle and tried to solve problems with counting strategies. The result of this paper provides an empirical foundation on how first graders recognize and think of various patterns.

• School Mathematics
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• v.13 no.3
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• pp.405-422
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• 2011

In this study, we consider the meaning of one-to-one correspondence through theoretical background under operation of matrix. On algebraic point of view, its significance is 'through one-to-one correspondence from a set with given structure, become a methods in order to induce an algebraic system in to a new set.' That is a key idea making isomorphic structure. Such process experiences necessity of mathematical fact, as well as the deep understanding of one-to-one correspon -dence. Also that becomes a base for develop a various mathematical concepts, such as matrix, exponential laws, symmetric difference, permutation and so on. This study help teachers and students to understand of mathematical concepts meaningfully and to facilitate teacher's professional development.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.573-588
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• 2014

How will the field of education react to the big data craze that has recently seeped into every aspect of society? To search for ways to use big data in mathematics education, this study first examined the concept of big data and examples of its application, and then pursued directions for future research in two ways. First, changes in the representation and acceptance of data are required because of changes in technology and the environment. In other words, the learning content and methodology of data treatment need to be changed by describing a myriad amount of data visually or by 'analyzing and inferring' data to provide data efficiently and clearly. Additionally, the mathematics education field needs to foster changes in curricula to facilitate the improvement of students' learning capacity in the 21st century. Second, it is necessary to more actively collect data on general education and not merely on teaching or learning to identify new information, pursue positive changes in the teaching and learning of mathematics, and stimulate interest and research in the field so that it can be used to make policy decisions regarding mathematics education.

• Communications of Mathematical Education
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• v.26 no.3
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• pp.317-338
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• 2012

This paper compared and contrasted the views of effective mathematics instruction by 223 elementary school teachers and 151 middle school mathematics teachers using a questionnaire with 4 main domains (i.e., curriculum and content, teaching and learning, classroom environment and atmosphere, and assessment) and a total of 48 sub-elements. The analysis of results showed that elementary school teachers put their priority on the curriculum and content domain, while middle school counterparts did on the teaching and learning domain. The teachers commonly agreed with instruction which fosters students' self-directed learning ability, reconstructs the curriculum tailored to students' diverse levels, and establishes appropriate interaction between the teacher and students. However, elementary school teachers agreed more than middle school teachers with regard to the 23 elements related to effective mathematics instruction. In contrast, middle school teachers agreed more than their counterparts as for only 2 elements (instruction fostering mathematical representation and instruction eliciting students' learning motivation). This paper includes suggestions and implications related to Korean teachers' perception of effective mathematics instruction.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.589-623
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• 2015

This study is to find out a way to foster self-directed learning math skills for the low-income youth at child care centers. Taking advantage of EBS materials, we found the youth, low-income youth in particular, were positively influenced to learn mathematics in the way of self-directed and action learning. This program gives a model of the self-directed math learning using the EBS mathematics materials. From the survey of this study, we found see that students started to have a positive attitude for learning and they started to gain new mathematical concept, and improved their problem solving, reasoning, communication and representation skills with these new leaning environments. This study tells us that this type of cooperative learning could help them to have an objective assessment, and gave a positive impact on self-directed learning.

• School Mathematics
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• v.19 no.3
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• pp.553-570
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• 2017

The purpose of this study was to gain insights into investigating the feasibility on integrating computational thinking(CT) into school mathematics. Definitions and the components of CT were varied among studies. In this study, CT in mathematics was focused on thinking related with mathematical problem solving under ICT supportive environment where computing tools are available to students to solve problems and verify their answers. The focus is not given on the computing environment itself but on CT in mathematics education. For integrating CT into mathematical problem solving, providing computing environment, understanding of tools and supportive curriculum revisions for integration are essential. Coding with language specially developed for mathematics education such as LOGO, and solving realistic mathematical problems using S/W such as Excel in mathematics classrooms, or integrating CT into math under STEAM contexts are suggested for integration CT into math education. Several conditions for the integration were discussed in this paper.

• Journal of the military operations research society of Korea
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• v.29 no.2
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• pp.61-80
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• 2003

A fire sequencing problem is considered. Fire sequencing problem is a kind of scheduling problem that seeks to minimize the overall time span under a result of weapon­target allocation problem. The assigned weapons should impact a target simultaneously and a weapon cannot transfer the firing against another target before all planned rounds are consumed. The computational complexity of the fire sequencing problem is strongly NP­complete even if the number of weapons is two, so it is difficult to get the optimal solution in a reasonable time by the mathematical programming approach. Therefore, a genetic algorithm is adopted as a solution method, in which the representation of the solution, crossover and mutation strategies are applied on a specific condition. Computational results using randomly generated data are presented. We compared the solutions given by CPLEX and the genetic algorithm. Above $7(weapon){\times}15(target)$ size problems, CPLEX could not solve the problem even if we take enough time to solve the problem since the required memory size increases dramatically as the number of nodes expands. On the other hand, genetic algorithm approach solves all experimental problems very quickly and gives good solution quality.