• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1101-1110
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• 2008

The present paper investigates about the formation of the logical thinking and the intuitive thinking in mathematical concepts with reference to secondary talented students (students aged 16$\sim$17 years). As a main result, we conclude that their preference between the logical and the intuitive thinking does not related to the distinction of the school level and sex, while their consistence between them relates.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.135-140
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• 2012

In this paper, we introduce the concepts of $DC^{p}_{k}$-spaces for maps which are the dual concepts of $C^{f}_{k}$-spaces for maps, and characterize $DC^{p}_{k}$-spaces for maps using the dual Gottlieb sets for maps and the LS cocategories.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• Honam Mathematical Journal
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• v.44 no.4
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• pp.628-635
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• 2022

For another study of soft context and soft concept closely related to formal context and formal concept, in this paper, we propose the notions of conditional concepts, decision concepts and soft decision context based on soft contexts. Subsequently, the notions of consistent soft decision context and consistent set are introduced, and some properties for consistent set of soft decision contexts are investigated.

• Journal for History of Mathematics
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• v.32 no.6
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• pp.281-299
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• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• Research in Mathematical Education
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• v.25 no.2
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• pp.99-115
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• 2022

This study examined difficulties middle school students have in learning mathematics and proposed a flipped classroom consisting of Khan Academy activities, small-group problem solving, and mathematical modeling to help improve their learning. A mixed-method approach was used to identify difficulties students have in learning mathematics, explore how the flipped classroom helped them reduce the learning difficulties identified, and examine if there were differences in students' mathematics achievement and their affective characteristics after participating in the flipped classroom. Qualitative analyses showed that students had difficulties in understanding mathematical concepts and finding effective ways to learn as well as negative views towards learning mathematics. This study also found that each activity of the flipped classroom had a different impact on student learning. Before class, the Khan Academy activities were most likely to help students understand mathematical concepts. In class, small-group problem solving activities were most helpful for students who had trouble finding effective learning methods and environments. Mathematical modeling activities were most likely effective in changing students' negative views towards mathematics. A quantitative analysis showed that the flipped classroom not only significantly improved the students' mathematics achievement, but also positively affected their confidence and motivation and how much they valued learning mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Research in Mathematical Education
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• v.16 no.1
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• pp.79-90
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• 2012

This research investigated if the embodied symbol using a turtle metaphor in a microworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners' concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

• East Asian mathematical journal
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• v.32 no.4
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• pp.443-464
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• 2016

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students' mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.

• Korean Journal of Childcare and Education
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• v.15 no.3
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• pp.115-133
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• 2019

Objective: The purpose of the study was to develop a mathematics education program utilizing food to improve the mathematical abilities of 4-year-olds and to analyze the effects of this program on 4-years-olds' mathematical concepts (number and operation, algebra, geometry, measurement, data analysis, and probability). Methods: The study selected 30 4-year-olds from two daycare centers located in K city. The experimental group (N=15) participated in the mathematics education program utilizing food, 10 times for five weeks, while the comparative group (N=15) participated in the seasonal mathematics education program based on the Nuri Curriculum. The activities of this intervention program were designed to cover all domains of Mathematical Exploratory areas in the Nuri Curriculum. For data processing and analysis, pre-test and post-test score differences between the two groups were analyzed through MANCOVA. Results: The experimental group had significantly higher scores on five mathematical concepts compared with the control group. A mathematics education program utilizing food had the positive effect of improving 4-year-olds' mathematical ability. Conclusion/Implications: Mathematic education programs utilizing food are recommended as necessary pedagogical data to develop the mathematical abilities of children in education centers, families, or relating to parenting education.