• Journal of Elementary Mathematics Education in Korea
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• v.7 no.1
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• pp.45-64
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• 2003

This study analyzes divisor and multiple in elementary school mathematics textbooks published according to the first to the 7th curriculum, in a view point of the didactic transposition theory. In the first and second textbooks, the divisor and the multiple are taught in the chapter whose subject is on the calculations of the fractions. In the third and fourth textbooks, divisor and multiple became an independent chapter but instructed with the concept of set theory. In the fifth, the sixth, and the seventh textbooks, not only divisor multiple was educated as an independent chapter but also began to be instructed without any conjunction with set theory or a fractions. Especially, in the seventh textbook, the understanding through activities of students itself are strongly emphasized. The analysis on the each curriculum periods shows that the divisor and the multiple and the reduction of a fractions to the lowest terms and to a common denominator are treated at the same period. Learning activity elements are increase steadily as the textbooks and the mathematical systems are revised. The following conclusion can be deduced based on the textbook analysis and discussion for each curriculum periods. First, loaming instruction method also developed systematically with time. Second, teaching method of the divisor and multiple has been sophisticated during the 1st to 7th curriculum textbooks. And the variation of the teaching sequences of the divisor and multiple is identified. Third, we must present concrete models in real life and construct textbooks for students to abstract the concepts by themselves. Fourth, it is necessary to develop some didactics for students' contextualization and personalization of the greatest common divisor and least common multiple. Fifth, the 7th curriculum textbooks emphasize inquiries in real life which teaming activities by the student himself or herself.

• The Journal of Korean Philosophical History
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• no.52
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• pp.107-130
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• 2017

The purpose of this study is to catch the characteristics of the Hanju Yi Jinsang (寒洲 李震相, 1818~1886)'s thought of the 'Li(理)' through Hanju's view on the Ido-seol(理到說), the Toegye Yi Hwang(退溪 李滉, 1501~1570)'s latter Mulgyuk(物格) theory, and to establish the foundation for identifying the aspects of development about Toegye School's concept of Li from Toegye's Ido-seol. The Ido-seol was criticized for regarding Li - the immovable principle - as 'living thing'. Toegye School's scholars tried to solve this problem by translating the 'word' correctly. Hanju also translated the word 'Do(到)', the verb of 'Ido', as meaning of 'perfectly understood' based on his translation of the word 'Gyuk(格)' as 'Ku(究)'. On the other hand, he also regarded the principle-application structure of Li and the its characteristic the 'Li as Hwalmul(活物)' as the main point of Toegye's Neo-confucianism thought his methodology 'Three viewpoints[三看法]'. Before Hanju, scholars dose not have more opinion from the translation of the word, and it is too difficult to identifying their scholarly identity through their viewpoints on Ido-seol. On the other hand, Hanju thought that the lack of the idea for comprehensive approach between Xin(心) and Li(理) will cause the misunderstanding the relationship between Xin and Li. In this reason, he evaluated Toegye's Ido-seol based on the concept of 'One principle and its manifoldness[理一分殊]'. Consequently, he concatenated the characteristic of Xin which includes all things with concept of Mulgyuk, and emphasized that Xin which penetrates the principle of all things has the characteristic of 'One principle(理一)'.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.359-380
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• 2007

This study was conducted with two 6-graders to identify how were their proportional reasoning abilities, whether they evolved proportional thinking in a various context, and what had influence on their proportional thinking. The findings, as previous researches noted, suggested that the proportional expression obtaining by instrumental understanding could not provide rich opportunities for students to improve understanding about ratio and proportion and proportional reasoning abilities, while being useful for determining the answers. The students were able to solve proportional problems with incorporating their knowledge of divisor, multiples, and fraction into proportional situations, but not the lack of number sense. The students easily solved proportional problems experienced in math and other subjects but they did not notice proposition in problems with unfamiliar contexts.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.6
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• pp.113-119
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• 2001

In this paper, we propose an improved watershed algorithm that resolves the oversegmentation problem shown in the previous watershed algorithm and its modifications when the spatial video segmentation is performed. The principal idea of the proposed algorithm is merging the shallow catchment basin whose depth is less than a given threshold into the deeper one during flooding step. In the flooding process, the growth of the existing catchment basins and the extraction of newly flooded ones are accomplished. We present the experimental results using several MPEG test sequences in the last part of the paper. As a consequence, the proposed algorithm shows good segmentation results according to the thresholds applied by adding very small amount of calculations.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.1-25
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• 2008

The purpose of this study was to identify pre-service teachers' Pedagogical Content Knowledge (PCK) about decimal calculation. A written questionnaire was developed dealing with decimal calculation. A total of 152 pre-service teachers from 3 universities were selected for this study; they had taken an elementary mathematics teaching method course and had no teaching experience. The results were as follows: First, with regard to the method of decimal calculation, most pre-service teachers were familiar with algorithms introduced in the textbook. But with regard to the meaning of decimal calculations, they had difficulties in understanding decimal multiplication or decimal division with decimal number. Second, pre-service teachers recognized reasons of errors as well as errors patterns that student might make. But this recognition was limited mainly to errors related to natural number calculation. Third, pre-service teachers frequently commented about decimals algorithms, picture models, the meanings of decimal calculations, and connections to natural number calculations. Many of them represented the meanings of decimal calculations through picture models as to help students' understanding, while they just mentioned algorithms or treated decimal calculation as natural number calculations with decimal point.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.81-86
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• 2016

Three hundred years ago, the fractional differential equation that is one of concept of fractional calculus released. Now, many researchers continue to try best effort applying into the control engineering, mathematics and physics. In this paper, the dynamics equation which is represented by Van der Pol, represent integer order and fractional order that having real order. Then this paper performs the comparisons between integer and real order as time series and phase portrait according to variation of parameter value for real order.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.12
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• pp.1389-1394
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• 2015

Recently many effort appears applying the concept of fractional calculus that can be represented by fractional differential equation in the control engineering, physics and mathematics. This paper describes the fractional order with real order for Duffing equation which can be represented by integer order. This paper also confirms the existence of chaotic behaviors by using time series and phase portrait with varying the parameter of real order.

• The Mathematical Education
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• v.52 no.1
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• pp.97-109
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• 2013

Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student's personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.

• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.287-313
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• 2005

The decimal fraction concept plays an important role in understanding the real number which is one of the major concepts in school mathematics. In the school mathematics of Korea, the decimal fraction is treated merely as a sort of name of the common fraction, while many other important aspects of the decimal fraction concept are ignored. In consequence students fail to understand the decimal fraction concept properly, and merely consider it as a kind of number for formal computation. Preceding studies also identified students' narrow understanding of the decimal fraction concept. But none of them succeeded in clarifying the essences of the decimal fraction concept, which are crucial for discussing the didactical problems of it. In this study we attempted a didactical analysis of the decimal fraction concept and disclosed the roots of didactical problems and presented measures for its improvement. First, we attempted a phenomenological analysis of the decimal fraction concept and extracted 9 elements of the decimal fraction concept. Second, we has analyzed of the essence of the decimal fraction concept more clearly by relating it to the situations where it functions and its representations. For this we tried to construct the conceptual field of the decimal fraction. Third, we categorized he developmental levels of the decimal fraction concept from the aspect of external manifestation of the internal order. On the basis of these results, we attempted hierarchical structuring of the elements of the decimal fraction concept. And using the results of such a didactical analysis on the decimal number concept we analyzed the mathematics curriculum and textbooks of our country, investigated levels of students' understanding of the decimal fraction concept, and disclosed related problems. Finally we suggested directions and measures for the improvement of teaching decimal fraction concept.