• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.1
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• pp.107-114
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• 2011

In this study, a correlation between the roughness of nanoscale lapping surface and its laser scattering pattern has been identified experimentally. The characteristics of laser scattering on a reflected surface are investigated, and a laser scattering mechanism is newly designed by adopting the dark-field method. Laser scattering patterns resulting from nanoscale lapping shape are in the shape of crossed irregular lattice. In addition, optimum laser scattering images are obtained by the design of experiment, and the roughness of nanoscale lapping surface is estimated using regression analysis certain useful features of the laser scattering patterns. The results of fifty experiments on three types of nanoscale lapping surfaces show that the roughness of nanoscale lapping surfaces can be accurately estimated by the proposed mathematical modeling method.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.251-272
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• 2005

Given that cognitive demands of mathematical tasks can be changed during instruction, this study attempts to provide a detailed description to explore how tasks are set up and implemented in the classroom and what are the classroom-based factors. As an exploratory and qualitative case study, 4 of six-grade classrooms where high-level tasks on ratio and proportion were used were videotaped and analyzed with regard to the patterns emerged during the task setup and implementation. With regard to 16 tasks, four kinds of Patterns emerged: (a) maintenance of high-level cognitive demands (7 tasks), (b) decline into the procedure without connection to the meaning (1 task), (c) decline into unsystematic exploration (2 tasks), and (d) decline into not-sufficient exploration (6 tasks), which means that the only partial meaning of a given task is addressed. The 4th pattern is particularly significant, mainly because previous studies have not identified. Contributing factors to this pattern include private-learning without reasonable explanation, well-performed model presented at the beginning of a lesson, and mathematical concepts which are not clear in the textbook. On the one hand, factors associated with the maintenance of high-level cognitive demands include Improvising a task based on students' for knowledge, scaffolding of students' thinking, encouraging students to justify and explain their reasoning, using group-activity appropriately, and rethinking the solution processes. On the other hand, factors associated with the decline of high-level cognitive demands include too much or too little time, inappropriateness of a task for given students, little interest in high-level thinking process, and emphasis on the correct answer in place of its meaning. These factors may urge teachers to be sensitive of what should be focused during their teaching practices to keep the high-level cognitive demands. To emphasize, cognitive demands are fixed neither by the task nor by the teacher. So, we need to study them in the process of teaching and learning.

• School Mathematics
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• v.19 no.1
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• pp.117-135
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• 2017

Even though patterns and correspondence serve a fundamental basis of function for elementary students, there has been lack of research in this field. This study explored prior studies to extract the key instructional elements on how to teach patterns and correspondence. This study then analyzed the unit of 'patterns and correspondence' in the mathematics textbooks in terms of four key instructional elements (i.e., relation to real-life contexts, diversity of pattern tasks, exploration for a correspondence relationship, and teaching variables). The results of this study showed that topics dealing with patterns and correspondence were represented with relation to real-life contexts but diversity of pattern tasks and exploration for a correspondence relationship were needed to be further considered in the textbooks. Another noticeable result was that teaching variables was not explicitly addressed in the textbooks. Based on these results, this study provides textbook writers with implications on what to further consider in dealing with patterns and correspondence.

• School Mathematics
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• v.15 no.3
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• pp.633-650
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• 2013

The aim of this paper is to explore and understand, using in-depth interviews, the participant's interests and discourse analytic expressions in studying the notion of infinity and limit. In addition we tried to understand how the participant's ways of dealing with math and thinking patterns on the polygons whose boundary is infinite but area is finite as they brought up such examples. Further follow-up questions are posed on the infinite sum of a smallest number close to 0 and the sum of infinite sets of different smallest numbers close to 0. Larger aspects of two pre-service teachers' subjective thinking patterns and colloquial discourses were sketched by contrasting the three posed tasks. Cross case discussions are provided with several suggestions for the future research directions.

• School Mathematics
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• v.5 no.1
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• pp.135-149
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• 2003

We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.

• Journal of Science Education
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• v.34 no.1
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• pp.1-11
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• 2010

This study analyzes the factors influencing academic achievement on mathematic and scientific subject and its change in Korean youth by using a sample from KYPS(Korea Youth Panel Survey) data. The results are as follows: First, academic achievement on mathematic and scientific subject of Korean youth shows quadratic curve that their interrelationship between intercept and slope of academic achievement are negative which is statistically significant. Second, analysis of Latent Growth Models shows that parents, teacher, peer group, self esteem, income of family, high school tracks are found to be a statistically significant factor on mathematic. And scientific subject is affected by parents, teacher, peer group, self esteem, income of family, high school tracks. Also, Interesting finding is that father's job is not significant to dependent variables. These findings show that academic achievement on mathematic and scientific subject of the Korean youth are the quadratic curve and influenced by parents, teacher, peer group, self esteem, income of family, high school tracks. To improve youth's mathematic and scientific, Korea educational fields and educators should have policy to care youth's relationship with parents, teachers and self esteem.

• Journal of the Korean Society of Industry Convergence
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• v.6 no.1
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• pp.31-36
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• 2003

8개의 수정진동자 위에 서로 다른 종류의 Lipid를 코팅하여서 만든 센서 배열을 가지고 유기용매를 인식할 수 있는 System을 구성한다. 유기용매 인식센서에 대한 수학적 모델을 사용하여 여러 가지 유기용매에 대한 센서의 응답으로부터 센서 표면과 유기용매 간의 물질 전달속도 패턴과 친화력 패턴을 얻어 유기용매 종류를 인식하였다. 패턴인식은 인공신경망을 이용하였으며 인공신경망의 연결 강도 수정은 Levenberg-Marquardt 알고리즘을 사용하였다. 신경망의 출력은 4개로 하였고, 디지털 신호인 0과 1의 조합으로 유기용매 종류를 구분하였다. 이 시스템을 이용하여 9개의 유기용매 Acetone, Benzene, Chloroform, Carbon-tetrachloride, Ethylacetate, Buthylacetate, Cyclohexane, Dichloromethane, 1,1,2,2,Tetrachloroethane, 2,2,4Trimethylpentane을 구분하여 인식할 수 있었다.

• Journal of KSNVE
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• v.4 no.4
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• pp.397-403
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• 1994

본 고에서 제시한 타이어 소음발생기구에 대한 수학적 모델은 실제활용을 목적으로 정립된 것이다. 이 모델은 프로그램화 되어 타이어 패턴 소음 예측을 위한 컴퓨터 시뮬레이션에 활용되었다. 시뮬레이션에서는 전체 소음도 뿐만아니라 스펙 트럼 특성까지도 예측할 수 있으며, 몇가지 실추결과와 비교하여 만족스러운 수준 의 일치를 확인하였다. 이 기술의 장점은 저소음 타이어 개발에 따르는 시간과 돈을 크게 절약할 수 있다는 것이다. 즉 타이어 설계자가 구상하고 있는 패턴을 컴퓨터에 입력함으로서 타이어의 기본기능을 손상하지 않는 범위에서 최선의 소음특성을 갖는 패턴을 결정할 수 있다. 선진 타이어 업체들은 이미 이같은 방법을 사용하고 있는 것으로 알려져 있으며, 이제 우리도 그 수준에 도달했다고 자부할 수 있다. 그러나 모든 과학기술 이론이 그러하듯이 이 글에서 제시한 모델 역시 결코 완벽하다고 볼 수는 없다. 이 글의 내용이 국내 관심있는 학자들에게 시작할 수 있는 계기가 될 것을 기대하며, 국산 자동차의 저소음화 노력이 더욱 활성화 되기를 희망한다.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.85-96
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• 2004

The Resealed range statistical analysis and Hurst exponent which are standard methods to test the chaotic model are used to examine sinusoid pattern. We notice that the Hurst exponent can be used as a measure to examine the time series data that show semi-cyclic trend with noise.

• The KIPS Transactions:PartB
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• v.10B no.4
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• pp.451-458
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• 2003

Dynamic Programming Matching (DPM) is a mathematical optimization technique for sequentially structured problems, which has, over the years, played a major role in providing primary algorithms in pattern recognition fields. Most practical applications of this method in signature verification have been based on the practical implementational version proposed by Sakoe and Chiba [9], and is usually applied as a case of slope constraint p = 0. We found, in this case, a modified version of DPM by applying a heuristic (forward seeking) implementation is more efficient, offering significantly reduced processing complexity as well as slightly improved verification performance.