• Communications of Mathematical Education
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• v.29 no.1
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• pp.131-155
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• 2015

The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.199-223
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• 2016

The purpose of this study is to investigate how first and second graders in middle school take in integrated understanding about the concept of function. The data was collected through the questionnaire conducted by the first and second-year students at A, B middle school in Cheongju. The questionnaire consisted of 14 questions related to the extent of understanding a concept of function, the ability to express function and to translate function. The results are summarized as follows. First, the percentage of correct answer made a difference according to the types of representation. Questions leading students to translate a task into a table or an equation showed quite high correct response rates. However, questions asking students to translate a task into graphs showed high incorrect responses. Second, the result shows that students have the different viewpoints depending on their grades when they have to determine whether the suggested situation belongs to function. The first-year students tended to consider function as the concept of 'definition'. On the other hand, the second-year students emphasized 'equation' of function. Finally, only a few students can distinguish the various situations and representations into the definition of function. This result shows that students didn't get the integrated understanding of the concept of function.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016

The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Journal of the Korean BIBLIA Society for library and Information Science
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• v.6 no.1
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• pp.133-160
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• 1984

The main purpose of the present study is to survey the major abstracting bulletins of national nature in Korea, to define such problem areas as lacunae, duplicates and limitation in coverage in the abstracting services currently available in Korea, and to make some suggestions for action for improving the abstracting services in the light of general principles and the tradition and situations unique to Korea. The major conclusions reached at this study are summarised as follows: (A) A new abstracting bulletin of general nature covering the whole field needs to be created in each of the following fields where no established abstracting service is available for the outcome of research and development activities in Korea. (1) Language (2) Religion (3) Art (4) Language (5) Literature (6) History (B) A new specialised abstracting bulletin needs to be created in each of the following fields of science where abstracting services limited in coverage are partially available. (a) Statistics (b) Sociology (c) political science (d) Public administration (e) Law (f) Folk lore (g) Military science (2) Pure sciences (a) Mathematics (b) Chemistry (c) Astronomy (d) Geology (e) Mineralogy (f) Life sciences (g) Botany (h) Zoology (3) Applied sciences (a) Agriculture (b) Architectural engineering (c) Mechanical engineering (d) Electrical engineering (e) Chemical engineering (f) Manufacturing industry (g) Domestic science (C) Publication of the abstracting bulletins suggested in (A) and (B) above may be ideally carried on by a qualified learned society established in the respective field. and should be financially supported by the public fund under the provisions of Art. 27 of the Research Promotion Act of 1979. (D) The current practice of adding the author's abstract and keywords to each of the records of the "Doctoral Theses in Humanities and Social Sciences" part of the" Catalogue of Doctoral and Master's Theses Submitted to the Universities in Korea" published by the National Assembly Library should be applied to all the other parts, i. e. to the parts of the "Master's Theses in Humanities and Social Sciences" and of the "Doctoral and Master's Theses in Natural Sciences': which will not only increase the Catalogue's use value but also discourage appearance of various theses abstracts of individual academic institutions such as the" Abstracts of the Doctoral and Master's Theses Submitted to Korea Advanced Institute of Science and Technology" which will in turn reduce inefficiency involved in the abstracting services at national level. (E) A general abstracting bulletin covering most part of the outcome of research and development activities in Korea other than that covered by the existing abstracts needs to be created to be temporarily. used till the abstracting journals suggested in this study will be fully available. A realistic way of having such a bulletin may be to expand the present coverage of "The Abstracts of the Reports of the Government-sponsored Projects" currently published by Korean Research Foundation.

• Journal of The Korean Association For Science Education
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• v.43 no.4
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• pp.403-414
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• 2023

In this study, we examined the adaptive practices of science teachers in their classrooms and their perspectives on the distinguishing features of these practices within science subjects. Our analysis comprised 339 cases from 128 middle and high school science teachers nationwide, and 199 cases on the characteristics of adaptive practices in science disciplines. The primary findings were as follows: First, the most significant characteristic of adaptive practice in science disciplines pertained to experimental procedures. Within the 'suggestion of additional materials/activities' category, the most frequently cited adaptive practice, teachers incorporated demonstrations to either facilitate student comprehension or enhance motivation. Additionally, 'experimental equipment manipulation or presentation of inquiry skills' emerged as the second most common adaptive practice related to experiments. Notably, over 50% of teacher responses regarding the characteristics of adaptive practices in science pertained to experiment guidance. Second, many adaptive practices involving difficulties experienced by students in learning situations were presented, particularly in areas such as numeracy and literacy. Many cases were related to the basic ability of mathematics used as a tool in science learning and understanding scientific terms in Chinese characters. Third, beyond 'experiment guidance', the characteristic adaptive practices of science subjects were related to 'connections between scientific theory and the real world', 'misconception guidance in science', 'cultivation of scientific thinking', and 'convergence approaches'. Fourth, the cases of adaptive practice presented by the science teachers differed by school level and major; therefore, it is necessary to consider school level or major in future research related to adaptive practice. Fifth, most of the adaptive action items with a small number of cases were adaptive actions executed from a macroscopic perspective, so it is necessary to pay attention to related professionalism. Finally, based on the results of this study, the implications for science education were discussed.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.229-250
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• 2013

The purpose of this study is analyzing 'observation and recommendation letter by teacher', which is being submitted to screen and enhance the utilization of gifted students in accordance with recently introduced gifted students observation, recommendation and screening system. For the purpose, this study will provide with objective securing plan of 'observation and recommendation letter by teacher' by developing an optimum evaluation model. The research findings were as follows: First, the result of analysis on the mathematically gifted students behavior characteristic as appeared in 'observation and recommendation letter by teacher' suggested that the recommending teachers have the tendency of giving superficial statement instead of giving concrete case description. When it was analyzed for frequency by the 'observation and recommendation letter by teacher' analysis framework devised by the author, the teachers showed the tendency of concentrating on specific questions. Meanwhile, there was a tendency that teachers concentrate on specific gifted behavior characteristic or area for which concrete case had been suggested. The reason is believed that such part is easy to observe and state while others are not, or, teachers did not judge the other part as the characteristic of gifted students. Second, the gifted students behavior characteristics as appeared in 'observation and recommendation letter by teacher' were made into scores by Rubric model. When the interrater reliability was analyzed based on these scores, the correlation coefficient of 1st scoring was .641. After a discussion session was taken and 2nd scoring was done 3 weeks later, the correlation coefficient of 2nd scoring increased to .732. The reason is believed that; i) the severity among scorers was adjusted by the discussion session after the 1st scoring, ii) the scorers established detail judgment standard on various situations which can appear because of the descriptive nature, and, (iii) they found a consensus on scoring for a new situation appeared. It implies that thorough understanding and application of scorers on evaluation model is as important as the development of optimum model for the differentiation of mathematically gifted elementary students.