• Communications of Mathematical Education
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• v.28 no.1
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• pp.19-44
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• 2014

This study aims to develop strategies for improving the affective characteristics of Korean students based on results from international achievement tests. In pursuing the goal, different research methods are employed including a) analysis of the theories and literature regarding the affective domains included in PISA and TIMSS studies; b) analysis of the current situation and needs of Korean students with respect to the affective factors based on PISA and TIMSS results; c) case studies of best practices in relation to students' affective domains in Korea and abroad; and d) development of strategies for improving and supporting Korean students' affective characteristics. In this paper, first of all, relevant theories on affective characteristics in literature are introduced. In other words, the concepts of three affective domains in question - interest, self-efficacy, and value - are reviewed, and their definitions for the present study are made. Also, teaching strategies and support plans for improving students' affective factors are extracted from previous studies. Furthermore, this paper reviews recent trends in research on how the affective domains are related to mathematics education and how one can teach them effectively. The teaching guidelines for each affective domain are developed according to the instruction principles extracted through literature review in general for all subjects. Based on the results of the findings mentioned above, this paper establishes and suggests the guidelines on how to teach mathematics reflecting the affective characteristic.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.349-366
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• 2017

The 2015 revised curriculum is an integrated curriculum that reflects national and societal needs to foster creative convergent talent in the school curriculum. Along with these changes, the Ministry of Education introduced a system to change the major from 2017 to the fourth year of university. Therefore, each university should prepare to reflect the curriculum and institutional change before welcoming students who have completed the 2015 revised curriculum. The university needs to study the countermeasures for implementing the 2015 revised curriculum and expanding the period of major change when preparing the curriculum and contents of the calculus courses that freshmen take. Handong University has been studying the operation methods of new students who want to decide their major at the first grade, such as operating calculus courses at various levels and allocating appropriate proportions of calculus for preliminary examinations. This case is similar to the basic purpose of the revised curriculum in 2015, so it can suggest implications for the operation of the university calculus class after the curriculum revision. In this paper, we have analyzed the results of the recent freshman mathematics test for the recent 5 years and the students' calculus grades and compared them with the contents of the calculus curriculum operated by Handong University and the 2015 revised higher mathematics curriculum. As a result, we proposed five classes of calculus suitable for college major and it was found that the calculus curriculum should include the missing quadratic method in the 2015 revised curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.401-420
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• 2010

The purpose of this research is to find out effectiveness of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. In order to proof this research problem, the controlled experiment was done on two groups of 6th graders in N elementary school; one group went through the geometry learning style through spatial reasoning activities, and the other group went through the general geometry learning style. As a result, the experimental group and the comparing group on mathematical problem solving ability have statistically meaningful difference. However, the experimental group and the comparing group have not statistically meaningful difference on mathematical attitude. But the mathematical attitude in the experimental group has improved clearly after all the process of experiment. With these results we came up with this conclusion. First, the geometry learning through spatial reasoning activities enhances the ability of analyzing, spatial sensibility and logical ability, which is effective in increasing the mathematical problem solving ability. Second, the geometry learning through spatial reasoning activities enhances confidence in problem solving and an interest in mathematics, which has a positive influence on the mathematical attitude.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.393-419
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• 2020

Trigonometry allows us to recognize the usefulness of mathematics through connection with real life and other disciplines, and lays the foundation for the concept of higher mathematics through connection with trigonometric functions. Since international comparisons on the trigonometry area of textbooks can give implications to trigonometry teaching and learning in Korea, this study attempted to compare trigonometry in textbooks in Korea, Australia and Finland. In this study, through the horizontal and vertical analysis presented by Charalambous et al.(2010), the objectives of the curriculum, content system, achievement standards, learning timing of trigonometry content, learning paths, and context of problems were analyzed. The order of learning in which the three countries expanded size of angle was similar, and there was a difference in the introduction of trigonometric functions and the continuity of grades dealing with trigonometry. In the learning path of textbooks on the definition method of trigonometric ratios, the unit circle method was developed from the triangle method to the trigonometric function. However, in Korea, after the explanation using the quadrant in middle school, the general angle and trigonometric functions were studied without expanding the angle. As a result of analyzing the context of the problem, the proportion of problems without context was the highest in all three countries, and the rate of camouflage context problem was twice as high in Korea as in Australia or Finland. Through this, the author suggest to include the unit circle method in the learning path in Korea, to present a problem that can emphasize the real-life context, to utilize technological tools, and to reconsider the ways and areas of the curriculum that deal with trigonometry.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.303-320
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• 2024

This study presents the development and performance evaluation of a custom GPT-based chatbot tailored to provide solutions following Polya's problem-solving stages. A beta version of the chatbot was initially deployed to assess its mathematical capabilities, followed by iterative error identification and correction, leading to the final version. The completed chatbot demonstrated an accuracy rate of approximately 89.0%, correctly solving an average of 57.8 out of 65 image-based problems from a 6th-grade elementary mathematics textbook, reflecting a 4 percentage point improvement over the beta version. For a subset of 50 problems, where images were not critical for problem resolution, the chatbot achieved an accuracy rate of approximately 91.0%, solving an average of 45.5 problems correctly. Predominant errors included problem recognition issues, particularly with complex or poorly recognizable images, along with concept confusion and comprehension errors. The custom chatbot exhibited superior mathematical performance compared to the general-purpose ChatGPT. Additionally, its solution process can be adapted to various grade levels, facilitating personalized student instruction. The ease of chatbot creation and customization underscores its potential for diverse applications in mathematics education, such as individualized teacher support and personalized student guidance.

• Journal of Platform Technology
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• v.11 no.5
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• pp.72-83
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• 2023

ChatGPT, commercial launch in late 2022, has shown successful results in various professional exams, including US Bar Exam and the United States Medical Licensing Exam (USMLE), demonstrating its ability to pass qualifying exams in professional domains. However, further experimentation and analysis are required to assess ChatGPT's scholastic capability, such as logical inference and problem-solving skills. This study evaluated ChatGPT's scholastic performance utilizing the Korean College Scholastic Ability Test (KCSAT) subjects, including Korean, English, and Mathematics. The experimental results revealed that ChatGPT achieved a relatively high accuracy rate of 69% in the English exam but relatively lower rates of 34% and 19% in the Korean Language and Mathematics domains, respectively. Through analyzing the results of the Korean language exam, English exams, and TOPIK II, we evaluated ChatGPT's strengths and weaknesses in comprehension and logical inference abilities. Although ChatGPT, as a generative language model, can understand and respond to general Korean, English, and Mathematics problems, it is considered weak in tasks involving higher-level logical inference and complex mathematical problem-solving. This study might provide simple yet accurate and effective evaluation criteria for generative artificial intelligence performance assessment through the analysis of KCSAT scores.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.43.3-44
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• 2015

We analyze the clustering of large scale structure in the Universe in a model independent method, accounting for anisotropic effects along and transverse to the line of sight. A large sample of 690,000 galaxies from The Baryon Oscillation Spectroscopy Survey Data Release 11 are used to determine the Hubble expansion H, angular distance D_A, and growth rate GT at an effective redshift of z=0.57. After careful bias and convergence studies of the effects from small scale clustering, we find that cutting transverse separations below 40 Mpc/h delivers robust results while smaller scale data leads to a bias due to unmodelled nonlinear and velocity effects. The converged results are in agreement with concordance LCDM cosmology, general relativity, and minimal neutrino mass, all within the $68{\backslash}%$ confidence level. We also present results separately for the northern and southern hemisphere sky, finding a slight tension in the growth rate -- potentially a signature of anisotropic stress, or just covariance with small scale velocities -- but within $68{\backslash}%$ CL.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.665-668
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• 2012

For a given graph G we consider a set S(G) of all symmetric matrices A = [$a_{ij}$] whose nonzero entries are placed according to the location of the edges of the graph, i.e., for $i{\neq}j$, $a_{ij}{\neq}0$ if and only if vertex $i$ is adjacent to vertex $j$. The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to $n$ - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number $p$(T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = $p$(T).

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.331-346
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• 2016

The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.