• Communications of Mathematical Education
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• v.30 no.1
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• pp.67-83
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• 2016

Correcting an imbalance between cognitive and affective aspects of mathematics in schools is recognized as a crucial issue with regards to mathematics education in Korea. Therefore, research and studies about affective aspects have been increasing and themes relating to affective aspects were diverse. Their theme included the improvement of affective aspect, investigation of factors of affective aspect, and development of measurement tools for affective aspect. The purpose of this study is to analyze and organize the research that has been done with respect to affective aspect and drive trend, implication, and their instruction to mathematics education. This study has investigated 103 studies released from 2005 to 2015 on KCI, Korea Citation Index. The results of this study are as follow. First, since released research of affective aspects in mathematics has not increased in number in the last 11 years, academic interest in the affective aspects seems lower than recent interest arousing in Korea. Second, most studies utilized quantitative research as a tool to analyze phenomena and the cause and effect of affective aspects. Third, middle school students were the most common subjects of the studies, followed by elementary school students. Fourth, the studies had various themes such as analyzing the cause and effect of affective aspect, recognizing changes of affective aspects, and measuring affective aspects. The studies, especially, focused most on analyzing how to improve affective aspects by applying it to programs such as mathematic activities and solving mathematic problems. It is necessary for future research to have a long-term perspective and to provide a space for communication. Research should not only focus on how recognize affective aspects differently, which is based on its cultural background, but also to draw affective solutions from them.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.67-75
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• 1984

Let X be a topological space. We consider a groupoid G over X and the quotient groupoid G/N for any normal subgroupoid N of G. The concept of groupoid (topological groupoid) is a natural generalization of the group(topological group). An useful example of a groupoid over X is the foundamental groupoid .pi.X whose object group at x.mem.X is the fundamental group .pi.(X, x). It is known [5] that if X is locally simply connected, then the topology of X determines a topology on .pi.X so that is becomes a topological groupoid over X, and a covering space of the product space X*X. In this paper the concept of the locally simple connectivity of a topological space X is applied to the groupoid G over X. That concept is defined as a term '1-connected local subgroupoid' of G. Using this concept we topologize the groupoid G so that it becomes a topological groupoid over X. With this topology the connected groupoid G is a covering space of the product space X*X. Further-more, if ob(.overbar.G)=.overbar.X is a covering space of X, then the groupoid .overbar.G is also a covering space of the groupoid G. Since the fundamental groupoid .pi.X of X satisfying a certain condition has an 1-connected local subgroupoid, .pi.X can always be topologized. In this case the topology on .pi.X is the same as that of [5]. In section 4 the results on the groupoid G are generalized to the quotient groupoid G/N. For any topological groupoid G over X and normal subgroupoid N of G, the abstract quotient groupoid G/N can be given the identification topology, but with this topology G/N need not be a topological groupoid over X [4]. However the induced topology (H) on G makes G/N (with the identification topology) a topological groupoid over X. A final section is related to the covering morphism. Let G$_{1}$ and G$_{2}$ be groupoids over the sets X$_{1}$ and X$_{2}$, respectively, and .phi.:G$_{1}$.rarw.G$_{2}$ be a covering spimorphism. If X$_{2}$ is a topological space and G$_{2}$ has an 1-connected local subgroupoid, then we can topologize X$_{1}$ so that ob(.phi.):X$_{1}$.rarw.X$_{2}$ is a covering map and .phi.: G$_{1}$.rarw.G$_{2}$ is a topological covering morphism.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.357-367
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• 2013

It is important to make students do research for oneself. But the practice of inquiry activity is not easy in the mathematics education field. Intellectual curiosities of students are unpredictable. It is important to meet intellectual curiosities of students. We could get a sequence in the process solving a problem. This sequence was expressed in a form of the recurrence relation $a_n=a_{n-1}+a_{n-3}$ ($n{\geq}4$), $a_1=a_2=a_3=1$. We tried to look for the general terms of this sequence. This sequence is similar to Fibonacci sequence, but the process finding the general terms is never similar to Fibonacci sequence. We can get two general terms expressed in different form after our a great deal of effort. We hope that this study will give the spot of education energy.

• Journal of the Korean School Mathematics Society
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• v.19 no.2
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• pp.153-176
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• 2016

The purpose of this study is to suggest ways to promote student engagement by analyzing how a teacher's student engagement strategies and questioning strategies affect class participation and problem solving in a peer mentoring teaching method. As for the purpose, after recording 7th grader's classroom using a peer mentoring and transcribing classroom discourse, we analyzed student engagement strategies for class participation and questioning strategies for helping mathematical concepts and problem solving, and compared mathematics achievements in mid-term and final exams. As results, in learning environments based on comfortable atmosphere, diverse student engagement strategies and appropriate questioning strategies with effectiveness of peer mentoring encouraged students to participate in class by motivating them, helped them to develop mathematical concepts and deepen understanding of problem solving through effective social interactions, and improved student achievement in mathematics. The results can practically help to develop class design considering both student engagement strategy and questioning strategy by specifically presenting a teaching method for promoting student engagement and teacher's contributions to it.

• The Journal of Art Theory & Practice
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• no.7
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• pp.165-188
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• 2009

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term 'vanishing point'. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of 'vanishing points'. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.

• Education of Primary School Mathematics
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• v.2 no.1
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• pp.53-64
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• 1998

Two different CAI programs have been developed to study the affect of CAI element for the types of learners'performance; (i) one is the 'CAI program 1' including the open questions for the fourth grade (the fourth period of the 'Time and Angle' in chapter 3 of the first term) of the mathematics class in the elementary school, and (il) the other is 'CAI program 2' for the existing methods. The fourth grade of Andong Songhyun elementary school has been chosen as the study subjects (243 learners), and the t-test and learners'interview have also been used to analysis the results of CAI programs. The CAI programs have only been used as the control variable. The developed CAI programs have been applied two different learners'groups to investigate the degree of performance among the superior, average, and inferior learners. For the superior group (p＜.0023) at the t＜3.2268 level and for the average group (p＜.0706) at the t＜1.8211 level the learner' group using CAI program 1 shows the higher performance compared with the learners' group using the CAI program 2, whereas fur the inferior group (p＜.8073) at the t＜.2458 level two programs did not show any difference. The learners interviews show that the superior and average groups have an interest for the open problems, whereas the inferior group do not shows an interest for the open problems. Thus, the CAI programs including the open questions (open fields, open evaluation) will be helped to the learners' group with the individual differences. Furthermore, it is expected that the CAI programs including the open questions as the mathematics and the program model of CAI can be used to develope the CAI program in future.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.87-103
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• 2013

This study was investigated to examine the effects of writing activities based on Polya's Problem Solving Stages on Learning Accomplishment and Attitudes. A total of 54 students were selected from two Grade 6 classes of P Elementary School in G City to form an experimental group(n=27) and a control group (n=27). The experimental group was applied to a class which was creating writing activities according to Polya's Problem Solving Stages to problem solving and inquiry activities. The control group was taught by the traditional method to the same activities. The five questions for each area were selected as a descriptive assessment of the second semester of Grade 5 in the area of the Academic Achievement pre-test, developed by the G Education and Science Research. The post-test was selected by a descriptive assessment of the content of the first semester in Grade 6. The same questions were posed for both the pre-test and the post-test of the Mathematical Attitudes assessment. We examined the pre-test at the beginning of the school term, then the students were re-examined after one semester, using the same questions as the pre-test. This research showed that there was a meaningful difference in Learning Accomplishment as a result of T-test in the 5% level of significance. Secondly, there was a meaningful difference in the Mathematical Attitudes as a result of T-tests. It shows that writing activities based on Polya's Problem Solving Stages have an influence on improving Learning Accomplishment and Attitudes.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.299-324
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• 2020

The purpose of this study was to identify high school students' mathematics learning style and its characteristics according to their personality disposition types and to propose mathematics learning strategies fit into each personality disposition type. For this purpose, MBTI personality test and survey to find mathematics learning style for 375 high school students were executed. The results were as follows. First, many students highly evaluated the effects of private education and prefer reference book to textbook. Second, there were significant differences on following variable domains of mathematics learning style such as learning attitude, learning habit(concentrativeness to concept understanding), problem solving strategies(effort for problem comprehension, use of various strategies), self management(metacognition) by MBTI personality disposition types(SJ, SP, NT, NF groups). Third, based on the results, the following mathematics learning strategies fit into each personality disposition type were recommended. SJ type students are needed to effort creative approach for open problem and to use mindmap as mathematics learning strategy. SP type students are needed to fulfill stepwise problem solving process and to effort constantly practice long/short term learning objectives. NT type students are needed to expand opportunity to study with friends and to use SRN(self reflection note) or mathematics journal writings as mathematics learning strategy. NF type students are needed to use mathematics learning note writing activity which include logical basis for each step of problem solving and to invest more time on learning algebra which need meticulous calculation.

• Journal of the Daesoon Academy of Sciences
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• v.28
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• pp.207-241
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• 2017

In the scripture of Daesoon Jinrihoe, the expression 'Dosu (度數)' is frequently used and Jeungsan, Jeongsan, and Wudang also left behind many teachings related to Dosu. In this paper, the concept of Dosu is analyzed in detail and the achievement of an in-depth understanding of the concept of Dosu is attempted. The term Dosu is often used in traditional literature. In the classics, Dosu was used to mean institutions, standards, rules, law, figures, and the laws of heavenly bodies. In other words, Dosu is used to mean the laws of astronomy and the norms of human society. This meaning is expanded and used as the principle of the universe and nature. This concept of Dosu is related to the mathematical cosmological understanding of numbers as the principle of the universe. This type of mathematical cosmology was systematized by Shao Yong (邵雍). In the Joseon Dynasty, Seo Gyungduk (徐敬德) accepted it positively, and it thereby became an influential trend in Korean thought. In the world view of Daesoon thought, there exists the view that numbers as a principle of the universe, and of course this world view is connected to mathematical cosmology. In Daesoon thought, the concept of Dosu is based on the concept of traditional Dosu and adds an additional meaning which connects it to the Reordering of the Universe (Cheonjigongsa). Also, Dosu is used to mean the process of changing the principles and laws of cosmos through Jeungsan's Reordering of the Universe. It is especially the case that discourse about Dosu is widely used when describing the Reordering of the Universe. Jeungsan corrected, reorganized, and adjusted Dosu, as well as establishing new Dosu. Jeongsan, who succeeded Jeungsan, followed the Reordering of the Universe by Jeungsan, and also realized Dosu. In other words, Jeongsan acted and practiced according to the Dosu that had been enacted by Jeungsan. Also, Dosu means the process of the transformation of principle according to the Reordering of the Universe, and Wudang used the concept of Dosu to describe the historical process of Daesoon Jinrihoe. This means that the foundation of Mugeukdo, the change to Taegukdo, the establishment of Daesoon Jinrihoe, and the contruction of Yeoju headquarters are episodes in a divine history carried out through Dosu. Through this discourse, Daesoon Jinrihoe asserts a legitimacy that distinguishes itself from other sects, and believers can be inspired by the sacred meaning that they are participating in the Dosu of heaven and earth. This empowers their devotion and sincerity.

• Biotechnology and Bioprocess Engineering:BBE
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• v.5 no.6
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• pp.441-448
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• 2000

Experimental work was carried out on nitrogen and phosphorus removal from real wastewater using a bench-scale SBR process. The phosphorus removal was stable and the phosphorus concentration remaining in the reactor was maintained within 1.5ppm, regardless of the addition of an external carbon source. In the case of nitrogen, an external carbon source was necessary for denitrification. The effect on denitrification with the addition of various carbon sources, such as glucose, methanol, acetate, and propionate, was also investigated. Acetate was found to be the most effective among those tested in this study. When 100ppm (theoretical oxygen demand) of sodium acetate was added, the average rate of denitrifiaction was 2.73mg NO$_3$-N (g MLSS)(sup)-1 h(sup)-1, which was ca. 4 times higher than that with the addition of 200 ppm of methanol. The phosphorus and nitrogen concentrations were both maintained within 1.5ppm by the addition of an appropriate amount of a carbon source during a long-term operation of the SBR. The mathematical modeling was performed using Monod kinetics, other microbial kinetics, mass balances, and stoichiometry. The modeling was found to be useful for predicting the SBR operation and optimizing the HRT.