• Communications of Mathematical Education
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• v.26 no.3
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• pp.317-338
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• 2012

This paper compared and contrasted the views of effective mathematics instruction by 223 elementary school teachers and 151 middle school mathematics teachers using a questionnaire with 4 main domains (i.e., curriculum and content, teaching and learning, classroom environment and atmosphere, and assessment) and a total of 48 sub-elements. The analysis of results showed that elementary school teachers put their priority on the curriculum and content domain, while middle school counterparts did on the teaching and learning domain. The teachers commonly agreed with instruction which fosters students' self-directed learning ability, reconstructs the curriculum tailored to students' diverse levels, and establishes appropriate interaction between the teacher and students. However, elementary school teachers agreed more than middle school teachers with regard to the 23 elements related to effective mathematics instruction. In contrast, middle school teachers agreed more than their counterparts as for only 2 elements (instruction fostering mathematical representation and instruction eliciting students' learning motivation). This paper includes suggestions and implications related to Korean teachers' perception of effective mathematics instruction.

• The Mathematical Education
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• v.60 no.4
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• pp.509-527
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• 2021

We investigated whether and how pre-service teachers took the realistic contexts seriously in the course of solving word problems; additionally, we investigated how pre-service teachers evaluated students' realistic and non-realistic answers to word problems. Many pre-service teachers, similar to students, solved some of the realistic problems unrealistically without taking the realistic contexts seriously. Besides, they evaluated students' non-realistic answers higher than the realistic answers. Whether the pre-service teachers could solve problems realistically or not, they did not appreciate students' realistic considerations for the reasons that those were not fitted to the intentions of the word problems, or those were evidence of the flaws of the problem. Furthermore, the analysis of premises implied in the pre-service teachers' evaluation comments showed the implicit didactic contracts about realistic word problem solving that they accepted and also anticipated students to follow. Our analysis of the pre-service teachers' conceptions of realistic word problems can help teacher educators design the teacher program to challenge and revise pre-service teachers' folk pedagogy.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.285-301
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• 2013

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.277-291
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• 2011

It is necessary for the teacher to understand why teach mathematics in order to implement the visions and expectations of the national mathematics curriculum in her actual classroom. This study conducted a survey of examining how elementary school teachers might understand the purpose of teaching mathematics. The results of this study showed that teachers' conceptions of the purpose of teaching mathematics were related mainly to the development of logical thinking, practical use of mathematics in everyday life, and a tool for studying other subjects or disciplines. However, teachers did not perceive much other purposes of mathematics education such as understanding the world, appreciating aesthetic value of mathematics, and developing communicative ability as well as sociality. Whereas teachers did not think of the significance of mathematics as an intellectual field when asked to write down how they would explain students why they had to learn mathematics, they tended to strongly agree it in the Likert-scale responses. Teachers' conceptions were not different according to their gender but teachers with less than five years' teaching experience were relatively negative than others with more experience. Given these results, this study provided issues and implications of teachers' conceptions of the purpose of teaching mathematics.

• Education of Primary School Mathematics
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• v.11 no.1
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• pp.59-74
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• 2008

Mathematical knowledge is not exact definition but the supposition. Considering the nature of mathematics, realization of mathematics teaching which pursues critical thinking and rationality would be our problems. Accordingly, I set the subject of this study whether learning of constructivist discussion, which induces reflective thinking through communicating with others by expression with language of mathematical thinking in discussion, is effective against attitude on Mathematics and Mathematics achievement and study themes are as follows; A. Is learning of constructivist discussion effective against attitude on Mathematics? A-1. Is there any difference of self-conception on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-2. Is there any difference of attitude on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-3. Is there any difference of learning habits on the subject between experimental group applied to learning of constructivist discussion and comparative group? B. Is learning of constructivist discussion effective against mathematics achievement? The objects of study are 30 children of one class in the third grade of elementary school in Seoul for experimental group, and another one class with 30 children is comparative group. Study results and conclusion based on those results are as follows; First, students make reflective thinking through communication each other, therefore, instructor should create discussion environment for communication to express and form their mathematical thinking. Next, adaptability in student's mathematics activities and mathematical ideas should be permissible, and those should become divergent thinking. However, this study analyzed comparative results from only two each class having enrollment of thirty in the third grade. Accordingly, results from students in various grades and environment that are required to get more significant conclusion statistically.

• Journal of Korean Medical classics
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• v.33 no.1
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• pp.29-50
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• 2020

Objectives : Objectiveness and accuracy of numbers could allow for a new way of understanding the principle of Ten Heavenly Stems(THS) and Twelve Earthly Branches(TEB) when applied. Methods : The order of the THS and TEB, the Five phases of direction and change, conversion of other, conversion of self of the Stems and Branches were examined through numbers. Results & Conclusions : The numerical combination of the Stems and Branches depends on the identification of the Three Points. Conversion of self of the Heavenly Stems are as follows: for 甲 3+5=8, for 乙 8+4=12, for 丙 7+1=8, for 丁 2+8=10, for 戊 5+7=12, for 己 10+10=20, for 庚 9+9=18, for 辛 4+6=10, for 壬 1+3=4, for 癸 6+2=8. Conversion of self of the Earthly Branches are as follows: for 子 1+2=3, for 丑 5+5=10, for 寅 3+2=5, for 卯 8+4=12, for 辰 5+1=6, for 巳 2+8=10, for 午 7+7=14, for 未 10+10=20, for 申 9+7=16, for 酉 4+9=13, for 戌 5+6=11, for 亥 6+3=9. Here the Stems and Branches could be understood intensively. Among the Stems and Branches, the Great Points are 壬, 癸, 戌, 亥, 子, Emperor Points are 甲, 戊, 丑, 午, and Empty Points are 己, 未.

• The Mathematical Education
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• v.56 no.1
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• pp.19-39
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• 2017

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don't appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers' understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson's statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• Korean Journal of Environmental Biology
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• v.20 no.4
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• pp.277-286
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• 2002

An increase in the overall biological effect under the combined action of ionizing radiation with another inactivating agent can be explained in two ways. One is the supposition that synergism may attribute to a reduced cellular capacity of damn-ge repair after the combined action. The other is the hypothesis that synergism may be related to an additional lethal or potentially lethal damage that arises from the interaction of sublesions induced by both agents. These sublesions ave considered to be in-effective when each agent is applied separately. Based on this hypothesis, a simple mathematical model was established. The model can predict the greatest value of the synergistic effect, and the dependence of synergy on the intensity of agents applied, as well. This paper deals with the model validation and the peculiarity of simultaneous action of various factors with radiation on biological systems such as bacteriophage, bacterial spores, yeast and mammalian cells. The common rules of the synergism aye as follows. (1) For any constant rate of exposure, the synergy can be observed only within a certain temperature range. The temperature range which synergistically increases the effects of radiation is shifted to the lower temperature fer thermosensitive objects. Inside this range, there is a specific temperature that maximizes the synergistic effect. (2) A decrease in the exposure rate results in a decrease of this specific temperature to achieve the greatest synergy and vice versa. For a constant temperature at which the irradiation occurs, synergy can be observed within a certain dose rate range. Inside this range an optimal intensity of the physical agent may be indicated, which maximizes the synergy. As the exposure temperature reduces, the optimal intensity decreases and vice versa. (3) The recovery rate after combined action is decelerated due to an increased number of irreversible damages. The probability of recovery is independent of the exposure temperature for yeast cells irradiated with ionizing or UV radiation. Chemical inhibitors of cell recovery act through the formation of irreversible damage but not via damaging the recovery process itself.

• Journal of Engineering Education Research
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• v.5 no.1
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• pp.77-84
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• 2002

The 18th century Joseon(朝鮮) science philosopher Hong Dae-Yong(洪大容, 1731-83) tried to create his own scientific system, while partially keeping the Eastern view of nature and accepting Western science and technology. Most of all, he confirmed that Western science and technology was based on mathematical principles and accurate observation and wrote a math book, [Juhaesuyong(籌解需用)]. Therefore, we have good reason to call him a mathematician. He produced so many achievements that he can be considered a natural scientist in the late Joseon era; he accepted the Eastern view of nature critically and sometimes refused it. He also suggested new and various scientific thoughts, including an infinite universe theory, on the basis of Western scientific thought. Hong Dae-Yong emphasized the importance of practice. He understood the principle of the Western Honcheonui(渾天儀) and manufactured an alarm clock with a craftsman's help. He was an excellent engineer and he set a personal observatory. Considering the level of scientific technology at that time, it is reasonable to regard Hong Dae-Yong as a 'scientific technologist in the 18th century Joseonera', well equipped as a mathematician, a natural scientist, and an engineer. In conclusion, it is with 'mathematical thinking, creative conception, and practical activities' that Hong Dae-Yong maintained throughout his life that we can set a guide to produce excellent Korean scientific technologists and engineers in the 21st century.