• Communications of Mathematical Education
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• v.37 no.4
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• pp.591-614
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• 2023

For a long time, mathematics education institutions such as NCTM(National Council of Teachers of Mathematics) have emphasized the essential role of writing, and recent surveys by the Ministry of Education report a decline in foundational academic skills in the post-COVID19 period. The purpose of this study is to redefine the significance of mathematics writing in mathematics education, focusing on competencies highlighted in the field, particularly in the areas of problem-solving, communication, and reasoning. The research findings indicate that writing in problem-solving enhances cognitive organization, fostering the ability to grasp concepts and methods. Writing in communication builds confidence through the meta-cognitive process, and writing in inference allows self-awareness of step-by-step identification of areas lacking understanding. Particularly in the future society where artificial intelligence(AI) is utilized, changes in the learning environment necessitate research for the establishment of authenticity judgment through writing and the cultivation of a proper writing culture.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.507-522
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• 2009

In general, we do fold paper and unfold, it remain paper traces. We can be obtained by using rectangular paper, a mathematical fact and the program had a combination. Depending on the direction of the rectangle, folding paper in the form of variety shows valley and ridge signs of the appearance of this paper. By using (0,1)-code and (0,1)-matrix, we study four kinds of research. Therefore, traces of this view upside down rectangle folding paper how to fold inductive reasoning ability of the code and explore the relationship of traces. Finally, the mathematical content and program development can practice in the field.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• The Mathematical Education
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• v.42 no.3
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• pp.353-368
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• 2003

Analogy, based on a similarity, is to infer the properties of the similar object from properties of an object. It can be a very useful thinking tool for learning mathematical patterns and laws, noticing on relational properties among various situations. The purpose of this study, when manipulating hint condition, figure and table conditions and the amount of original learning by using algebra word problems, is to verify the effects of analogical transfer in solving equivalent, isomorphic and similar problems according to the similarity of source problems and target ones. Five study questions were set up for the above purpose. It was 354 first grade students of S and G middle schools in Seoul that were experimented for this study. The data was processed by MANOVA analysis of statistical program, SPSS 10.0. The results of this studies would indicate that most of the students would be poor at solving isomorphic and similar problems in the performance of analogical transfer according to the similarity of source and target problems. Hints, figure and table conditions did not facilitate the analogical transfer. Merely, on the condition that amount of teaming was increased, analogical transfer of the students was facilitated. Therefore, it is necessary to have students do much more analogical problem-solving experience to improve their analogical reasoning ability through the instruction program development in the educational fields.

• School Mathematics
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• v.7 no.1
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• pp.17-32
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• 2005

The purpose of this study is to analyze the effects of calculator use, which is drawing more attention in elementary mathematics, on students' learning of mathematics and to suggest effective ways of using calculators. The present study examined appropriate items commonly used in other papers in the areas of number sense and concepts, problem solving, pattern exploration and reasoning ability. The process of item selection about calculator use were investigated through preservice elementary school teachers' responses to the Questionnaire. The use of calculators In elementary school should be based on teachers' under-standing about why calculators are useful tools for learning mathematics. For more effective use of calculators, more sophisticated experimental studies need to be conducted about selected questions.

• School Mathematics
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• v.13 no.1
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• pp.1-17
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• 2011

This study investigated the Chinese national university entrance examination (Gaokao) in mathematics administered in 2009 and 2010 to draw out some implications on the College Scholastic Ability Test (CSAT) in mathematics of Korea. To evaluate the attainments of basic mathematical skills and multilateral abilities required for further studies in university, the Gaokao mathematics is set in two forms(Art/Science), based on the Chinese national mathematics curriculum. The types of items in the Gaokao mathematics are multiple-choice, single-answer, and write-out-answer. The mathematical abilities that the Gaokao mathematics evaluates are mathematical reasoning, operation, geometrical imagination, application, and creativity. As a result, some implications on the Korean CSAT are drawn out in terms of the level of difficulty, the types of items, the arrangements, and the scores of items.

• 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 School Mathematics Society
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• v.24 no.3
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• pp.261-282
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• 2021

This study identified the meaning of mathematical justification and its characteristics for middle school math gifted students. 17 middle school math gifted students participated in questionnaires and written exams. Results show that the gifted students recognized justification in various meanings such as proof, systematization, discovery, intellectual challenge of mathematical justification, and the preference for deductive justification. As a result of justification exams, there was a difference in algebra and geometry. While there were many deductive justifications in both algebra and geometry questionnaires, the difference exists in empirical justifications: there were many empirical justifications in algebra, but there were few in geometry questions. When deductive justification was completed, the students showed satisfaction with their own justification. However, they showed dissatisfaction when they could not deductively justify the generality of the proposition using mathematical symbols. From the results of the study, it was found that justification education that can improve algebraic translation ability is necessary so that gifted students can realize the limitations and usefulness of empirical reasoning and make deductive justification.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2003.11a
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• pp.69-76
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• 2003

In this paper, a novel speed control system that implements the fuzzy logic controller(FLC) is proposed. Fuzzy controller is shown more excellent efficency than a conventional controllers in the strength aspect and non-linear controller using IF-THEN rule which can control without process the accurate mathematical modeling about induction motor. But we cannot expect that conventional fuzzy controller divide equally the space of input and output parameter and use the certain shape of triangle membership function. Therefore to develop the efficiency of conventional fuzzy controller, We need to scale the range of membership functions. In this study, proposed fuzzy controller has the ability controlling scale of membership functions using by output scaling factor.