• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.143-153
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• 2004

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

• Research in Mathematical Education
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• v.16 no.4
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• pp.265-276
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• 2012

These days, with the emphasis on statistical literacy, the importance of communication is the focus of attention. Communication about statistics is important since it is a way of describing the understanding of concepts and the interpretation of data. However, students usually have trouble with expressing what they understand, especially through writing. In this paper, we examined preservice teachers' difficulties when they wrote about statistical concepts. By comparing preservice teachers' written responses and interview transcripts of the variance concept task, we could find the missing information in their written language compared to their verbal language. From the results, we found that preservice teachers had difficulty in connecting terms contextually and conceptually, presenting various factors of the concepts that they considered, and presenting the problem solving strategies that they used.

• Research in Mathematical Education
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• v.6 no.2
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• pp.117-122
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• 2002

From the beginning of the 20th century, calculus is gradually offered to high school students in many countries. However, in Chinese high school, the instruction on calculus is nearly an untouched field. Many people don't believe that high school students can study calculus well. They think calculus knowledge in students' brains is likely to become the “half-cooked food”, and this can produce a bad effect on the study of formal calculus at university. The authors consider that the emphasis of calculus in high school should be the intuitive understanding of fundamental calculus concepts, and it is also the basis of the understanding of formal concepts. Traditional mathematics course with chalk can't meet the needs of calculus teaching. The use of technologies can enhance the calculus teaching, especially the informal and visual calculus teaching, help students understand the underlying concepts. The authors describe how the use of technologies can improve the calculus teaching and learning, and point out that the use of technologies can clear up people's doubts.

• The Mathematical Education
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• v.40 no.2
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• pp.335-343
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• 2001

Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

• Research in Mathematical Education
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• v.24 no.2
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• pp.111-130
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• 2021

This exploratory study focuses on analyzing three mathematics textbooks in Germany, Singapore and South Korea to reveal similarities and differences in their introductions of fraction concepts. Findings reveal that all three countries' textbooks introduce fraction concepts predominantly by using pictorial representations such as area models, but the introductions of multiple fraction constructs vary. The Singaporean and South Korean textbooks predominantly used a part-whole construct to introduce fractional concepts while the German textbook introduced various constructs sequentially in the first pages using several scenarios from different real-life situations. The findings were represented using visual representations, which we called textbook signatures. The textbook signatures provided configurations of the textbook features across the three countries. At the end of paper, we share insights and limitations about the use of textbook signatures in the research on textbook analysis.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• Research in Mathematical Education
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• v.11 no.1
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• pp.33-51
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• 2007

The present study explores mathematics teachers' understanding of division by zero and their approaches to explaining the impossibility of division by zero. This study analyzes Chinese and Korean middle school mathematics teachers' responses to the teaching task of explaining the impossibility of dividing 7 by zero, and examples of teachers' reasoned explanations for their answers are presented. The findings from this study suggest that most Korean teachers offer multiple types of mathematical explanations for justifying the impossibility of division by zero, while Chinese teachers' explanations were more uniform and based less on mathematical ideas than those of their Korean counterparts. Another finding from this study is that teachers' particular conceptions of zero were strongly associated with their justifications for the impossibility of division by zero, and the influence of the teachers' conceptions of zero was revealed as a barrier in composing a well-reasoned explanation for the impossibility of division by zero. One of the practical implications of this study is those teachers' basic attitudes toward always attempting to give explanations for mathematical facts or mathematical concepts do not seem to be derived solely from their sufficient knowledge of the facts or concepts of mathematics.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.247-260
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• 2024

In real life, the concepts of number range and approximation are frequently used. These concepts are closely related to various mathematical concepts, and the need for research on the defining and learning of these related terms is emphasized. The learning contents of seven mathematical terms related to the range of numbers and approximation were analyzed, focusing on the definition of terms and the context of real life. As a result of analyzing the contents of 10 currently used elementary school mathematics textbooks, the lessons were organized according to the achievement standards presented in the curriculum, but the composition and order, real-life context, examples used in definitions, and the highlighted parts and directions of the activities varied depending on the author's intent. Based on the analysis results, implications for textbook writing and classroom instruction were presented.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.265-272
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• 1999

In this paper we define generalized concepts of cardinal-ity of a fuzzy-valued function and obtained some properties of these new concepts.