• East Asian mathematical journal
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• v.26 no.2
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• pp.165-177
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• 2010

The purpose of this study is to review previous studies regarding the relationship between graphing calculators usage and teaching and learning school mathematics and to suggest practical implications for further research in mathematics education. Through reviewing the total of 21 studies five subsections are divided in order to gain the answers to the research questions. The results of this study are as follows: students typically used graphing calculators in drawing graphs of functions, and they used graphing calculators as a tool for calculations, transformations, data collection and analysis, visualization, and checking. The implications for further research are suggested corresponding to these results.

• Research in Mathematical Education
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• v.15 no.1
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• pp.81-91
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• 2011

The aim of this study was to explore the grade 1-3 students' geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 1-3. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele's model merely level 0 (Visualization) across textbooks for grades 1-3.

• Communications of Mathematical Education
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• v.15
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• pp.281-286
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• 2003

The primary purpose of this study was to investigate how and to what extent 'representations' affect the students' understanding and the growth of understanding in a technology [GSP]-based collegiate mathematics classroom. There are three themes related as frames of the study along with this purpose, which are mentioned in the first chapter and extended in the second chapter: technology in mathematics education; images on computer screen - visualization and representation; understanding and growth of understanding. Three research questions guided this study: 1) How do students present each component of representations when they study 'transformations' in a technology [GSP]-based classroom? If there is any difference between the first and second presentation for each component, how are they different?; 2) How and to what extent do representations affect the students' understanding and the growth of understanding in a technology [GSP]-based classroom?; What types of benefits and obstacles are there when students study 'transformations' in a technology [GSP]-based classroom?

• Communications of Mathematical Education
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• v.25 no.1
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• pp.245-259
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• 2011

In this study, the instrument of mathematical creative problem solving ability test were considered the differences between Korean and American sixth grade students in mathematical creativity ability and mathematical thinking ability. The instrument consists of 9 items. The participants for the study were 212 Korean and 148 American students. SPSS were carried out to verify the validities and reliability. Reliabilities(Cronbach ${\alpha}$) in mathematical creativity ability is 0.9047 and in mathematical thinking ability is 0.9299 which were satisfied internal validity evaluation on the test items. Internal validity were analyzed by BIGSTEPS based on Rasch's 1-parameter item response model. The results of this study can serve as a foundation for understanding the Korean and American students differences in mathematical creativity ability and mathematical thinking ability. Especially we get the some informations on mathematical creativity ability for American's fifth grade to seventh grade students.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.29-48
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• 2010

The purpose of this paper is to discuss about the use of technology in teaching-learning school mathematics. In this paper, we study the theoretical background of teaching-learning school mathematics by the use of technology. For the purpose of successful use of technology in teaching-learning school mathematics, we research the present states of it appeared in textbooks of high school mathematics And we give suggestions for the effective use of technology in teaching-learning school mathematics. Furthermore, we introduce models for teaching-learning school mathematics in areas of mathematics by the use of computer programs such as GSP, Maple, and GrafEq.

• The Mathematical Education
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• v.56 no.1
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• pp.41-62
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• 2017

The purpose of this study is to propose the possibility of integrating creativity and character education and its need in mathematics education by developing and validating a testing tool assessing students' perceptions of mathematical creativity and character. For this purpose, we developed sixty questions in total to extract factors of mathematical creativity and character based on a literature review. Then, questionnaire data were collected for 1258 middle school students. After the collected data were randomly divided into two (n1=615, n2=643), the first group of data was used for exploratory factor analysis and the second one was employed for confirmatory factor analysis. As a result, 45 problems showing nine factors were extracted. The cognitive components of creativity includes divergent thinking, convergent thinking, imagination/visualization, and reasoning, whereas its affective components are interest, motivation, and openness. The character components contain participation, communication, responsibility, and promise. In addition, it is concluded that the developed testing tool, in which character in the model of this study impacts creativity meaningfully, has a measurement consistency which is not affected by gender and grade differences. These results have implications for a guide to curriculum development promoting creativity and character at school by showing objective and practical foundations of helping how to integrate creativity and character education.

• Proceedings of the Korean Institute Of Construction Engineering and Management
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• 2004.11a
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• pp.543-547
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• 2004

Visualization of construction process simulation and physical modeling were considered to overcome the limitations of current graphical simulation. The output of discrete-event simulation programs which are the most common mathematical statistical simulation tool for construction processes were analyzed for the visualization of earthmoving process that dealing with objects without fixed. Object-oriented models for equipment, material and work environments were devised to effectively visualize the numerical simulation results of the working time, the queuing time as well as the amount resources etc. The oscillation of the crane's cable and the lifted material that should be considered to rationally modeled and simulated by construction graphical simulation. The derived equation of motion was solved by numerical analysis procedure. Then obtained results was used for physical modeling.

• Communications of Mathematical Education
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• v.27 no.1
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• pp.1-17
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• 2013

This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.151-168
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• 2020

The use of software is effective in developing mathematical understanding that provides mathematical problems and ensures mathematical communication. In particular, various software may provide all of the skills and conceptual activities students need to understand mathematical concepts. Based on these arguments, I analyze domestic prior studies based on the perspective of how the shape education using software affects mathematics learning. Based on the five categories of visualization, manipulation, cognitive tools, discourse promoters, and ways of thinking, domestic studies have shown that the number and categories of research related to shape education using software are limited. In addition, it was confirmed that previous studies in South Korea have been focused on the application of software rather than analysis of the changing aspects of learners' mathematics learning. These implications might be used as a basis for setting the direction of research on mathematics education related to the education of software utilization in the future.