• The Mathematical Education
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• v.50 no.4
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• pp.403-428
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• 2011

The direction of recent education literature points to the importance of creativity and creative practices, which also plays an important role in character education and has been recognized as being invaluable for the educational goals of the 21st century. As such, the goal of mathematics educators and researchers has also been on emphasizing the importance of building character and promoting creative practices. In this research, we study the pedagogical measures that can be easily implemented in classrooms to foster creative mathematical thinking and practices in students. In particular, the mathematical topic of interest is three-dimensional geometry, and especially polygons, and processes in which mathematical knowledge and creative practices play out in classrooms. For example, we explore how these creative lessons can be organized as the target internalization lessons, concepts definition lessons, regularity and relationship lessons, question posing lessons, and narrative story lessons. All of these lessons share three commonalities: 1) they require specific planning and execution challenges in order to achieve creative tasks, 2) they take advantage of open-ended problems, and 3) they are activity-oriented. Through this study, we hope to further our understanding on successful creative mathematical educational practices in the field of mathematics education, and help establish model lessons and materials for teachers and educators to use towards such goals.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.385-406
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• 2018

The purpose of this study is to investigate the effect of mathematics classes focused on mathematical problem posing activities on 10th grade students' mathematics achievement and affective characteristics of mathematics. This study was conducted in a total of 45 regular mathematics classrooms with 81 students from two classes through a nonequivalent control group design. The results of the study showed that the teaching method based on mathematical problem posing activities had a more positive effect on students' mathematics achievement and the affective characteristics of mathematics than the teaching method that focuses on problem solving. The teaching method based on problem posing activities proposed in this study could induce students' self-reflective learning motivation, which in turn gave them a more solid understanding of the mathematical concepts they had learned. In addition, it was found that students' problem solving ability, mathematical communication ability, and mathematical thinking ability were positively influenced by problem posing activities. Regarding the affective characteristics of mathematics, the mathematical problem-posing activity suggested in this study turned out to be a very effective strategy for improving students' interest in mathematics.

• The Mathematical Education
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• v.59 no.4
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• pp.331-355
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• 2020

The purpose of this study is to systematically analyze the results of the existing research on mathematical beliefs, compare and synthesize the valuable results and to suggest implications for mathematical beliefs and research. As a result of checking the methodological quality of 59 articles in total using the MQA(Methodological Quality Assessment) checklist, most of them surveyed mathematical beliefs using questionnaires, and most of the studies were conducted on prospective teachers. As a result of systematic review, the conceptual characteristics of mathematical beliefs, object-specific characteristics, and the educational influence of mathematical beliefs were able to synthesize the meaning. Mathematical beliefs had important educational influences in the practice of teachers, students, and math classes. As the results of the study, we emphasize the importance of changing the beliefs of students and teachers in order to solve the problem of mathematical education, where students rely on private education rather than activity thinking, and teachers do not pay attention to students thinking. It has been shown that concrete support is needed for practicing participatory instruction focused on mathematical thinking.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.521-538
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• 2006

The purpose of this study is to examine the effect of teaching mathematical proofs that made use of the 'proof assisted cards' at the second year of middle school and to investigate students' ability to geometric proofs as well as changes of mathematical attitudes toward geometric proofs. The subjects are seven students at the 2nd year of D Middle School in Daegu who made use of the 'proof assisted cards' during five class periods. The researcher interviewed the students to investigate learning questions made by students as well as the 'proof assisted cards' before and after use. The findings are as follows: first, the students made change of geometric proof ability by proof activity with the 'proof assisted cards' and second, the students made significant change of mathematical attitudes toward geometric proofs by proof activity using the cards.

• Journal of Elementary Mathematics Education in Korea
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• v.8 no.1
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• pp.23-43
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• 2004

The purposes of this study are, by referring to various previous studies on problem posing, to re-construct problem posing steps and a variety of problem posing learning materials with a problem posing teaching-learning model, which are practically useful in math class; then, by applying them to 4-Ga step math teaming, to examine whether this problem posing teaching-learning model has positive effects on the students' problem solving ability and mathematical attitude. The experimental process consisted of the newly designed problem posing teaching-learning curriculum taught to the experimental group, and a general teaching-learning curriculum taught to the comparative group. The study results of this experiment are as follows: First, compared to the comparative group, the experimental group in which the teaching-teaming activity with problem posing was taught showed a significant improvement in problem solving ability. Second, the experimental group in which the teaching-learning activity with problem posing was taught showed a positive change in mathematical attitude.

• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of the Korean Society for Library and Information Science
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• v.14
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• pp.93-130
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• 1987

Scientific communication is an information exchange activity between scientists. Scientific communication is carried out in a variety of informal and formal ways. Basically, informal communication takes place by word of mouth, whereas formal communication occurs via the written word. Science is a highly interdependent activity in which each scientist builds upon the work of colleagues past and present. Consequently, science depends heavily on scientific communication. In this study, three mathematical models, namly Brillouin measure, logistic equation, and Markov chain are examined. These models provide one with a means of describing and predicting the behavior of scientific communication process. These mathematical models can be applied to construct quality filtering algorithms for subject literature which identify synthesized elements (authors, papers, and journals). Each suggests a different type of application. Quality filtering for authors can be useful to funding agencies in terms of identifying individuals doing the best work in a given area or subarea. Quality filtering with respect to papers can be useful in constructing information retrieval and dissemination systems for the community of scientists interested m the field. The quality filtering of journals can be a basis for the establishment of small quality libraries based on local interests in a variety of situations, ranging from the collection of an individual scientist or physician to research centers to developing countries. The objective of this study is to establish the theoretical framework for informetrics which is defined as the quantitative analysis of scientific communication, by investigating mathematical models of scientific communication.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.785-801
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• 2009

The education of mathematics is comprised of formal thoughts so students lose interest and they don't have a chance to have a liberal mind. To solve this problem, recently, the flow of mathematic education is changing from formal mathematics to experimental mathematics, which focuses on student's activity and experience. Experimental mathematics can improve student's interest and participation. This study is about teaching methods of trigonometric functions through experimental mathematics measuring height and width of buildings. For measuring height of buildings we use clinometer and for measuring width of buildings we developed a mathematical tool with which we can measure angle for width of buildings. Through this activity, students obtained an interest in mathematics and they gained a positive attitude for the lesson. If we use this experimental mathematics method in high school, it's possible to reduce fears of mathematics and to increase an interest for mathematics.

• 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.