• Journal of Gifted/Talented Education
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• v.25 no.4
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• pp.581-605
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• 2015

The purpose of this study is to build an instruction method focused on the mathematical process and apply it to 12, 5-year-olds from Kindergarten located in Seoul with a view to explore the changes in their mathematical thinking. In addition, surveys with parents and teachers, as well as those conducted in the field of early childhood education, were conducted to analyze the current situation. The effects focused on the five mathematical processes, namely problem solving, reasoning and proof, connecting, representing and communication was found to help the interactions between teacher-child and child-child stimulate the mathematical thinking of the children and induce changes. The mathematical process-focused instruction aimed to advance mathematical thinking internalized mathematical knowledge, presented an integrated problematic situation, and empathized the mathematical process, which enabled the children to solve the problem by working together with peers. As such, the mathematical thinking of the children was integrated and developed within the process of a positive change in the mathematical attitude in which mathematical knowledge is internalized through mathematical process.

• Education of Primary School Mathematics
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• v.12 no.1
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• pp.31-38
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• 2009

This paper aims to develop a program which cultivates statistical ability for elementary students. For this purpose, I examined the relationship between mathematical thinking and statistical thinking. I developed statistical programs including classification, discussion of data, generating statistical problem and project program. As result, this study suggests implications for further elementary statistical education.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.9-33
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• 2004

The purpose of this paper is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. We emphasize for these practices the changing nature of student' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.161-178
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• 2016

Mathematics problem based learning(PBL), which has recently attracted much attention, is a teaching and learning method to increase mathematical ability and help learning mathematical concepts and principles through problem solving using students' mathematical prerequisite knowledge. In spite of such a quite attention, it is not easy to apply and practice PBL actually in school mathematics. Furthermore, the recent instructional situations or environments has focused on student's self construction of their learning and its process. Because of this reason, to whom is related to mathematics education including math teachers, investigation and recognition on the degree of students' acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) is an very important work. Thus, developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recently, connection or integration of one subject and the other subject in school is emphasized, and then mathematics might be one of the most important subjects to have a significant role to connect or integrate with other subjects. While considering the reason is that the ultimate goal of mathematics education is to pursue an enhancement of mathematical thinking ability through the enhancement of problem solving ability, this study aimed to implement basically what is the meaning of the integrated thinking ability in problem based learning theory in Mathematics. In addition, using historical materials, this study was to develop mathematical materials and a sample of a concrete instructional guideline for enhancing integrated thinking ability in problem based learning program.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.201-219
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• 2008

The purpose of this study was to provide useful information for teachers by analyzing various levels of teacher-student communication in elementary mathematics classes and students' mathematical thinking. This study explored mathematical communication of 3 classrooms with regard to questioning, explaining, and the source of mathematical ideas. This study then probed the characteristics of students' mathematical thinking in different standards of communication. The results showed that the higher levels of teacher-student mathematical communication were found with increased frequency of students' mathematical thinking and type. The classroom that had a higher level of Leacher-student mathematical communication was exhibited a higher level of students' mathematical thinking. This highlights the importance of mathematical communication in mathematics c1asses and the necessity of further developing skills of mathematical communication.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.87-101
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• 2005

The purpose of this paper is to propose a teaching method which is focused on the mathematical thinking skills such as the use of induction, counter example, analogy, and so on mathematicians use when they explore their research fields. Many have indicated that students have learned mathematics exploring to use very different methods mathematicians have done and suggested students explore as they do. In the first part of the paper, the plausible whole processes from the beginning time they get a rough idea to a refined mathematical truth. In the second part, an example with Euler characteristic of 1. In the third, explaining the same processes with ${\pi}$, a model modified from the processes is designed. It is hoped that the suggested model, focused on a variety of mathematical thinking, helps students learn mathematics with understanding and with the association of exploring entertainment.

• School Mathematics
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• v.2 no.2
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• pp.403-426
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• 2000

In this study, we tried to suggest a meaningful teaching method that is a mathematical thinking-oriented. After referring to the recent trend of mathematics education, we examined the direction that school mathematics should go. Next, we considered previous studies that deals with teaching methods focusing on the mathematical thinking. On the basis of the above examination, we accomplished case studies that aims at mathematical thinking-oriented teaching. And we explained that these case studies reflects the key points didactics of mathematics such as the education of ‘open mathematics’, constructivism etc. Finally, we proposed the necessity of mathematical thinking-oriented teaching in the current state of school mathematics.

• Research in Mathematical Education
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• v.17 no.4
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• pp.291-307
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• 2013

Piaget's revolutionary study on the cognitive development of children has focused on the development of logic. Logical operations and a variety of classifications based on the set of accepted rules involve convergent thinking. Children and adults have logical and creative thinking which deal with a reality of thinking. This study aims to examine a cognitive structure of students, which is closely related to the Piaget's cognitive development theories of students when creative thinking. Students were given an open mathematical problem and were expected to be able to take advantage of sensitivity, fluency, flexibility, originality, and elaboration which can be seen as clearly of their structure cognitive.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.681-700
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• 2010

These days, the importance of the mathematics interaction is strongly emphasized, which leads to the need of research on how the interaction is being practiced in the math class and what can be the desirable interaction in terms of mathematical thinking. To figure out the correlation between the mathematical interaction patterns and mathematical thinking, it also classifies mathematical thinking levels into the phases of recognizing, building-with and constructing. we can say that there are all of three patterns of the mathematics interactions in the class, and although it seems that the funnel pattern is contributing to active interaction between the students and teachers, it has few positive effects regarding mathematical thinking. In other words, what we need is not the frequency of the interaction but the mathematics interaction that improves students' mathematical thinking. Therefore, we can conclude that it is the focus pattern that is desirable mathematics interaction in the class in the view of mathematical thinking.

• The Mathematical Education
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• v.46 no.3
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• pp.293-302
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• 2007

In this paper, we review definition and concept of mathematical creativity. A couple of criteria have established for perspectives in mathematical creativity, The first is specific domain(mathematics) vs general domain(creativity) and the second is process(thinking process) vs outcome(divergent production). By these criteria, four perspectives have constructed : mathematics-thinking process approach(McTd), mathematics-divergent production approach(MctD), creativity-thinking process approach(mCTd), creativity-divergent production approach(mCtD). When mathematical creativity is researched by the specific reason and particular focus, an appropriate approach can be chosen in four perspectives.