• Education of Primary School Mathematics
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• v.20 no.3
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• pp.237-252
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• 2017

The era of the Fourth Industrial Revolution has also influenced the direction of mathematics education. In particular, the convergence capability that recognizes how mathematics can be applied and utilized in various fields is an important point. The purpose of this study is to examine the point of convergence and to develop a fusion program that can be used in the mathematics classroom. Specifically, we analyze the tiles used in ancient Islamic architecture from a mathematical point of view and develop mathematics and multifamily convergence programs based on them. Through the mathematical analysis of the geometric tiling made 500 years earlier than Penrose, I hope that understanding of design, the use of mathematics and the possibility of convergence of other disciplines through mathematics will be widened.

• Archives of design research
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• v.20
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• pp.61-72
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• 1997

This study aims to promote understanding level for mathematical model, to improve methods and necessity of application in the process of product design and also to promote approaching and applying methods as a guideline for beginners. For the procedure and method of study first, it was emphasized by linking method and necessity of scientific analysis and a quality of product design and design process. Next, the corresponding relations between mathematical model and design probelem was desciebed, the mathematical model was examinated appeying process of product design. Lastly, approaching and applying methods for beginners was presented based on the discribed studied contents. As the result of the study, some points are by a result or problem : frist, the point that mathematical model is useful to grasp the design problems which various elements are complicately involved quantitatively and structurally, and its necessity can be especially utilized as a tool to justify and convince the convince the conclusion of the designer himself to the persons concerned. Second, the point that in order to apply mathematical model to the design process skillfully, first of all, the substance of all mathematical models which can be applid, and it is not easy to command in perfect method without using computer. Third, the point that since there are many kindsof mathematical models used is mathematical modeland the models which can be applidied to solve design problems differ in accordance with the design types and design process, its applying method can be presented as one kind of standardization or concretely. Fourth the point that in case of approaching mathematical model for the first time, it can start to select model corresponding with design type by stage of design process bassed on understanding for some mathematical knowledge and computer program.

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.31-40
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• 2012

In this paper, we developed teaching learning models using a numeral operation for the mathematical gifted focused on the design of a circle using GSP and investigated effects of this models. This model gave gifted-students to be able to produce creative outputs with mathematical principles and practicality and beauty of mathematics. We found following facts. Firstly, a developed teaching-learning model improves a mathematical gifted student's mathematical creativity as analytic thinking and deductive inference. Secondly, a circular design using GSP helps gifted students to understand the abstract rules because mathematical patterns was represented visually by a circular design. Lastly, a circular design using a numeral operation is helpful to gifted students revealing to creativity and beauty of mathematics.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.235-256
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• 2020

The purpose of this study was to investigate the experience of pre-service mathematics teachers who attended at a university course combined with teaching practicum based on design thinking process to identify the change of their awareness of its activities. For the research, 8 pre-service mathematics teachers participated in a mathematics major course, consisting of 5 phases of design thinking formed by Stanford d.school. In the end of the course, qualitative data were collected through individual and focus group interviews and the course activities. By data analysis, the results of this study were as follows. Firstly, the participants' perspectives of design thinking activities were changed from the difficulty and ambiguity of its activity in the beginning of the process to positiveness with competence of solving authentic problem in terms of teaching practicum over time. Secondly, the participating pre-service teachers emphasized that design thinking activities helped them prepare well teaching practicum and raise understanding of students they met in the school fields. Thirdly, some research participants went through the difficulty in utilizing their products drawn from 4th phase (prototyping) of design thinking process depending on the acceptance of their guidance teachers. Fourthly, the research participants also pointed out that the design thinking was a significant activity in that they learned how to understand and communicate with their students and how to collaborate with team members and it gave an insight about the preparation for a class. Through these results, this study identified the possibility of using the design thinking process for pre-service mathematics teachers' teaching practicum. In addition, the research put forward some implications for better use of design thinking in teacher education.

• Communications of Mathematical Education
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• v.28 no.2
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• pp.281-302
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• 2014

The purpose of this paper is to offer a history of golden ratio, the criterion raised by Markowsky, and misconceptions about golden ratio. Markowsky(1992) insists that the golden ratio does not appear in the great pyramid of Khufu. On the contrary, we claim that there exists the golden ration on it. Elementary and middle school text books, and domestic history books deal with the great pyramid of Khuff and the Parthenon by examples of the golden ratio. Text books make many incorrect statements about golden ratio; so in teaching and learning the golden ratio, we recommend the design-composition of dynamic symmetry, for example, industrial design, aerodynamic, architecture design, and screen design. Finally we discuss the axial age how to affect the school mathematics with respect to the subject of Thales and the golden ratio.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.57-63
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• 2014

Recently, some storytelling materials based on music or CAS tools have been introduced. Activities or concepts in art can be utilized as such material. In this article, we propose a mathematical storytelling material based on design scheme.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.539-560
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• 2013

The purpose of this study was to investigate characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Eight mathematically gifted high school students, who already learned graphs of functions and inequalities necessary for design activities, were selected to work in pairs in our experiment. Results indicate that logical thinking and mathematical abstraction, intuitive and structural insights, flexible thinking, divergent thinking and originality, generalization and inductive reasoning emerged in the design activities. Nonetheless, fine-grained analysis of their mathematical activities also implies that teachers for gifted students need to emphasize both geometric and algebraic aspects of mathematical subjects, especially, algebraic expressions, and the tasks for the students are to be rich enough to provide a variety of ways to simplify the expressions.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.04a
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• pp.1013-1016
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• 2010

시스템의 올바른 동작이 반드시 보장되어야 하는 안전필수 시스템의 안전성과 신뢰성을 확보하기 위한 방법으로 정형기법이 있다. 정형기법은 수학과 논리를 기초로 하는 방법으로, 초심자에게는 다소 난해하고 어려운 부분이 있다. 이와 같은 어려움을 조금이나마 덜 수 있는 방법으로 본 논문에서는 정형기법을 적용한 디자인 패턴을 제안한다.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.241-254
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• 2015

We have announced a series of Archimedean stars on the mathematical art galleries of Bridges conference since 2012. We are developing a systematic approach and methodology about the composition process of Archimedean stars on geometric tube design. We will introduce the various information about the Archimedean horizontal stars under certain introductory level as well as the underlying information of Archimedean stars to provide them as useful sources for certain creative experimental mathematics education.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.