• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.297-312
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• 2006

As research on the instruction method of the concept of irrational numbers, this thesis is theoretically based on the Freudenthal's Mathematising Instruction Theory and a conducted case study in order to find an introduction method of irrational numbers. The purpose of this research is to provide practical information about the instruction method ?f irrational numbers. For this, research questions have been chosen as follows: 1. What is the introducing method of irrational numbers based on the Freudenthal's Mathematising Instruction Theory? 2 What are the Characteristics of the teaming process shown in class using introducing instruction of irrational numbers based on the Freudenthal's Mathematising Instruction? For questions 1 and 2, we conducted literature review and case study respectively For the case study, we, as participant observers, videotaped and transcribed the course of classes, collected data such as reports of students' learning activities, information gathered through interviews, and field notes. The result was analyzed from three viewpoints such as the characteristics of problems, the application of mathematical means, and the development levels of irrational numbers concept.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.251-262
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• 2016

In this paper, we investigate the bracing rectangular frameworks problem and provide a new proof of this problem using the angle sequence according to deformed rectangular frameworks in a view of mathematising. And also we provide the algorithm to determine the rigidity of braced rectangular frameworks.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.543-556
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• 2002

The purpose of this study is to find a method to improve geometry instruction. For this purpose, I have investigated aims and problems of geometry education. I also reviewed related literature about discovery methods as well as verification. Through this review, “Mathematising teaching and learning methods” by Freudenthal is Presented as an alternative to geometry instruction. I investigated the capability of dynamic software for realization of this method. The result of this investigation is that dynamic software is a powerful tool in realizing this method. At last, I present one example of mathematic activity using dynamic software that can be used by school teachers.

• School Mathematics
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• v.8 no.1
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• pp.27-43
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• 2006

The objective of this paper is to design teaching units to foster secondary pre-service teachers' mathematising abilities. In these teaching units we focus on generalizing area of a 2-dimensional triangle and volume of a 3-dimensional tetrahedron to n-volume of n-simplex In this process of generalizing, principle of the permanence of equivalent forms and Cavalieri's principle are applied. To find n-volume of n-simplex, we define n-orthogonal triangular prism, and inquire into n-volume of it. And we find n-volume of n-simplex by using vectors and determinants. Through these teaching units, secondary pre-service teachers can understand and inquire into n-simplex which is generalized from a triangle and a tetrahedron, and n-volume of n-simplex which is generalized from area of a triangle and volume of a tetrahedron. They can also promote natural connection between school mathematics and academic mathematics.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.373-389
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• 2008

In this paper, we designed a teaching unit for the learning mathematization of secondary pre-service teachers through exploring the relationship between partition models and generalized fibonacci sequences. We first suggested some problems which guide pre-service teachers to make phainomenon for organizing nooumenon. Pre-service teachers should find patterns from partitions for various partition models by solving the problems and also form formulas front the patterns. A series of these processes organize nooumenon. Futhermore they should relate the formulas to generalized fibonacci sequences. Finding these relationships is a new mathematical material. Based on developing these mathematical materials, pre-service teachers can be experienced mathematising as real practices.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.1-25
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• 2012

The purpose of this study is to extract the conceptual nature of contextualization in mathematical problems and to analyze problems according to its conceptual framework based on the perspective of RME (Realistic Mathematical Education) which emphasizes mathematising through realistic context in mathematics textbooks of the 4th grade in Korean textbooks and the U. S. materials. "Contextualization" was analyzed by three elements such as everydayness, variety, and mathematical immanence. As results, Korean textbook showed much less in the amount of contextual problems and also represented lower contextualization in contextual problems than that of American textbooks.

• School Mathematics
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• v.11 no.2
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• pp.243-260
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• 2009

In this paper, we have designed a teaching unit for the learning mathematising of secondary pre-service teachers by exploring generalized fibonacci sequences. First, we have found useful formulas for general terms of generalized fibonacci sequences which are expressed as combinatoric notations. Second, by using these formulas and CAS graphing calculator, we can help secondary pre-service teachers to conjecture and discuss the limit of the sequence given by the rations of two adjacent terms of an m-step fibonacci sequence. These processes can remind secondary pre-service teachers of a series of some mathematical principles.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.123-140
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• 1997

Researchers have insisted that mathematics should be learned not as a product but as a process. Nevertheless school mathematics has chosen ‘top-down’ method and has usually instilled into the mind of students the mathematical concepts in the form of product. Consequently school mathematics has been teamed by students without the process of inquiring and mathematical thinking. According to Freudenthal, it is a major source of all problems of mathematics education. He suggested mathematising as the method for 'teaching to think mathematically' 'Teaching to think mathematically' through the process of mathematization, interpreting and analysing mathematics as an activity, is a means to embody the purpose of mathematics education.

• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).