• Research in Mathematical Education
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• v.14 no.3
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• pp.219-231
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• 2010

Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).

• The Mathematical Education
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• v.41 no.1
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• pp.79-90
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• 2002

In this article we study on connecting paper 131ding activities of triangle with mathematical proof Folding median, bisector of angle, and hight of paper triangle, we from and extract some ideas that help us to proof some important theorems of plane geometry. In this study using formed ideas in the process of paper folding activities, we suggest some interesting new mathematical proofs of the following theorems: 1. three medians of triangle are intersect in a point; 2. three bisectors of interior angles of triangle are intersect in a point; 3. three heights of triangle are intersect in a point.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.752-757
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• 2001

The characteristics of heat energy distribution on the fire-proof clay with microwave heating drying are numerically investigated using finite element method. The modelled regular hexahedron chamber$(50cm\times50cm\times50cm)$ filled with air consists of vertical heat source and sink walls, a fire-proof clay model, and adiabatic plates on the top and bottom walls. With different geometrical aspect ratios of the fire-proof clay model, the heat energy distribution is throughly investigated. The model gave a good prediction of the microwave heating characteristics of fire-proof clay. The optimal shape of the fire-proof clay for given chamber geometry and microwave power is analyzed.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.325-337
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• 2011

There have been several studies regarding strict and formal proof in the field of geometry in middle school curriculum, and the level of proof has been gradually lowered along with the changes in the curriculum. In the 2011 Revised Middle School Math Curriculum, there have been efforts to eliminate the term 'proof' and instead to replace it with the new one, 'justification'. Therefore, this study intends to present specific and practical examples of justification by analyzing the current math textbook especially in the field of geometry. As a result, it identified that strict and practical proof has been sharply increased in the second year of middle school. It also witnessed the possibility of justification from the various examples presented in the first, second, and the third year of the middle school math textbook.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.455-467
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• 2008

We need to reflect the establishment of meaning and level of 'proof and argumentation in middle school mathematics'. It should be considered as human activity through communication in community. Thus, we should design instruction from this standpoint. From this point of view, we had been operated 'Geometry Inquiry Class' aimed at middle school students in eighth grade for two years to improve current geometry class in middle school. In this study, we will observe how individual students' original proof schemes are developed and accepted to the class through the process of mutual negotiation between the teacher and students. The episode with four phases begins with the initial proof schemes students have offered. Through the negotiation of class participants, it gives birth to the proof scheme unique to the current geometry classroom. Why do we pay attention to the process? It is because we think that the value of this type of instruction lies in the process of communication and mutual understanding and mutual reference, not in the completeness of the final product. This is the very appropriate proof in the middle school mathematics classroom.

• East Asian mathematical journal
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• v.39 no.4
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• pp.479-492
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• 2023

Although Euclidean plane geometry is implemented in the middle school course, there are three major problems in high school space geometry that can be intuitively taken for granted or misinterpreted as circular arguments. In order to solve this problem, this study proved three major problems using sets, Euclidean plane geometry, and parallel line postulates. This corresponds to a logical sequence and has mathematical and mathematical educational values. Furthermore, it will be possible to configure spatial geometry using sets, and by giving legitimacy to non-Euclidean spatial geometry, it will open the possibility of future research.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.621-634
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• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.143-156
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• 2008

In this study, we divided the teaching and learning of proof into three steps in the demonstrative geometry of the middle school mathematics. And then we surveyed the student's difficulties in the teaching and learning of proof by using of questionnaire. Results of this survey suggest that students cannot only understand the meaning of proof in the teaching and learning of proof but also they cannot deduce simple mathematical reasoning as judgement for the truth of propositions. Moreover, they cannot follow the hypothesis to a conclusion of the proposition It results from the fact that students cannot understand clearly the meaning and the role of hypotheses and conclusions of propositions. So we need to focus more on teaching students about the meaning and role of hypotheses and conclusions of propositions.