• The Mathematical Education
• /
• v.56 no.3
• /
• pp.257-280
• /
• 2017

The purpose of this study is to analyze middle school students' learning characteristics they showed on the inquiry-based learning process of circumcenter using various teaching tools, and then to identify the effects of using teaching tools in the middle school students' learning process of circumcenter. For this purpose, we developed teaching materials for inquiry-based learning of circumcenter using textbook, origami, ruler and compass, GeoGebra and sand experiment. Then we applied them on the learning process of circumcenter for five groups of middle school students. From the analyzing of audio/video materials and documents which are collected from the process of participants' inquiry-based learning of circumcenter, we identified the following results. First, inquiry-based learning of circumcenter using various teaching tools promoted mathematical discourses among participants of this study. For example, they conjectured mathematical properties or justified their opinions after manipulated teaching tools in the process of learning circumcenter. Second, inquiry-based learning of circumcenter using various teaching tools promoted participants' divergent thinking. They tried many inquiry methods to find new mathematical properties relate to circumcenter. For example, they tried many inquiry methods to know whether there is unique circle containing four vertices of given quadrangles. Third, we found several didactic implications relate to inquiry-based learning of circumcenter using various teaching tools which are due to characteristics of teaching tools themselves. Participants showed several misconceptions about mathematical properties during they participated inquiry-based activity for learning of circumcenter using various teaching tools. We identified their misconceptions were not due to any other variables containing their learning characteristics but to characteristics of teaching tools.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.2
• /
• pp.227-239
• /
• 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 of the Korean School Mathematics Society
• /
• v.12 no.3
• /
• pp.171-188
• /
• 2009

This study was designed for the purpose of identifying the influences of improved teaching method which constructed at the base of results of survey for finding present teaching-learning method of incenter and circumcenter of triangle. For this, we surveyed the students' understanding and math teachers' teaching method of incenter and circumcenter of triangle. Then, we designed alternative teaching method which innovated the problems from the resultic approaches of Incenter and circumcenter of triangle. And then, we taught students through new method and analyzed the influences of it to students.

• Communications of Mathematical Education
• /
• v.22 no.1
• /
• pp.27-39
• /
• 2008

In this paper we study triangle's properties related with angle bisectors, perpendiculars, circumcenter using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to investigate intersection of segments, how to prove equalities and inequalities using the principle of the lever in triangle.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.3
• /
• pp.355-375
• /
• 2011

This paper was designed for the purpose of helping the functional comprehension on the concept of a circumcenter and an incenter of triangle and offering the help for teaching-learning process on their definitions. We analysed the characteristic of the definition on a circumcenter and an incenter of triangle and studied the context, mean and purpose on the definition. The definition focusing on the construction is the definition stressed on the consistency of the concept through the fact that it is possible to draw figure of the concept. And this definition is the thing that consider the extend of the concept from triangle to polygon. Meanwhile this definition can be confused because the concept is not connected with the terminology. The definition focusing on the meaning is easy to memorize the concept because the concept is connected with the terminology but is difficult to search for the concept truth. And this definition is the thing that has the grounds on the occurrence but is taught in a made-knowledge. The definition focusing on both the construction and meaning is the definition that the starting point is vague in the logical proof process. We hope that the results are used to improve the understanding the concept of a circumcenter and an incenter of triangle in the field of mathematical education.

• Communications of Mathematical Education
• /
• v.23 no.4
• /
• pp.1059-1078
• /
• 2009

In this paper we study metric equalities related with distance between excenter and other points of triangle. Especially we find metric equalities between excenter and incenter, circumcenter, center of mass, orthocenter, vertex, prove these formulas, and transform these formulas into new formula containing another elements of triangle. We in detail describe proof process of these equalities, indicate references of some formulas that don't exist within secondary school curriculum.

• The Mathematical Education
• /
• v.55 no.2
• /
• pp.233-249
• /
• 2016

In this study, we extracted the background meaning of the condition that four points lie on a circle, analyzed textbooks critically and proposed the orientation to improve the content in the textbook. As results, the condition has a realistic background meaning which is 'mathematical modeling of finding a fair location'. The condition has a mathematical background meanings which are 'a first complex situation distinguished from two points and three points', 'the condition described in the perspective of side and angle in order to overcome the disadvantages of the perpendicular bisectors context' and 'being possible to transfer more than five points'. However it is difficult to understand the reason why the condition is on four points in the current textbook. In addition, it is difficult to recognize the connectivity of a circumcenter of triangle. To overcome these problems, we proposed five orientations to improve the content in the textbook.

• Journal for History of Mathematics
• /
• v.34 no.4
• /
• pp.137-149
• /
• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.25 no.3
• /
• pp.296-303
• /
• 2014

In this paper, we propose an algorithm to visualize radio wave environment based on the measured Received Signal Strength Indication( RSSI) and 3D geographic information. We estimate the source position using the circumcenter of the triangle and visualize the radio wave environment using the empirical propagation models. A mode seeking algorithm(mean-shift clustering) is used to seek the peak points and the center of gravity is utilized to reduce the estimation errors. Our approach finds its applications in the radio wave monitoring systems for the efficient utilization of radio resources.

• Communications of Mathematical Education
• /
• v.31 no.2
• /
• pp.203-221
• /
• 2017

The purpose of this study is to suggest didactical principles for using mathematical teaching aids and to applicate didactical principles in a relation with curriculum. First, we meta-analyzed related literature to suggest didactical principles for using mathematical teaching aids. And we suggested didactical principles as follows: principle of activities, principle of instruments, principle of learning. Using mathematical teaching aids with didactical principles in mind would help avoiding situations in which mathematical teaching aids are only used as interesting tools. Second, we concretized the meaning to applicate didactical principles and use mathematical teaching aids in a relation with curriculum. We considered domain, key concept, function, achievement standard, which were presented in the curriculum of mathematics, and suggested concrete activities. Third, we produced two designs for lessons on incenter and circumcenter of triangle and linear function's graph using mathematical teaching aids.