• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.445-452
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• 2005

본 연구는 중 고등학교 교사 50명에 대하여 기하 문제의 논증기하적 또는 해석기하적 문제해결 전략이 학생들의 평가에 어떤 영향을 미치는가를 조사한 것이다. 중학교에서 고등학교로 진학하면 도형의 문제에 대한 해석기하적인 문제해결 능력은 교육과정 상 대단히 중요하게 가르쳐야 할 내용이다. 유클리드 기하에 바탕을 둔 논증기하의 지식은 좌표평면의 도형을 방정식으로 나타내고 연구하는 해석기하의 기본이다. 그럼에도 불구하고 많은 학생들은 논증기하적 문제해결을 선호하는 반면 해석기하적 문제해결은 어려워한다. 또한 논증기하적 문제 형태에는 논증기하적 문제해결 전략, 해석기하적 문제 형태에는 해석기하적 문제해결 전략을 구사하는 경향을 보인다. 본 연구는 중 고등학교 교사들의 기하 문제에 대한 내용 지식이 학생 평가에 미치는 영향에 초점이 맞추어져 있다.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.701-725
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• 2017

Students need to have opportunities to share their ideas with peers by taking part in the conversation voluntarily that is, by persuading others and reflecting the consequences. Recognizing the importance of this point, this study intended to examine students' argumentation occurring in the process of performing tasks in the math classroom. Also, it tried to explore the types of the argument that students used in the classroom and the reason why they employed them with a focus on 'rebuttal', which is one of the six elements of the argument scheme such as claim, data, warrent, backing, qualifiers, and rebuttal. The analysis of argumentation is based on the five argumentation schemes suggested by Verheij(2005). The experimental class was conducted twice a week with four participants who are third grade middle school students. In the argumentation class students were promoted to address two different kinds of geometrical tasks. After the second session of class, the researcher conducted the semi-structured interview. Accordingly, this study contributes to the existing research by making students to have concrete and active argumentation while obtaining the sound understanding of the argumentation.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.451-466
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• 2007

Geometry in school mathematics is the field that has the possibility of diverse approach such as Synthetic Geometry and Analytic Geometry. Synthetic Geometry is handled in middle schools and Analytic Geometry in the first year of high schools. Therefore, this research show for the possibility of using Synthetic Geometry in high schools which was learned already in middle schools and the way of integrating both of them concretely. This is expected to help students understand the mathematical meaning of figures a lot.

• School Mathematics
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• v.18 no.1
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• pp.85-103
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• 2016

This study was to find characteristics of argumentation derived from a discourse in a math-gifted 5 grade class, which was held for finding a Pick's formula using Geoboard function of TI-73 calculator. For the analysis, a video record of the class, transcript of its voice record, and activity paper were used as data and Toulmin's argument schemes were applied as analysis standard. As a result of the study, we found that the graphing calculator helped the students to create an experimental environment that graphing a grid-polygon and figuring out its area. Furthermore, it also provided a basic demonstration through 'data->claim' composition and reasoning activities which consisted of guarantee, warrant, backing, qualifier and refutal for justifying. The basic argumentation during the process of deriving the Pick's theorem by the numbers of boundary points and inner points was developed into a 'collective argumentation' while a teacher took a role of a conductor of the argumentation and an authorizer on the knowledge at the same time.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.411-429
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• 2015

In this study we investigated the effects of using GSP in solving geometric problems. Especially we focused the effects of GSP in leveled students' connection of geometry and algebra. High leveled students prefer to use algebraic formula to solve geometric problems. But when they did not know the geometric meaning of their algebraic formula, they could recognize the meaning after using GSP. Middle and low leveled students usually used GSP to obtain hints to solve the problems. For the low leveled students GSP was usually used to understand the meaning of the problem, but it did not make them solve the problem.

• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.373-394
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• 2016

The "Figure Equation" chapter of current high school curriculum prevents students from relating the concept with what they studied in middle school Euclidean geometry. Woo(1998) concerns that the curriculum introduces the concept merely in algebraic ways without providing students with opportunities to relate it with their prior understanding of geometry, which is based on Euclidean one. In the present study, a sequence of GeoGebra-embedded-geometry lessons was designed so that students could be introduced to and solve problems of the Analytic Geometry by triggering their prior understanding of the Euclidean Geometry which they had learnt in middle school. The study contributes to the field of mathematics education by suggesting a sequence of geometry lessons where students could introduce to the coordinate geometry meaningfully and conceptually in high school.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.1-23
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• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Communications of Mathematical Education
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• v.14
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• pp.197-215
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• 2001

최근 수학적 사고력 연구가 구체적 수학내용에 기반한 활동과 조작에 대한 연구보다는 활동이나 조작을 통한 결과로 수학적 사고력에 접근하는 일회성 연구로 이루어지는 경향이 있다. 본고에서는 교육 내용을 선정하기 위해 학교수학에서 아동들이 어떤 수학적 사고를 하는데 장애을 겪는지에 주목하여, 이러한 장애를 극복하는 것을 통해 수학적 사고력의 신장을 생각해보고자 하였다. 이에 대수에서는 문자도입에 따른 추상적 상징의 수용과 이용부분에서, 기하에서는 논증기하의 증명도입과정에서 형식적, 연역적 사고 시작으로 아동이 수학적 사고에 어려움을 겪는다는 사살에 주목하였다. 특히 논증 기하의 연역적, 형식적 증명은 논리와 추론이 바탕이 되어야 한다. 그런데 논리와 추론은 고등학교 1학년과정 집합과 명제부분에 들어있어 아동은 논리와 추론에 대한 어떤 경험도, 교육도 받지 않은 상태에서 증명을 하게 된다. 이에 교육 내용으로 수학적 사고력을 신장을 위해 가장 필요한 내용이 논증 기하가 도입되기 이전에 초등학교 5,6학년 아동을 대상으로한 논리와 추론교육이라고 본다. 또한 교육 방법으로는 컴퓨터를 이용한 교육공학적 접근을 하고자 하였다. 교육공학적 접근이 적극 권장되는 교육적 현실과 정규교육과정에서 이를 받아들일만한 시간적 여유가 없음을 감안하여, 교과 내용과 연계된 컴퓨터 교육을 제안하는 바이다. 이에 논리 및 추론 교육은 컴퓨터 교육으로 초등학교의 특기적성 시간이나 정규수업 시간에 이용할 것을 제안한다. 논리와 추론교육을 위해 무엇을 어떻게 가르칠 것인가에 대한 답으로 논리와 추론교육에 적합한 수학적 내용으로 크게 이산수학과 중등 기하의 초등화하여 탐구하도록 하는 내용을, 교육 방법 측면에서는 논리와 추론 교육을 위한 LOGO 기반 마이크로월드를 설계, 이용하여 수학적 사고력을 신장시키고자 한다. 여기까지가 수학적 사고력을 위한 가능성을 모색한 것이라면 후속연구로 이러한 가능성을 실험연구로 검증하고자 한다.

• 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.