• 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.

• School Mathematics
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• v.8 no.2
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• pp.215-237
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• 2006

In this study, we research distinctive features of geometry problem solving of middle school students whose mathematical achievement levels are distinguished by National Assessment of Educational Achievement. We classified 9 students into 3 groups according to their level : advanced level, proficient level, basic level. They solved an atypical geometry problem while all their problem solving stages were observed and then analyzed in aspect of development of geometrical concepts and access to the route of problem solving. As those analyses, we gave some suggestions of teaching on mathematics as students' achievement level.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.451-472
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• 2011

In this paper we studied problem solving related with geometric interpretation of algebraic expressions. We analyzed algebraic expressions, related these expressions with geometric interpretation. By using geometric interpretation we could find new approaches to solving mathematical problems. We suggested new problem solving methods related with geometric interpretation of algebraic expressions.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.655-678
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• 2010

In the elementary mathematics, geometric education emphasize spatial sense and understandings of figures through development of intuitions in space. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and methods in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. First, we investigate visualization methods for plane problem solving and space problem solving respectively, and analyse in diagram form how progress understanding of figures and visualization process. Next, we derive constituent factor on visualization process, and make a check errors which represented by difficulties in visualization process. Through these analysis, this paper aims at deriving an influence of visualization on geometric problem solving in the elementary mathematics.

• Journal of the Korean Operations Research and Management Science Society
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• v.1 no.1
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• pp.51-54
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• 1976

1964년에 Duffin과 Zener는 기하적 계획법(Geometric Programming)이란 새로운 비선형 계획법(Nonlinaer Programming)을 개발하였다. 이 새로운 기하적 계획법은 수주한 형태의 비선형 계획문제에만 적용이 가능하지만 반면 적용이 가능한 문제에 관해서는 매우 강력한 계획법중에 하나가 된다. 지금부터 기하적 계획법의 원리와 그에 따르는 문제해결 예제를 들면서 적용 가능한 비선형 문제를 해결하겠다.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.39-54
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• 2008

This paper investigate Descartes' , which is significant in the history of mathematics, from standpoint of problem-solving. Descartes has clarified the general principle of problem-solving. What is more important, he has found his own new method to solve confronting problem. It is said that those great achievements have exercised profound influence over following generation. Accordingly this article analyze Descartes' work focusing his method.

• The Mathematical Education
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• v.60 no.4
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• pp.543-554
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• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• 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.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.221-221
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• 2010

고대의 인도수학은 산스크리트어로 쓰여 있고, 최초의 기하학은 베다문헌으로 경전 속에 포함되어 있으며, 성스런 제단이나 사원을 설계하기위해서 발전하였다. 고대 인도의 많은 수학자들은 힌두교의 성직자들로 일찍이 십진법, 계산법, 방정식, 대수학, 기하학, 삼각법 등의 연구에 공헌하였다. 인도 기하학은 양적이며 계산적이지만 원리를 가지고 문제를 해결하는 특성이 있다. 그러나 고대 그리스 기하학은 공리적이고 연역적으로 전개되는 완전한 학문으로 발전하였다. 고대 인도와 타 문명권의 기하학을 비교하는 것은 오늘날 문제해결을 중시하는 현대과학의 시대에 가치와 의미가 있는 것으로 사료된다.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.