• Journal of the Korean School Mathematics Society
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• v.26 no.2
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• pp.111-135
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• 2023

This study conducted a student-centered inquiry lesson on the similarity of figures using AlgeoMath, with student learning aspects analyzed from a communication perspective. This approach aimed to inform pedagogical implications related to teaching geometric similarity. Through utilizing AlgeoMath, students were able to visually confirm that their chosen figures were similar, experiencing key mathematical concepts such as the ratio of similarity to the area of similar figures, and congruency and similarity conditions of triangles. In the lessons applying this concept, we categorized the features of similarity learning displayed by students, as seen in the communication aspects of their exploratory activities, into 'Understanding similarity ratios', 'Grasping conditions of similarity in triangles', and 'Comparing concepts of congruency and similarity'. Through exploratory activities based on AlgeoMath, students discussed the meaning and mathematical relationships of key concepts related to similarity, such as the ratio of similarity to the area of figures, and the meaning and conditions of congruence and similarity in triangles. By improving misconceptions about the similarity of figures, they were able to develop deeper mathematical understanding. This study revealed that in teaching and learning the geometric similarity using AlgeoMath, obtaining meaningful pedagogical outcome was not solely due to the features of the AlgeoMath environment, but also largely depended on the teacher's guidance and intervention that stimulated students' thinking.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.393-407
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• 2009

In this article the definition of similarity and its introduction in Korean middle school textbooks based on the 7th national curriculum are analysed critically. As a result four suggestions are presented. First, on the consideration that the contents related with similarity has been removed in the elementary school curriculum, the meaning of 'constant rate' needs to be understood through the rich experience of drawing enlarged/reduced figures when similarity is introduced in middle school, Second, there are two different ways in enlargement/reduction of figures and in the definition of similarity. Teachers have to keep the limitations of the two ways in mind. Third, the activity of drawing similar figures in enlarged/reduced squared paper needs to be practiced. Last, on 'the relation of similarity' which is in the definition of similarity, it has to be examined whether 'similarity' should be presented in the documents of the national curriculum as a term.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.469-482
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• 2006

It ill give much interest both to the teacher and student that paper crane makes interesting mathematical investment possible. It is really possible for the middle school students to invest mathematical activity such as the things about triangle and square, resemblance, Pythagorean theorem. I reserched how this mathematical investment possible through folding and unfolding paper crane and analyzed the mathematical meaning.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.4
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• pp.521-526
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• 2012

The performance of arrow from a manufacturing process depends on arrow's trajectory(archer's paradox) and intensity of an impact points. Especially, when conducting a shooting experiment over and over in the same experiment condition, the intensity of impact point is an objective standard to judge the performance of the arrow. However, the analysis method for the impact point is not enough, a previous research of the arrow's performance has been focused on a skill to optimize a manufacturing variables(feathers of an arrow, barb of an arrow, arrow's shaft, weight, external diameter, spine). In this paper, We propose measurement system of arrow's impact point with Mamdani fuzzy inference system and similarity of polygon for automation of impact point's measurement. Measuring the impact point data of the arrow moving with a high speed(approximately 275km/h) by using line laser and photo diode array, then the measured data are mapped to arrow's impact point with fuzzy inference and similarity of polygon.

• The Journal of Information Technology
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• v.3 no.3
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• pp.1-9
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• 2000

In this paper, we propose the design and implementation of Multi-media Title for the similar figure learning. The algebra problems of mathematics are usually solved by algorithm, but the diagram problems of geometry have various solution methods. This made us educate the students by memorizing the principle and property of diagram. In this paper, we applied the courseware to the students and analyzed the result. Therefore we could notice the possibilities, "f we teach students by using the courseware, we can improve their learning achievement."

• Communications of Mathematical Education
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• v.25 no.1
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• pp.261-288
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• 2011

We examined the effects of pair assistant collaborative learning on academic achievement of the 2nd year middle school students in the three subjects such as the Probability, Properties of Figures and Similarities of Figures. In order to carry out this study, we selected 2 classes of 2nd year students in a girls middle school in the Fall semester of 2009 and set up the experiment group and comparison group by the result of academic achievement tests given in the end of the Spring semester of 2009. Pair assistant collaborative learning was adopted for students in problem solving 2 or 3 times per a week in the experiment group and each academic achievement was given at the end of each subject in both groups. Also, we had a final survey to find out students' attitude to this collaborative learning. The achievement and survey were analysed by statistical methods. We conclude that our pair assistant collaborative learning was effective in Probability and Similarities of Figures Units. According to the result of survey, this collaborative learning brought about an opportunity to promote students' community spirit through reflecting each one's role in the group.

• 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.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.261-275
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• 2012

There are some geometry achievement standards presented indistinctly in middle school mathematics curriculum revised in 2011. In this study, indistinctness of some geometric topics presented indistinctly such as symbol $\overline{AB}{\perp}\overline{CD}$ simple construction, properties of congruent plane figures, solid of revolution, determination condition of the triangle, justification, center of similarity, position of similarity, middle point connection theorem in triangle, Pythagorean theorem, properties of inscribed angle are discussed. The following three agenda is suggested as conclusions for the development of next middle school mathematics curriculum. First is a resolving unclarity of curriculum. Second is an issuing an authoritative commentary for mathematics curriculum. Third is a developing curriculum based on the accumulation of sufficient researches.

• Annual Conference of KIPS
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• 2011.04a
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• pp.1441-1444
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• 2011

본 논문에서는 초등학교 교육과정에서 교육목표로 다루고 있는 창의성이라는 주제와 학교현장에서 초등학생들에게 쉽게 접목시킬 수 있는 교육용 프로그래밍 언어인 LOGO 프로그래밍과 프랙탈 기하이론을 초등학교 컴퓨터교육에 활용하기 위한 방안을 제시한다. 향후 컴퓨터교육과정은 알고리즘과 프로그래밍 영역이 포함될 예정이며, 이러한 알고리즘과 프로그래밍 교육에는 교육용 프로그래밍 언어 사용이 필수적이며 이의 활용에 대한 연구가 시급한 상황이다. LOGO 프로그래밍과 프랙탈을 함께 지도함으로서 규칙성, 반복성, 유사성, 닮음 등 수학적 개념을 쉽게 이해하는 것이 가능하므로, 이를 활용하여 초등학교 수학과 교육과정에서 반드시 학습해야 할 도형, 측정, 규칙성과 문제 해결 영역과 연계하여 지도하면 좋은 효과를 얻을 수 있을 것으로 기대된다.

• Archives of design research
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• v.17 no.1
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• pp.211-220
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• 2004

The Chaos theory of complexity and Fractal theory which became a prominent figure as a new paradigm of natural science should be understood not as whole, and not into separate elements of nature. Fractal Dimensions are used to measure the complexity of objects. We now have ways of measuring things that were traditionally meaningless or impossible to measure. They are capable of describing many irregularly shaped objects including man and nature. It is compatible method of application to express complexity of nature in the dimension of non-fixed number by placing our point of view to lean toward non-linear, diverse, endless time, and complexity when we look at our world. Fractal Dimension allows us to measure the complexity of an object. Having a wide application of fractal geometry and Chaos theory to the art field is the territory of imagination where art and science encounter each other and yet there has not been much research in this area. The formative word has been extracted in this study by analyzing objective data to grasp formative principle and geometric characteristic of (this)distinct figures of Fractals. With this form of research, it is not so much about fractal in mathematics, but the concept of self-similarity and recursiveness, randomness, devices expressed from unspeakable space, and the formative similarity to graphic design are focused in this study. The fractal figures have characteristics in which the structure doesn't change the nature of things of the figure even in the process if repeated infinitely many times, the limit of the process produces is fractal. Almost all fractals are at least partially self-similar. This means that a part of the fractal is identical to the entire fractal itself even if there is an enlargement to infinitesimal. This means any part has all the information to recompose as whole. Based on this scene, the research is intended to examine possibility of analysis of fractals in geometric characteristics in plasticity toward forms in graphic design. As a result, a beautiful proportion appears in graphic design with calculation of mathematic. It should be an appropriate equation to express nature since the fractal dimension allows us to measure the complexity of an object and the Fractla geometry should pick out high addition in value of peculiarity and characteristics in the complex of art and science. At the stage where the necessity of accepting this demand and adapting ourselves to the change is gathering strength is very significant in this research.