• Communications of Mathematical Education
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• v.13 no.2
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• pp.693-700
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• 2002

대학수학(미분적분학의 이해, 생활과 수학)수업에서, 공간좌표 단원과 도형편을 지도할 때, 구체적인 모델을 들고 또, 구체적인 예- 쌍곡기하에서는, i)삼각형의 세 내각의 크기의 합은 180도 보다 작다 ii) 피타고라스 정리가 성립하지 않는다. iii) 세 내각의 크기가 90도이고 한 내각의 크기가 90도 보다 작은 사각형이 존재한다. 는 예를 들어 유클리드 기하와 쌍곡기하에 대해 비교 설명하며 수업에 흥미를 불러 일으키고, 새로운 세계에 대한 생각을 할 수 있는 기회를 제공한다.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.511-528
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• 2010

Students' intuition in formal proof should be expressed as symbols according to the deductive process. The symbol will play a role of the mediation between the intuition and the formal proof. This study examined the evolution process of intuition mediated by the symbol in geometry proof. According to the results first, symbol took the great roles when students had the non-formed intuition for the proposition. The signification of symbols could explain even the proof process of the proposition with the non-expectable intuition. And when students proved it by symbols, not by figure nor words, they could evolute the conclusive intuition about the proposition.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.437-452
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• 2007

Complementarity, complementary principle and complementary approach have been often used in school mathematics but its meaning has not been obvious. Thus this paper tries to make explicit the meaning by looking around complementary characteristic of mathematical knowledge. First of all, we examines the general meaning of complementarity and Investigate complementary characteristics of mathematical concepts through incommensurability and zeno's paradox. From this, complementary approach to school mathematics is studied. To understand and uncover complementary characteristics of mathematical concepts make it possible for student to have an insight. It is the most important thing that students can have an image of mathematics as a living system rather than as a mechanical application of rules and fragmentary in formations.

• Journal of the Korea Society of Computer and Information
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• v.26 no.6
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• pp.37-46
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• 2021

In this paper, we designed and implemented a program to measure and to judge the accuracy of yoga postures using Azure Kinect. The program measures all joint positions of the user through Azure Kinect Camera and sensors. The measured values of joints are used as data to determine accuracy in two ways. The measured joint data are determined by trigonometry and Pythagoras theorem to determine the angle of the joint. In addition, the measured joint value is changed to relative position value. The calculated and obtained values are compared to the joint values and relative position values of the desired posture to determine the accuracy. Azure Kinect Camera organizes the screen so that users can check their posture and gives feedback on the user's posture accuracy to improve their posture.

• The Mathematical Education
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• v.57 no.2
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• pp.93-110
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• 2018

One of the biggest changes in the 2015 revised mathematics curriculum is shifting to the second year of middle school in Pythagorean theorem. In this study, the following subjects were studied. First, Pythagoras theorem analyzed the expected problems caused by the shift to the second year middle school. Secondly, we have researched the reconstruction method to solve these problems. The results of this study are as follows. First, there are many different ways to deal with Pythagorean theorem in many countries around the world. In most countries, it was dealt with in 7th grade, but Japan was dealing with 9th grade, and the United States was dealing with 7th, 8th and 9th grade. Second, we derived meaningful implications for the curriculum of Korea from various cases of various countries. The first implication is that the Pythagorean theorem is a content element that can be learned anywhere in the 7th, 8th, and 9th grade. Second, there is one prerequisite before learning Pythagorean theorem, which is learning about the square root. Third, the square roots must be learned before learning Pythagorean theorem. Optimal positions are to be placed in the eighth grade 'rational and cyclic minority' unit. Third, Pythagorean theorem itself is important, but its use is more important. The achievement criteria for the use of Pythagorean theorem should not be erased. In the 9th grade 'Numbers and Calculations' unit, after learning arithmetic calculations including square roots, we propose to reconstruct the square root and the utilization subfields of Pythagorean theorem.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• 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.

• The Journal of Korean Association of Computer Education
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• v.4 no.1
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• pp.99-107
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• 2001

One of the main objects of geometry in mathematics education is to improve students' geometric intuition capability and logical reasoning capability based on them. A visual element related to intuition plays an important role in teaching and learning of geometry. Therefore, in this research, we focus on the development of multimedia title available to dynamic operation about visual elements and verify of effect of its application. This title for the learning of "the Pythagorean theorem and its practical use" in the third grade of middle school is designed and implemented by an authoring tool, Toolbook. And it enables learners to study mathematics individually and can be applied to the educational field, too. And we taught two groups, the applied group and the compared one of the second grade of middle school and surveyed Questions and evaluated study achievement. We calculated study achievement of two groups on t-test using SPSS. As the result, we knew that the applied group is higher than the compared one in the study achievement and provision of dynamic operation possibility on visual elements make students know very high learning effect and help improvement of intelligent capability.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.101-122
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• 2010

Chinese Taipei won the first place at the mathematics achievement of TIMSS 2007. Especially, there was a significant difference in the percentage of correct answers between Chinese Taipei and Korea, and Chinese Taipei' percentage of correct answers was higher than Korea. This study compared the education system, mathematics instruction environment, and instructional activities of two countries. And for algebra, curriculum and textbooks were compared between two countries based on TIMSS 2007 framework. It was found that Chinese Taipei emphasized homework and test, and MCFL of that was low. Their textbook was formal, and induced the hasty abstraction, Also, some themes were introduced earlier than Korea and repeated across different grades.

• School Mathematics
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• v.4 no.3
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• pp.347-360
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• 2002

This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.