• Research in Mathematical Education
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• v.2 no.2
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• pp.71-78
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• 1998

This paper investigates the practices of proof education in Korea by analyzing the teaching and learning of proofs in classes in the second year of middle school. With this purpose, this study examines the features and deficiencies of the ways of teaching proofs and investigates the difficulties which students have in learning them. Furthermore, it suggests methods for the improvement of teaching proofs.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.5
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• pp.1-6
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• 2017

Gear tooth micro-geometry modifications include the intentional removal of material from the gear teeth flanks, so that the shape is no longer a perfect involute. If the gear shapes are perfect, then the gear tooth meshing is better, therefore the gears will transmit input torque in a more efficient manner without the generation of high frequency engine fluctuation noise. In this paper, we study tooth micro-geometry optimization of rear gear set in 2 speed planetary gear reducers. Analysis revealed problems which are need of modification. Based on the results, tooth micro-geometry was used to deal with load distributions on the rear gear set.

• Journal of Korea Game Society
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• v.13 no.6
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• pp.95-110
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• 2013

Current up-to-date courses of study put emphasis on raising creative students. However, the cramming methods of teaching mathematics in the school seems far from the creativity and the number of students who feels mathematics difficult is increasing. To overcome this situation, the government proposed 'the mathematics education using storytelling', which leads to lots of developments of mathematics using serious game in many areas. However most of the current serious games couldn't do away with the deductive framework of mathematics, which makes it impossible to achieve the purpose of raising creative students. This is because existing mathematics serious games have not deeply contemplated many aspects such as the purpose and theories of teaching and teaching mathematics. Therefore, in order to overcome the limitations of cramming methods in existing mathematics educations, this research proposes the new method of developing serious game contents for elementary geometry that is useful to improve mathematical intuition, based on RME, the theory of teaching/learning mathematics.

• The Mathematical Education
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• v.55 no.4
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• pp.523-538
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• 2016

The purpose of this study is to explore the secondary mathematics teachers' technology integration self-efficacy with respect to geometry classes which they had experienced during last 1 year, 2015. For this study, we developed and validated the questionnaires based on TPACK framework in secondary geometry context. The questionnaires contained 28 items examining the secondary mathematics teachers' TPACK. We conducted the item analysis with 28 items and then the exploring factor analysis. As a result, 28 items was categorized into 5 constructs, TPCK, TCK, TK, PCK, PK, different from Mishra and Koehler's categorization. We analyzed the secondary mathematics teachers' technology integration self-efficacy with respect to geometry classes based on 5 TPACK constructs. The results indicated that there were no significant differences in technology integration self-efficacy according to gender. But technology integration self-efficacy according to the years of teaching experience differed significantly. The more years of teaching experiences teachers have, the lower level of TPCK and TK they have and the more years of teaching experiences teachers have, the higher level of PCK they have. The results also showed that there ware significant difference in TPCK according to the existence and non-existence of taking the technology courses during the time at university. Furthermore, we provide the implication for the professional preparation program for the mathematics teachers in middle schools.

• 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.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.451-465
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• 2012

Since there are several kinds of continuities of maps between digital spaces, the paper compares them, which can play an important role in digital topology and discrete geometry.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.383-410
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• 2004

DGS(dynamic Geometry System)와 WBI(Web Based Instruction)를 고찰해보고, 동적 기하 프로그램의 대표적인 프로그램인 GSP, Cabri, Cinderella를 이용하여 WBI를 제작해 보고 웹 환경 하에서 세 프로그램의 효율성을 비교 ${\cdot}$ 분석하였으며, 이들 세 프로그램의 장점을 정리하여 웹 환경에서 동적 기하 프로그램의 개선 방향을 제시하였다.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.115-134
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• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.