• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Research in Mathematical Education
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• v.25 no.2
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• pp.159-164
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• 2022

Critical mathematics education has developed in many directions and has a broad range of approaches. There will probably be many different ways of expressing critical mathematics education. The book, An Invitation to Critical Mathematics Education by Ole Skovsmose (2011) has elucidated critical mathematical education by discussing and reinterpreting its concerns and preoccupations. He reinterprets thoughts and arguments that have been taken for granted and premised in mathematics education, and also discusses unquestioned widespread notions by associating them with his projects or specific practices carried out by him and his colleagues. This review intoduced and examined his crucial notions of critical mathematics education, such as "Diversity of situations," "Students' foreground, Landscapes of investigation," "Mathemacy," and "Uncertainty." These notions will make you to meet his theories with his pratices and look back on something overlooked in mathematics education.

• Journal of the Korean School Mathematics Society
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• v.25 no.3
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• pp.243-260
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• 2022

This article examines the educational background of the knowledge system in mathematics education from three perspectives-behaviorism, cognitivism, and constructivism-centered on psychology in mathematics education. First, the relationship between mathematical education and learning psychology is reviewed according to the flow of time. Second, we examine the viewpoints of objectivism and constructivism for school mathematics. Third, we look at the psychology in mathematics education and constructivism from the perspective of learning theory. Lastly, we discuss the implications of mathematics education.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.205-223
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• 2021

It has been argued that as for the origin of the Pythagorean theorem, the theorem had already been discovered and proved before Pythagoras, and the historical records of ancient mathematics have confirmed various uses of this theorem. The purpose of this study is to examine the relevance of its name caused by Eurocentrism and the weakness of its use in Korean school mathematics and to seek improvements from a critical point of view. To this end, the Pythagorean theorem was reviewed from the perspectives of the history of mathematics and mathematics education. In addition, its name in relation to objective mathematical contents regardless of any specific civilization and its use as a starting point for teaching the theorem in school mathematics were suggested.

• East Asian mathematical journal
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• v.40 no.2
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• pp.127-148
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• 2024

Maximum and minimum have a historical background in mathematics and occupy an important part of the differential unit in school mathematics. As the curriculum is revised, there are changes and problems in the way definition introduced. Therefore, this study analyzes the changes in the method of introducing maximum and minimum definitions following the reorganization of the 2007 and 2009 revised mathematics curriculum, and analyzes the differences in maximum and minimum definition methods compared to the nine mathematics II textbooks in the 2015 revised mathematics curriculum and three real analysis. In addition, methods to improve the terms used in relation to the maximum and minimum values are presented.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.87-99
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• 2003

As the development of computer science discrete mathematics has been developed accordingly. Discrete mathematics is one of the vital element for the development of the computer and IT technologies since it is the theoretical basis for these field of technologies. Currently, according the Seventh Curriculum Standards in Mathematics, high school students may participate in the class of discrete mathematics as one of their optional curriculum. However, discrete mathematics is a new to the most students in high school. Therefore, the teaching methods for the class of discrete mathematics must be carefully designed so that students acknowledge the importance of this new subject. For this purpose, we first show that why the algorithm is needed and then analyze the problem involved in the method of the traditional matrix multiplications. Finally, we suggest two matrix multiplication algorithms which are more efficient than the traditional method.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.499-514
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• 2014

In this study, we conducted the survey to 116 SENKs (students who emigrated from North Korea to South Korea) about mathematical attitude and recognition on mathematics learning and mathematics lesson in South Korea. As the results of the study, SENKs' had positive index on mathematical attitude and recognition about mathematics lesson, but negative index on the recognition about their mathematics learning. SENKs' showed the favoring pictures about mathematics lesson and the needed supports for improving their mathematics understanding. Based on the results, we discussed the implications for teaching and learning of SENKs.

• School Mathematics
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• v.1 no.1
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• pp.135-156
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• 1999

The purpose of this study is to discuss about the role of the visualization as an effective method of teaching abstracted mathematics, to analyze visual materials in middle and high school mathematics and to suggest various visualized materials for teaching mathematics effectively. Though formal, symbolic and analytical teaching method is a major characteristic of mathematics, the students should be taught to understand through intuition and insight, and formalize the mathematical concepts progressively. Especially the sight is one of the most important basics of cognition for intuition and insight. Therefore, suggesting mathematical contents through the visual method makes the students understand and formalize the mathematical concepts more easily. In this study, we tried to investigate the meaning and role of visualization in mathematics teaching. And, we discussed about the four roles of visualization in the process of mathematics teaching and learning confirmation and memorization of the mathematical truth, proving theorem and solving problems which is one of the most important purposes of teaching mathematics, According to the roles of visualization, we analyzed visual materials currently taught in middle and high school, and suggested various visual materials useful in teaching mathematics. The investigated fields are algebra where visual materials are little used, and geometry where they are use the most. The paper-made-textbook can't show moving animation vigorously. Hence we suggested visual materials made by GSP and applets in IES .

• School Mathematics
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• v.17 no.4
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• pp.593-611
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• 2015

Under the assumptions that teachers' beliefs toward mathematics education play a role of a filter between teachers' knowledge and teaching practices, this study surveyed and analyzed elementary teachers' beliefs toward mathematics education: helping students to understand mathematics concepts, addressing students' mathematical misconceptions, engaging students in mathematics classroom, and improving students' mathematical thinking. From the analysis of survey results of the study, I found that there were dominant components in elementary teachers' beliefs system regarding teaching mathematics. In addition, there are some constructs affected by teachers' characteristics such as gender and educational backgrounds. In this study, I presented a representative model of elementary teachers' beliefs system toward mathematics education.