• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.309-325
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• 2009

The purpose of the study was to investigate the differences between Korean mathematics textbooks and CPMP textbooks in the view of conceptual network, structure of mathematical contents, instructional design, and teaching and learning environment to explore the implications for mathematics education in Korea. According to the results, Korean textbooks emphasized the mathematical structures and conceptual network, on the other hand, CPMP textbooks focused on making connections between mathematical concepts and corresponding real life situations as well as mathematical structures. And generalizing mathematical concepts at the symbolic level was very important objective in Korean textbooks, but in the CPMP textbooks, investigating mathematical ideas and solving problems in diverse contexts including real- life situations were considered very important. Teachers using Korean textbooks preferred an explanatory teaching method with the use of concrete manipulatives and student worksheet, however, teachers using CPMP textbooks emphasized collaborative group activities to communicate mathematical ideas and encouraged students to use graphing calculators when they explore mathematical concepts and solve problems.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.179-198
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• 2011

The understanding of mathematical concepts should be backed up on a constant basis in oder to grow problem-solving skills which is one of the ultimate goals of math education. The purpose of the study was to provide readers with the information which could be considered valuably for the math educators trying both to prevent mathematical misconceptions and to develop curricular program by estimating the actual conditions and developing backgrounds of the mathematical misconceptions held by the gifted education learners. Accordingly, this study, as the first step, theoretically examined the meaning and the developing background of mathematical misconception. As the second step, this study examined the actual conditions of mathematical misconceptions held by the participant students who were enrolled in the CTY(Center for Talented Youth) program run by a university. The results showed that the percentage of the correct statements made by participant students is only 35%. The results also showed that most of the participant students belonged either to the level 2 requiring students to distinguish examples from non-examples of the mathematical concepts or the level 3 requiring students to recognize and describe the common nature of the mathematical concepts with their own expressions based on the four-level of concept formulation. The causes could be traced to the presentation of limited example, wrong preconcept, the imbalance of conceptual definition and conceptual image. Based on the estimation, this study summarized a general plan preventing the mathematical misconceptions in a math classroom.

• The Mathematical Education
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• v.56 no.1
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• pp.101-118
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• 2017

In this article we study a reconstruction of mathematical knowledge on trigonometry by the method of ascent from the abstract to the concrete from the pedagogical viewpoint of dialectic. The direction of education is shifting in a way that emphasizes the active constitution of knowledge by the learning subjects from the perspective that knowledge is transferred from the teacher to the student. In mathematics education, active discussions on the construction of mathematical knowledge by learners have been going on since the late 1990s. In Korea, concepts and aspects of constructivism such as operational constructivism, radical constructivism, and social constructivism were introduced. However, examples of practical construction according to the direction of construction of mathematical knowledge are very hard to find. In this study, we discuss the direction of the actual construction of mathematical knowledge and suggest a concrete example of the actual construction of trigonometry knowledge from a constructivist point of view. In particular, we discuss the process of the construction of theoretical knowledge, the ascent from the abstract to the concrete, based on the literature study from the pedagogical viewpoint of dialectic, and show how to construct the mathematical knowledge on trigonometry by the method of ascent from the abstract to the concrete. Through this study, it is expected to introduce the new direction and new method of knowledge construction as 'the ascent from the abstract to the concrete', and to present the possibility of applying dialectic concepts to mathematics education.

• East Asian mathematical journal
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• v.38 no.4
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• pp.517-532
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• 2022

This study looked at how content reviews with mathematical games in class would influence the mathematical disposition of middle school students. In doing so, three games adapted from prior research were used as a supplementary instruction after school hours over three months. The mathematical topics of the games involved concepts of probability and trigonometry at the middle school level. The results of the pre- and post-survey on mathematical disposition indicate that incorporating mathematical games appeared to have some positive impacts on whether students might be more eager to learn mathematics and actually put more effort in learning materials.

• East Asian mathematical journal
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• v.24 no.4
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• pp.377-387
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• 2008

We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.

• Research in Mathematical Education
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• v.1 no.1
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• pp.75-85
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• 1997

One of the main objectives of school mathematics education is to develop a student' intuition and logical thinking [11]. But two -valued logical thinking, in fact, is not sufficient to express the concepts of a student's mind since intuition is fuzzy. Hence fuzzy -valued logical thinking may be a more natural way to develop a student's mathematical thinking.

• Journal for History of Mathematics
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• v.1 no.1
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• pp.14-32
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• 1984

The concepts of zero, minus, infinite, ideal point, etc. are not real existence, but are pure mathematical objects. These entities become mathematical objects through the process of a philosophical filtering. In this paper, the writer explores the relation between natural conditions of different cultures and philosophies, with its reference to fundamental philosophies and traditional mathematical patterns in major cultural zones. The main items treated in this paper are as follows: 1. Greek ontology and Euclidean geometry. 2. Chinese agnosticism and the concept of minus in the equations. 3. Transcendence in Hebrews and the concept of infinite in modern analysis. 4. The empty and zero in India.

• The Pure and Applied Mathematics
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• v.29 no.3
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• pp.207-230
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• 2022

In this article, we investigate several aspects of (R, S)-hyper bi-modules and describe some their properties. The concepts of fundamental relation, completes part and complete closure are studied regarding to (R, S)-hyper bi-modules. In particular, we show that any complete (R, S)-hyper bi-module has at least an identity and any element has an inverse. Finally, we obtain a few results related to the heart of (R, S)-hyper bi-modules.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.203-227
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• 2012

This was to investigate how the slow learners who specially belonged to low-SES, or North Korean defectors showed their errors in mathematical learning. To conduct the study, two groups for each minority group participated in the study volunteerly during the Winter vacation, in 2011. Based on the preliminary interviews, a total of 15 units were given, focusing on building mathematical basic concepts. As results, they had some errors in common. They both were in lack of understanding of the terminologies and not able to apply the meanings of definitions and theorems to a problem. Because of uncertainty of basic knowledge of mathematics, they easily lost their focus and were apt to make a mistake. Also, they showed clear differences. North Korean defectors were not accustomed to using or understanding the meanings of Chines or English in Korean words in expressing, writing mathematical terminologies and reading data on the context. Technical errors, and misinterpreted errors were found. However, students from the low SES showed that they were familiar with mathematical words and terminologies, but their errors mostly belonged to carelessness because of the lack of mastering mathematical concepts.

• The Mathematical Education
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• v.47 no.2
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• pp.155-168
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• 2008

The theory of representation, which has been an important topic of epistemology, has long history of study. But it has diverse meaning according to the fields of argument. In this paper the author set the meaning of mathematical representation as the interrelation of internal and external representations. With this concept, the following items were studied. 1. Survey on the concepts of mathematical representations. 2. Investigation of pedagogical significance of the mathematical representations, taking into account the characteristics of school mathematics. 3. Recommendation of principles for teaching representation to cope with the problems that are related with cause of disliking each domain of the secondary school mathematics. This study is expected to enable the development of teaching methods to help students strengthening their ability to comprehend mathematical sentences.