• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.175-184
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• 1998

The purpose of this study is that the Van Hiele theory can be applied to even vocational high school students. Through the comparison of Van Hiele level distribution of middle school students and high school students, it is that the aims of this study is to study the geomatric level of vocational high school students and to analize them, even so it can be to find for them the effective method of Geomatric education The subject of study is three kinds of vocational high school - commercial high school, industrial high school, fisheries high school - boys (240), girls (120) in Boryeong city, Chungchong Nam Do. We referred to Kim Mi-cheong′ thesis(1994) and Cheong Yean-sok′s thesis(1992) and compared my result with them. The method and the process of the study were based on the th method of CDASSG project. And we used Van Hiele Level Test as an instrument of measurement. We got the following conclusion as the result of the study 1. The 86％ of the subject of the study was applied to the theory of Van Hiele - "Any students can reach level n just through level n-1." Even so the propriety of the theory proved to be from this study again. 2. The 88% of the subject of the study is applicable to below level 2. So if the proof is introduced to them in the class, it was very difficult for them to understand it. 3. The geometric level of vocational high school students is the same as the second grade of middle school. But we think to be desirable that a basic concept puts first in importance through recomposed teaching materials, because 68% of the students is seldom changed at level 1.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.327-345
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• 2004

This study attempts to discuss holistic information in order to identify the characteristics of interactions using a graphing calculator. The use of a graphing calculator was divided into three stages: Visual, Analytical, and Self-regulated. The last stage can be called the Self-regulated instrument stage, because this last stage, the use of the calculator, is generally characterized as students actively controlling their ongoing efforts through self-regulating. The accomplishments of the operation can be divided into three levels: Immature, Maturing, and finally, Mature level. First, the characteristics of the Leading Statements were investigated to figure out who has the main role in cooperative learning. This study can support the previous study, which showed that computers could help improve the self-esteem of low-level students. Second, the point of transformation is referred to as the Turning Point. Several functions were observed in the Turning Point: student, instrument, and teacher. Third, when the students convert-sations reach a lull in class and then resume due to certain primary factors without the teachers intervention, this is a case of what is referred to as Structuralization. And last, in this study, the graphing calculator can be used as an auxiliary stimulus to help students control their stress and their attitudes, which in turn can also improve students social interaction.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.583-606
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• 2013

We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• Education of Primary School Mathematics
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• v.17 no.1
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• pp.57-75
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• 2014

Problem Solving has been emphasized for recent decades, and many research case studies have been used to improve students' Problem Solving abilities. However, the gap of students' abilities can be easily shown after enrollment into school in spite of scholar's attempt to reduce students' level of differentiation. Besides, it is clear that teachers have been too readily assisting students' and not allowing them to acquire the process of Problem Solving, and this may be due to impatience. Therefore, students seem to show signs of the dependent tendency towards teachers and other materials. This tendency easily allows students' to depend on teaching resources without attempting any developmental mechanism of Problem Solving. The presupposition of this study is that every student must solve a problem without any assistance, and also this study is to provide new cognitive strategies for both teachers and students who want to solve their problems by themselves through the process of visible Problem Solving. After applying the student-based problem-solving model by this study, it was found to be effective. Therefore this will lead to the improvement of the Problem Solving and knowledge acquisition of students.

• School Mathematics
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• v.13 no.3
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• pp.447-468
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• 2011

For the instruction of units dealing with the conic section, the most important factor that we need to consider is the connections. In other words, the algebraic approach and the geometric approach should be instructed in parallel at the same time. In particular, for the students of low proficiency who are not good at algebraic operation, the geometric approach that employs visual representation, expressing the conic section's characteristic in a dynamic manner, is an important and effective method. For this, during this research, to suggest the importance of dynamic visual representation based on GeoGebra in teaching Quadratic Curve, we taught an experimental class that suggests the instruction method which maximizes the visual representation and analyzed changes in the representation of students by analyzing the part related to the unit of a parabola from units dealing with a conic section in the "Geometry and Vector" textbook and activity book.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.399-422
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• 2011

There has been an agreement on the necessity for each citizen is to be educated, so called, to develop quantitative literacy or statistical literacy, dealing with real world data. For this reason, it is highly demanded to improve traditional statistics education. In particular, critical thought and statistical communication competency cultivation is becoming more crucial in statistics classes. In line with this reform movement in statistics education, we developed tasks facilitating statistical debate among students through inducing cognitive conflict. The tasks employed for this study resulted in playing crucial role to activate statistical debate. Including aforementioned feature about the tasks for this study, we obtained several positive results such as promoting critical thought and conceptual extension by designed teaching experiment focusing on statistical debate.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.297-312
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• 2006

As research on the instruction method of the concept of irrational numbers, this thesis is theoretically based on the Freudenthal's Mathematising Instruction Theory and a conducted case study in order to find an introduction method of irrational numbers. The purpose of this research is to provide practical information about the instruction method ?f irrational numbers. For this, research questions have been chosen as follows: 1. What is the introducing method of irrational numbers based on the Freudenthal's Mathematising Instruction Theory? 2 What are the Characteristics of the teaming process shown in class using introducing instruction of irrational numbers based on the Freudenthal's Mathematising Instruction? For questions 1 and 2, we conducted literature review and case study respectively For the case study, we, as participant observers, videotaped and transcribed the course of classes, collected data such as reports of students' learning activities, information gathered through interviews, and field notes. The result was analyzed from three viewpoints such as the characteristics of problems, the application of mathematical means, and the development levels of irrational numbers concept.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.121-139
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• 2011

This study conducted experimental problem posing activities using real-life materials. This study investigated the changes on students' mathematical thoughts and attitudes through the activities. This study is conducted via participation of students in a 5th grade class of N elementary school located in Daegu city. As a qualitative case study, this study focused on processes of problem posing rather than results. The problems applying new situations appear, and the used mathematical terms, units, and figures became more practical. The numbers of problems made are increased gradually, and more complex conditions are added as activities are performed. Most of the students revealed interests about problem making activities.