• Journal of Biomedical Engineering Research
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• v.23 no.4
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• pp.269-279
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• 2002

When we inject a current into an electrically conducting subject such as a human body, voltage and current density distributions are formed inside the subject. The current density within the subject and injection current in the lead wires generate a magnetic field. This magnetic flux density within the subject distorts phase of spin-echo magnetic resonance images. In Magnetic Resonance Current Density Imaging (MRCDI) technique, we obtain internal magnetic flux density images and produce current density images from $\bigtriangledown{\times}B/\mu_\theta$. This internal information is used in Magnetic Resonance Electrical Impedance Tomography (MREIT) where we try to reconstruct a cross-sectional resistivity image of a subject. This paper describes numerical techniques of computing voltage. current density, and magnetic flux density within a subject due to an injection current. We use the Finite Element Method (FEM) and Biot-Savart law to calculate these variables from three-dimensional models with different internal resistivity distributions. The numerical analysis techniques described in this paper are used in the design of MRCDI experiments and also image reconstruction a1gorithms for MREIT.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.321-336
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• 2012

Cognitive subject imposes structures on an object to shape it into a structured thing. Structures that the subject imposes on an object in a given problem context can be diverse horizontally and vertically. In view of the horizontal diversity of structure, problem-solving activities focusing on various structures may enrich the present problem-solving education which emphasizes applying and comparing a couple of problem-solving strategies. Finding an algebraic formula for a figural pattern should be regarded as a new starting point of searching for more various structures. In view of the vertical diversity of structure, it should be aware that students may see different structures from the structure that their teacher expect them to see. The vertical diversity of structure enables us to provide students with experience of progress.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.323-340
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• 2007

This study set out to analyze the learning types that most students were engaged in after school, to review the efficiency of private education through academic institutions or tutoring, and to examine the directions in the after-school learning in math under the current system. It also aimed to analyze the impacts of those after-school learning activities on school classes and to suggest some plans to help public education get back on the track. In the study the after-school learning activities in the math subject were categorized into taking classes at academic institutions, tutoring, and autonomous learning. The grades of the subject students were compared and analyzed for three semesters to find the directions right for the school classes.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.173-192
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• 2007

We define mathematical learning as a process of overcoming framing difference of teachers and students, two main subjects in a mathematics class. We have reached this definition to the effect that we can grasp a mathematical classroom per so and understand students' mathematical learning in the context. We could clearly understand the process in which the framing differences are overcome by analyzing mutual negotiation of informants in specific cultural models, both in its form as well as in its meaning. We review both of the direct and indirect forms of negotiation while keeping track of 'evolution of subject' in terms of content of negotiation. More specifically, we discuss direct negotiation briefly and review indirect negotiation from three distinct themes of (1) argument structure, (2) revoicing, and (3) development patterns and narrative structure of proof. In addition, we describe the content of negotiation under the title of 'Evolution of Subject.' We found that major modes of mutual negotiation are inter-reference and appropriation while the product of continued negotiation is inter-resemblance.

• School Mathematics
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• v.10 no.3
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• pp.463-487
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• 2008

The purpose of this study was to analyze teachers' pedagogical content knowledge on probability. Teachers' pedagogical content knowledge on probability was analyzed in detail into 2 categories: (a) subject matter knowledge, (b) knowledge of students' understanding and misunderstanding. The results showed, in terms of the subject matter knowledge, that the teachers have some probability misconception. And, it showed, in the point of the knowledge of students' understanding, they could not explain why students have difficulties to solve some tasks with regard to probability. This study raised several implications for teachers' professional development for effective mathematics instruction.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.45-64
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• 2004

The lambda calculus is a mathematical formalism in which functions can be formed, combined and used for computation that is defined as rewriting rules. With the development of the computer science, many programming languages have been based on the lambda calculus (LISP, CAML, MIRANDA) which provides simple and clear views of computation. Furthermore, thanks to the "Curry-Howard correspondence", it is possible to establish correspondence between proofs and computer programming. The purpose of this article is to make available, for didactic purposes, a subject matter that is not well-known to the general public. The impact of the lambda calculus in logic and computer science still remains as an area of further investigation.stigation.

• Journal of Gifted/Talented Education
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• v.16 no.1
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• pp.1-19
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• 2006

This research is the one, that is, analyze the results of SSH at the science and mathematics subject for the advanced student in Japan recently, and searched for the result and the problem. We analyze reported results separately in detail according to the item for the practical report that the school of the whole country where SSH had been experimented from 2002 to 2004 in 31 places had issued for this. Also we discuss some suggestions and ideas for the mathematics and science instruction on the science high school in Korea.

• Research in Mathematical Education
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• v.18 no.3
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• pp.171-185
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• 2014

Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers' lack of relevant subject content knowledge. However, recent research findings have revealed that teachers' knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers' knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive reasoning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.

• The Mathematical Education
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• v.62 no.1
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• pp.117-149
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• 2023

This study attempted to design a virtual space using ZEP, a metaverse platform, to enable mathematics classes in the metaverse space, to apply it to mathematics classes, and to find out changes in students' affective domain. As a result, students showed positive effects in terms of subject efficacy, subject interest, intrinsic motivation, class satisfaction and participation. In addition, we found the possibility of customized classes for each student level by performing different missions in classroom classes with limited time and space.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.229-244
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• 2005

In this paper, we study the third order ordinary differential equation : $$x'(t)=f(t,x(t),x'(t),x'(t)),t{\in}(0,1)$$ subject to the boundary value conditions: $$x'(0)=x'(\xi),x'(1)=^{m-3}{\Sigma}_{i=1}{{\beta}x'({\eta}i),x'(1)=0}$$. Here ${\beta}_{i}{\in}R,\;^{m-3}{\Sigma}_{i=1}\;{\beta}_{i}\;=\;1,\;0<{\eta}_1<{\eta}_2<{\cdots}<{\eta}_{m-3}<1,\;0<\xi<1$. This is the case dimKer L = 2. When the ${\beta}_i$ have different signs, we prove some existence results for the m-point boundary value problem at resonance by use of the coincidence degree theory of Mawhin [12, 13]. Since all the existence results obtained in previous papers are for the case dimKerL = 1, our work is new.