• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.723-740
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• 2021

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

• Research in Mathematical Education
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• v.15 no.1
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• pp.31-44
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• 2011

An impetus for reviving research in mathematical problem solving is the recent advance in methodological thinking, namely, the design experiment ([Gorard, S. (2004). Combining methods in educational research. Maidenhead, England: Open University Press.]; [Schoenfeld, A. H. (2009). Bridging the cultures of educational research and design. Educational Designer. 1(2). http://www.educationaldesigner.orgied/volume1/issue21]). This methodological approach supports a "re-design" of contextual elements to fulfil the overarching objective of making mathematical problem solving available to all students of mathematics. In problem solving, components critical to successful design in one setting that may be adapted to suit another setting include curriculum design, assessment strategy, teacher capacity, and instructional resources. In this paper, we describe the implementation, over three years, of a problem solving module into the main mathematics curriculum of an Integrated Programme school in Singapore which had sufficient autonomy to tailor-fit curriculum to their students.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.107-121
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• 2015

The purpose of the present study is to find out some implications from comparing mathematical education of Israel and Singapore. This study examined what values are represented in schooling of both Israel and Singapore and what factors are influencing mathematics teacher education of both countries. Education in Israel and Singapore plays a significant role for the survival of the nation and economic success, and the education system is focused on elitism, especially in terms that they have selective system of students and restrictive exams from the elementary school level. The educational system in both countries provides students with little opportunities for social mobility, because students from the low SES families are not equally exposed to educational facilities and experiences. The results of this study imply that the critical factor affecting students achievement in Israel and Singapore seems to be the quality of teacher education system and the quality of teachers. In particular, it seems that we need to be very careful of uncritically adopting mathematical ideas from both Israel and Singapore, because they both have very different contexts of educational goals, educational policies, racial and cultural factors from Korea.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.599-615
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• 2015

Teachers' philosophies have not been emphasized enough in the current teacher education curriculum even though teacher's philosophy palys a critical role in schools and classrooms. The examination on pre-service teachers' teaching philosophies is necessary to improve teacher education curriculum so that teaching philosophies are often discussed in the courses of 'pedagogical content knowledge' as well as 'general education.' Therefore, the current study investigated 44 pre-service teachers' teaching philosophies, their sub domains, and relationships among the sub domains. The previous studies regarding mathematics teacher's teaching philosophy were more about 'teacher's belief' and employed deductive inference approach using surveys or questionnaires. These studies commonly pointed out that there were three major domains of 'belief on mathematics itself,' 'belief on teaching mathematics,' and 'belief on learning mathematics.' As these three domains of teacher's philosophy has been strengthened, there were very few studies examining the other potential domains of teacher's teaching philosophy. According to the findings of the present study, which employed inductive inference approach and pre-service teachers' free essay writing assignment, 'belief on teacher's role in mathematics classroom,' 'belief on the purpose of mathematics education,' and 'motivation to be a mathematics teacher' were additionally illuminated as sub domains of teacher's teaching philosophy. Moreover, the interrelationship among the sub-areas of teacher's teaching philosophy was disclosed. Specifically, 'belief on the purpose of mathematics education' and 'motivation to be a mathematics teacher' influenced the other sub domains. This implies that the relationships among the sub domains of teacher's teaching philosophy were more likely to be causal and vertical relationships rather than independent and parallel relationships. Finally, the findings from the current study provide implications indicating how pre-service teachers' teaching philosophies might be established in mathematics education courses for future research and education.

• Research in Mathematical Education
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• v.16 no.4
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• pp.233-244
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• 2012

The purpose of this study is to investigate the relationship between creativity development and debate in solving a probability task. We developed the probability task with instructional strategies facilitating debating among students. 33 students in grade 11 who were identified as gifted participated in this study. The findings indicated that debating leads students to critical and reflective thinking on prior learning regarding probability concepts, which nurtured creative ideas on sample space.

• School Mathematics
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• v.10 no.3
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• pp.339-355
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• 2008

This article tried to review the meaning and implication of six stages theory of learning mathematics suggested by Zoltan Dienes in "Building up Mathematics" in 1971. It was not much concretely known to Korean mathematics education society. In particular, there is no mathematical example which could cover all the stages to know what the theory tells. So this article focused on the example which Dienes developed for learning integers in 2000 to dig the theory. As a result, some critical aspects and problems of six stages theory were found. And finally educational implication was described.