• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.157-177
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• 2001

Modern society's technological and economical changes require high-level education that involve critical thinking, problem solving, and communication with others. Thus, today's perspective of mathematics and mathematics learning recognizes a potential symbolic relationship between concrete and abstract mathematics. If the problems engage students' interests and aspiration, mathematical problems can serve as a source of their motivation. In addition, if the problems stimulate students'thinking, mathematical problems can also serve as a source of meaning and understanding. From these perspectives, the purpose of my study is to prove that mathematical modeling tasks can provide opportunities for students to attach meanings to mathematical calculations and procedures, and to manipulate symbols so that they may draw out the meanings out of the conclusion to which the symbolic manipulations lead. The review of related literature regarding mathematical modeling and model are performed as a theoretical study. I especially concentrated on the study results of Freudenthal, Fischbein, Lesh, Disessea, Blum, and Niss's model systems. We also investigate the emphasis of mathematising, the classified method of mathematical modeling, and the cognitive nature of mathematical model. And We investigate the purposes of model construction and the instructive meaning of mathematical modeling. In conclusion, we have presented the methods that promote students' effective model construction ability. First, the teaching and the learning begins with problems that reflect reality. Second, if students face problems that have too much or not enough information, they will construct useful models in the process of justifying important conjecture by attempting diverse models. Lastly, the teachers must understand the modeling cycle of the students and evaluate the effectiveness of the models that the students have constructed from their classroom observations, case study, and interaction between the learner and the teacher.

• Cross-Cultural Studies
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• v.45
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• pp.33-54
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• 2016

This study presents a comparative analysis of the calligrammic poetic dictions shown in the poems of the French poets Guillaume Apollinaire and Paul Eluard and in those of the Korean poet Lee Sang. They were adventurers in the avant-garde movement who used experimental techniques that led to futurism, expressionism, cubism, dadaism, and surrealism. They applied a typographic technique that combined pictorial arrangements of fonts, shapes of compositions and between lines, letters of the alphabet, mathematical symbols, and graphical elements, such as circles or lines, to make up a poem that also looked like a painting. Their works, valued as visual lyric poems, break up language and combine anti-poems. They rejected traditional poetic dictions or grammar, but developed a paratactic poem that freely uses letters and symbols. Their calligrammic poetic dictions arouse dynamic images like space extension. Lee Sang's calligrams seem like abstract paintings that apply geometric symbols like those used in technical drawings. As a result, crossing the boundaries between language and pictorial art by using experimental materials and techniques, their poems deconstruct the creative standards of rational and traditional poetic dictions, creating an adventurous, expressive technique. Their calligrammic, avant-garde poems introduced a new spirit of art into both French and Korean modern poetic literature.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.513-517
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• 2012

Let L(M) be the bundle of all linear frames over a smooth manifold M, $u$ an arbitrarily given point of L(M), and ${\nabla}:\mathfrak{X}(M){\times}\mathfrak{X}(M){\rightarrow}\mathfrak{X}(M)$ a linear connection on M. Then the following result is well known: the horizontal subspace at the point $u$ may be written in terms of local coordinates of $u{\in}L(M)$ and Christoel's symbols defined by ${\nabla}$. This result is very fundamental on the study of the theory of connections. In this paper we show that the local expression of the horizontal subspace at the point u does not depend on the choice of a local coordinate system around the point $u{\in}L(M)$, which is rarely seen.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.731-738
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• 2012

Let L(M) be the bundle of all linear frames over $M,\;u$ an arbitrarily given point of L(M), and ${\nabla}\;:\;\mathfrak{X}(M)\;{\times}\;\mathfrak{X}(M)\;\rightarrow\;\mathfrak{X}(M)$ a linear connection on L(M). Then the following results are well known: the horizontal subspace and the connection form at the point $u$ may be written in terms of local coordinates of $u\;{\epsilon}\;L(M)$ and Christoffel's symbols defined by $\nabla$. These results are very fundamental on the study of the theory of connections. In this paper we show that the local expressions of those at the point $u$ do not depend on the choice of a local coordinate system around the point $u\;{\epsilon}\;L(M)$, which is rarely seen. Moreover we give full explanations for the following fact: the covariant derivative on M which is defined by the parallelism on L(M), determined from the connection form above, coincides with $\nabla$.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.525-534
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• 2005

The purpose of this study is to analyze difficulties in the density word problem solving process of seventh graders and to search for the way to increase their problem solving ability in the density word problem. The results of this study could help teachers diagnose students' difficulties involved in density word problem and remedy the understanding of the concept of density, algebraic expressions, and algebraic symbols.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.77-84
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• 1998

In this note we show that if $T_{\varphi}$ is a Toeplitz operator with quasicontinuous symbol $\varphi$, if $\omega$ is an open set containing the spectrum $\sigma(T_\varphi)$, and if $H(\omega)$ denotes the set of analytic fuctions defined on $\omege$, then the following statements are equivalent: (a) $T_\varphi$ is semi-quasitriangular. (b) Browder's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (c) Weyl's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (d) $\sigma(T_{f \circ \varphi}) = f(\sigma(T_varphi))$ for every $f \in H(\omega)$.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.939-962
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• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.683-689
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• 2007

Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

• Research in Mathematical Education
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• v.15 no.1
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• pp.1-14
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• 2011

Logo has influenced many researchers and learners for the past decades as a 20 turtle geometry environment in the perspective of constructionism. Logo uses the metaphor of 'playing turtle' that is intrinsic, local and procedural. We, then, design an environment in which the metaphor of 'playing turtle' is applied to construct 3D objects, and we figure out ways to represent 3D objects in terms action symbols and 3D building blocks. For this purpose, design three kinds of representation systems, and asked students make various 3D artifacts using various representation systems. We briefly introduce the results of our investigation into students' cognitive burden when they use those representation systems, and discuss the future application measures and the design principles of Logo-based 3D microworld.

• The Mathematical Education
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• v.47 no.3
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• pp.373-386
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• 2008

In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.