• Research in Mathematical Education
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• v.19 no.2
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• pp.141-153
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• 2015

This paper compares and contrasts the perspectives of effective mathematics teaching by 135 elementary school teachers, 132 middle school teachers, and 124 high school teachers using a questionnaire in South Korea. All groups of teachers chose in common the teaching and learning strand as the most important for effective mathematics instruction. However, elementary school teachers placed greater importance on the curriculum and content strand than their counterparts did. Elementary school teachers tended to agree more upon the 48 items related to good mathematics teaching than their counterparts did. The similarities and differences among the groups of teachers are expected to provoke discussion of what constitutes high-quality mathematics instruction and how such perspectives may be situated in the socio-cultural context.

• The Mathematical Education
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• v.51 no.2
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• pp.145-160
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• 2012

Prospective teachers need to have an opportunity to critically examine their initial perception with regard to effective mathematics instruction during the teacher education period. This study analyzed the perception in relation to good mathematics instruction by a total of 265 prospective teachers from four institutes for elementary teacher education using a survey. The results of this study showed that the pre-service teachers regarded learner, teaching and learning method, selection of content, and construction of curriculum as important for high-quality mathematics instruction. However, they revealed relatively low levels of agreement against the importance of instructional materials, classroom environment and atmosphere, and assessment. On the basis of teachers' perception on each element of effective mathematics instruction, this paper raises issues for discussion and includes some implications for teacher education.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.777-791
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• 1996

Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1087-1098
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• 2013

We find a $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on $\mathbb{R}^k$, $k{\geq}3$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the Euclidean metric on $\mathbb{R}^k$, the scalar curvatures of $g_t$ are strictly decreasing in $t$ in the open unit ball and $g_t$ is isometric to the Euclidean metric in the complement of the ball. Furthermore we extend the discussion to the Fubini-Study metric in a similar way.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.367-373
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• 2006

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.

• Research in Mathematical Education
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• v.20 no.1
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• pp.1-9
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• 2016

An accurate evaluation of educational process is a promise for the progress of education, because evaluation provides a meticulous idea of what has actually been achieved as a result of education. However, for all its significance in the educational fields, there are not many discussions about evaluation in South Korea. We believe that in order to overcome this discrepancy, diverse evaluation theories along with a discussion about the merits or demerits or each theory should be introduced in South Korea. We propose that Eisner's educational evaluation model may suggest alternative ways of perceiving evaluation. Eisner's educational evaluation model, named educational connoisseurship and criticism, emerged as an approach to educational evaluation from the methods used in art and literary criticism.

• East Asian mathematical journal
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• v.34 no.2
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• pp.191-201
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• 2018

The character education has been regarded as important in nature and purpose of mathematics education. A discussion about models for the teaching of character to a student has been. However, The character education of teachers has not gathered as much attention as that of students in mathematics education. How to educate morally and ethically sound mathematics teachers is an important research topic to be sincerely inquired in current. Little attention has been given to the way how we prepare a morally humane pre-mathematics teacher. This paper inquires into the issues of character education in pre-mathematics teacher education.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.437-454
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• 2000

Let C be a smooth k-gonal curve of genus g. We study the number of pencils of degree k on C. In case $g\geqk(k-a)/2$ we state a conjecture based on a discussion on plane models for C. From previous work it is known that if C possesses a large number of pencils then C has a special plane model. From this observation the conjectures are split up in two cases : the existence of some types of plane curves should imply the existence of curves C with a given number of pencils; the non-existence of plane curves should imply the non-existence of curves C with some given large number of pencils. The non-existence part only occurs in the range $k(k-1)/2\leqg\leqk(k-1)/2] if k\geq7$. In this range we prove the existence part of the conjecture and we also prove some non-existence statements. Those result imply the conjecture in that range for $k\leq10$. The cases $k\leq6$ are handled separately.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1499-1512
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• 2018

Recently, Anderson and Dumitrescu's S-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of S-finitely presented modules and then of S-coherent rings which are S-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an S-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other S-versions of finitely presented modules and coherent rings. We prove that these last S-versions can be characterized in terms of localization.