• Research in Mathematical Education
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• v.24 no.2
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• pp.69-82
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• 2021

The purpose of this study is to explore how mathematics educators understand the terms having lexical ambiguity. Five terms with lexical ambiguity, leave, times, high, continuous, and convergent were selected based on literature review and recommendations of college calculus instructors. The participants consisted of four mathematics educators at a large Midwestern university. The qualitative data were collected from open-ended items in the survey. As a result of analysis, I provided participants' sentences with five terms showing their understanding of each term. The data analysis revealed that mathematics educators were not able to separate the meanings of the words such as leave and high when these words are frequently used in daily life, and the meanings in mathematics context are similar with that in daily context. Lexical ambiguity shown by mathematics educators can help mathematics teachers to understand the terms with lexical ambiguity and improve their instructions when those terms should be found in students' conversations.

• East Asian mathematical journal
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• v.18 no.2
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• pp.163-173
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• 2002

In this paper an inequality of Ostrowski type in terms of the lower and upper bounds of the first derivative is found.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.467-477
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• 2008

In this paper, we provide a criterion for Chow stability in terms of log canonical threshold of the Chow form in the Grassmannian.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Korean Journal of Child Studies
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• v.33 no.2
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• pp.203-222
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• 2012

The purpose of this study was to examine the factors influencing their mathematical learning abilities and mathematical learning potential in an attempt to assist their learning at the preschool level. The findings of the study were as follows : First. the female children performed at a much higher level than their male counterparts in terms of mathematical learning ability and mathematical learning potential training. The young children generally improved in their mathematical learning abilities and mathematical learning potential with age. Second, it was found that the participants had higher levels of both mathematical learning ability and mathematical learning potential when their mathematical attitudes and learning motivation were better. Third, there were significant differences in terms training-test and transfer-test scores between the 4 groups based on their relative levels of mathematical abilities and attitudes.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.61-71
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• 2003

We obtain a necessary condition for splitting T-space off a space in terms of cyclic maps, and also obtain a necessary condition for splitting co-T-spaces in terms of cocyclic maps.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.27-60
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• 1996

We compute low order terms of automorphisms of a quadric CR manifold defined by $v^a$ =< $A^az$, z > where there is a real vector ${\kappa}{\in}R^m$ such that $det({\kappa}{\cdot}A){\neq}0$.

• East Asian mathematical journal
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• v.34 no.5
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• pp.633-641
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• 2018

A viscoelastic wave equation in canonical form weakly nonlinear time dependent dissipation and source terms is investigated in this paper. And we establish a general decay result which is not necessarily of exponential or polynomial type.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.11-24
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• 2012

We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.