• Research in Mathematical Education
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• v.1 no.1
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• pp.1-5
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• 1997

We discuss some aspects of mathematics for teachers such as algebra for teachers, geometry for teachers, statistics for teachers, etc., which can be taught in teacher preparation courses. Mathematics for teachers should consider the followings: (a) Various solutions for a problem, (b) The dynamics of a problem introduced by change of condition, (c) Relationship of mathematics to real life, (d) Mathematics history and historical issues, (e) The difference between pure mathematics and pedagogical mathematics, (f) Understanding of the theoretical backgrounds, and (g) Understanding advanced mathematics.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.3
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• pp.96-107
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• 2024

We consider the bifocusing method (BFM) for a fast identification of small objects in microwave imaging. In many researches, it was very hard to measure the scattering parameter data if the location of the transmitter and the receiver is the same. Due to this reason, the imaging function of BFM has mainly been designed by converting unknown measurement data into the zero constant; this approach has yielded reliable imaging results, but the theoretical reason for this conversion has not been investigated yet. In this study, we converted unknown measurement data to a fixed constant and applied the BFM to retrieve small objects. To demonstrate the effect of the converted constant, we show that the imaging function of the BFM can be represented in terms of an infinite series of the Bessel functions of an integer order, antenna setting, material properties, and applied constant. Based on the theoretical result, we concluded that converting unknown measurement data to constant zero guarantees good imaging results, including the unique determination of the objects. Simulation results obtained with synthetic and real data support the theoretical result.

• Research in Mathematical Education
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• v.26 no.4
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• pp.291-310
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• 2023

In this paper, we propose a theoretical framework for Chinese high school mathematics teachers use new textbooks based on the work of Remillard (1999) and Chau (2014). Based on this framework, a multiple case approach was used to investigate how two high school mathematics teachers from Shanghai use new textbooks. The results suggest that in the curriculum mapping arena, both the novice teacher and the expert teacher often planned to appropriate the unit content, and sometimes planned to add supplemental content. When organizing the unit content, novice teacher always planned to follow the new textbook in sequence, while expert teacher often would follow the new textbook in sequence, but sometimes planned to rearrange the unit content. In the design arena, both the novice teacher and the expert teacher tended to appropriate the introduced tasks and definitions. The novice teacher often planned to appropriate the example problems and exercise problems, while the expert teacher often intended to flexibly use the example problems and exercise problems. In the construction arena, the novice teacher seldom adjusted the planned tasks; in contrast, the expert teacher adjusted the planned tasks more frequently. In the reflection arena, the novice teacher often thought she should improve the mathematics tasks, while the expert teacher almost always thought he needed to improve the mathematics tasks. The framework shown in this paper provides a tool to investigate how mathematics teachers use textbooks.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.

• The Mathematical Education
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• v.46 no.1 s.116
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• pp.1-18
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• 2007

The purpose of this study is to describe theoretical orientations guiding research in mathematics motivation and to discuss findings in terms of how they facilitate or inhibit achievement. First, definitions of motivation and distinctions among types of motivation in education are discussed. Second, theoretical approach and representative research from these approach are described. Third, a set of generalizable conclusions about the contextual factors, cognitive processes, and benefits of interventions that affect students' and teachers' motivational attitudes are noted. Last, criticisms regarding instrument, assessment, and use of theories in motivational research are raised.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.193-203
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• 2007

In this paper we consider the inverse minimum flow (ImF) problem, where lower and upper bounds for the flow must be changed as little as possible so that a given feasible flow becomes a minimum flow. A linear time and space method to decide if the problem has solution is presented. Strongly and weakly polynomial algorithms for solving the ImF problem are proposed. Some particular cases are studied and a numerical example is given.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.205-213
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• 2000

In this paper we introduce the concept of a fuzzy strongly regular relation on a sumihypergroup, and prove a few results concerning this concept.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.329-342
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• 2019

In this paper, we introduce the notion of L-fuzzy semi-prime ideals and the radical of L-fuzzy ideals in universal algebras and make a theoretical study on their basic properties.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.765-779
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• 2021

The fundamental goal of this paper is to investigate some inequalities involving the special beta function in n variables. Our theoretical results obtained here are extensions and refinements for some inequalities already discussed in the literature.

• Journal for History of Mathematics
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• v.17 no.1
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• pp.53-60
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• 2004

In this paper, we analyse several number theoretical proofs of the irrationality of $\sqrt{2}$ and reveal that these proofs are implied by The Completeness Axiom of the real number system.