• East Asian mathematical journal
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• v.33 no.4
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• pp.431-451
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• 2017

This is a descriptive study with the intent of providing a rich characterization of teachers' perceptions of rate of change. The nature of teachers' perceptions and differences among teachers were examined by collecting data through a survey on teachers' conceptions of rate of change in terms of learning goals, prerequisites, and beliefs about teaching and learning of rate of change, and an interview individually assessing teachers' concept images and definitions. The participating 13 teachers were selected to provide a range of similar and contrasting levels of experiences based on the teachers' educational background and the number of years they had been teaching. Findings and implications of this study are discussed.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.67-74
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• 2005

The purpose of this paper is to analysis with contents on thoughts and problems of philosophy of mathematics concerning around harmonical types of metaphysics and philosophy of mathematics. Moreover, we were gratefully acknowledged that the questions at issue of metaphysics and philosophy of mathematics are possible only in a philosophical position of mathematics in relation to nature of mathematical ion. These attitudes, important as they are in the study of an individual thinker, also have a pronounced effect on the future relation of mathematics to philosophy. And we can guess that many mathematician's research will have significant meaning in the future.

• The Mathematical Education
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• v.53 no.1
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• pp.147-162
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• 2014

The purpose of this study was to investigate the nature of pre-service elementary teachers' metaphors on mathematics textbooks. Their metaphors describe individual and collective patterns of thinking and action on mathematics teaching and learning. To analyze their metaphors, qualitative analysis method based on Lakoff and Johnson's theory of metaphor (1980) was adopted. Metaphors on mathematics textbooks were elicited from 161 pre-service elementary school teachers through writing prompts. The writing prompt responses revealed three types and thirteen categories: As Type I, there were (1) 'Principles', (2) 'Summary', (3) 'Manual', (4) 'Encyclopedia', (5) 'Code', (6) 'Guidelines', and (7) 'Example'. As TypeII, there were (9) 'Assistant', (10) 'Friend', (11) 'Scale', and (12) 'Ongoing'. As TypeIII, there was (13) 'Trap'. Among these categories, 'Guidelines', 'Assistant', and 'Ongoing' were the most frequently revealed. These results indicate that the relations of mathematics curriculum, textbooks, and classrooms are not a unilateral way but should communicate with each other.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.169-183
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• 2019

The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

• East Asian mathematical journal
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• v.38 no.4
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• pp.415-437
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• 2022

Recently, various platforms of education technology (Edu-Tech) that use artificial intelligence have been developed in the field of mathematics education. The case study in this paper reports the learning experience of a high school student who was directed to learn mathematics through the self-directed learning process provided by a mathematics learning platform using Edu-Tech with the intervention of mentoring provided by his teacher. The study found that the mentoring intervention could make an effective contribution to student's mathematics learning by playing the role of an auxiliary tool for the self-directed learning over time. In this paper, we explain the nature of the challenges that the student encountered in the process of self-directed learning and the roles that the teacher mentoring has played in this process.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.54-70
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• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1101-1129
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• 2023

In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.547-562
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• 2024

By utilizing coupling the strategy in the 5D Sprott B system, a new no equilibrium 7D hyperchaotic system is introduced. Despite the proposed system being simple with twelve-term, including solely two cross product nonlinearities, it displays extremely rich dynamical features such as hidden attractors and the dissipative and conservative nature. Besides, this system has largest Kaplan-Yorke dimension compared with to the work available in the literature. The dynamical properties are fully investigated via Matlab 2021 software from several aspects of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, offset boosting and so on. Moreover, the corresponding circuit is done through Multisim 14.2 software and preform to verify the new 7D system. The numerical simulations wit carryout via both software are agreement which indicates the efficiency of the proposed system.

• Research in Mathematical Education
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• v.27 no.2
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• pp.195-210
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• 2024

Researchers and curricula continue to call for proof to serve a central role in learning of mathematics throughout kindergarten to grade 12 and beyond. Despite its prominence and recognition gained during past decades, proof is still a stumbling block for both teachers and students. Research efforts have been made to address issues related to teaching and learning of proof. An area in which such research efforts have been made is analysis of curriculum material (i.e. textbook analysis) with a focus on proof. This study is another research effort in this area of research through investigating the guidance offered in curriculum materials with the following research question: What is the nature (e.g., kinds of content knowledge, pedagogical content knowledge) of guidance is offered for teachers to implement proof tasks in grade 8 geometry textbooks? Results indicate that the guidance offered for proof tasks are concerned more with content knowledge about the content-specific instructional goals than with pedagogical content knowledge which supports teachers in preparing in-class interactions with students to teach proof.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.899-910
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• 2004

In this paper we have proposed a new loss function, namely, non-linear exponential(NLINEX) loss function, which is quite asymmetric in nature. We obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions. Moreover, a numerical comparison among the Bayes estimators of power function distribution under SE, LINEX, and NLINEX loss function have been made.