• Communications of Mathematical Education
• /
• v.23 no.4
• /
• pp.1079-1092
• /
• 2009

The purpose of this study is to investigate Newton's binomial theorem that was on epistemological basis of the emergent background and developmental course of infinite series and power series. Through this investigation, it will be examined how finding the approximate of square root of given numbers, the method of the inverse method of fluxions by Newton, and Gregory and Mercator series were developed in the course of history of mathematics. As the result of this study pedagogical analysis and discussion of the history of mathematics on Newton's binomial theorem will be presented.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.1
• /
• pp.189-201
• /
• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• East Asian mathematical journal
• /
• v.26 no.2
• /
• pp.281-299
• /
• 2010

In this study we develop mathematical tools for measuring the Geumgang Ratio and we call them Geumgang Ratio Calipers. Also we show a teaching method for ratio through experimental mathematics. With Geumgang Ratio Calipers students measure the Geumgang Ratio in their bodies, materials for everyday life and the Sukgulam. Through this activity, students obtained an interest in mathematics and gained a positive attitude for mathematics.

• The Mathematical Education
• /
• v.48 no.4
• /
• pp.365-385
• /
• 2009

Recently, mathematical modeling has been attractive in that it could be one of many efforts to improve students' thinking and problem solving in mathematics education. Mathematical modeling is a non-linear process that involves elements of both a treated-as-real world and a mathematics world and also requires the application of mathematics to unstructured problem situations in real-life situation. This study provides analysis of literature review about modeling perspectives, case studies about mathematical modeling, and textbooks from the United States and Korea with perspective which mathematical modeling could be potential and meaningful to students even in elementary school. Further, teaching method with mathematical modeling was investigated to see the possibility of application to elementary mathematics classroom.

• East Asian mathematical journal
• /
• v.30 no.4
• /
• pp.545-570
• /
• 2014

This study was conducted to analyze the education theories applied to teaching-learning from the perspective of mathematical education. To this end, 41 papers regarding mathematical education theories were selected as study subjects from among 1,190 papers published in Korea between 2000 and 2013 in the Journal of the Korean Society of Mathematical Education and the Journal of the Korean Society of Educational Studies in Mathematics, which are journals that specialize in mathematics education. These papers were classified according to mathematical education theory, study method, content field, and study subject to obtain the numbers of papers and percentages by category in order to analyze their contents.

• Communications of Mathematical Education
• /
• v.20 no.4 s.28
• /
• pp.575-586
• /
• 2006

Both theory and experiment are very important parts in sciences. Especially in mathematics, theory seems to be very important, but experiment or practice doesn't. Numerical analysis of many parts in mathematics needs practice in computer. In this paper, I suggest that computer-practicing in teaching power method, inverse power method and deflation to calculate eigenvalues and eigenvectors is good in understanding the theory. It also makes students sure that mathematics is helpful.

• The Pure and Applied Mathematics
• /
• v.11 no.4
• /
• pp.275-285
• /
• 2004

In this paper, the time series models for the number of reported death claims of compulsory automobile liability insurance in Korea are studied. We found that IMA${(0, 1, 1)}\;{\times}\;{(0, 1, 1)}_{12}$ would the most appropriate model for the number of reported claims by the Box-Jenkins method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.31-40
• /
• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.1
• /
• pp.111-123
• /
• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Research in Mathematical Education
• /
• v.13 no.1
• /
• pp.31-48
• /
• 2009

Utilizing the path analysis method, the study explores the relationships among the influential factors in mathematics modeling academic achievement. The following conclusions are drawn: 1. Achievement motivation, creative inclination, cognitive style, the mathematical cognitive structure and mathematics modeling self-monitoring ability, those have significant correlation with mathematics modeling academic achievement; 2. Mathematical cognitive structure and mathematics modeling self-monitoring ability have significant and regressive effect on mathematics modeling academic achievement, and two factors can explain 55.8% variations of mathematics modeling academic achievement; 3. Achievement motivation, creative inclination, cognitive style, mathematical cognitive structure have significant and regressive effect on mathematics modeling self-monitoring ability, and four factors can explain 70.1% variations of mathematics modeling self-monitoring ability; 4. Achievement motivation, creative inclination, and cognitive style have significant and regressive effect on mathematical cognitive structure, and three factors can explain 40.9% variations of mathematical cognitive structure.