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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
Communications of Mathematical Education
Journal Basic Information
Journal DOI :
Korea Society of Mathematical Education
Editor in Chief :
Sang-Gu Lee, Hye-Jeang Hwang
Volume & Issues
Volume 22, Issue 4 - Nov 2008
Volume 22, Issue 3 - Sep 2008
Volume 22, Issue 2 - May 2008
Volume 22, Issue 1 - Feb 2008
Selecting the target year
Desirable Management of Basic Mathematics Curriculum in College
Jun, Jae-Bok ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 399~416
We have had much speculation on how to solve problems and challenges arising from "The 7th Curriculum" of middle school education. We suggest a scheme of curriculum appropriate to the current tendency to deal with those problems and challenges flexibly.
The Function Concept in Korean Engineering Freshmen and Some Suggestions on the Curriculum in the Function Area
Kim, Yeon-Mi ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 417~444
Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.
Effective Teaching of QR methods using Computer Practice
Lee, Gyou-Bong ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 445~457
Although both theory and experiment are very important parts in sciences, especially in mathematics, theory only seems to be very important. But the subject of numerical analysis needs both theory and practice in computer. In this paper, I provide some Matlab program codes and matrices which are used in good understanding OR methods in class.
A mathematical theory of the AHP(Analytic Hierarchy Process) and its application to assess research proposals
Yang, Jeong-Mo ; Lee, Sang-Gu ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 459~469
We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.
A research on Mathematical Invention via Real Analysis Course in University
Lee, Byung-Soo ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 471~487
Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.
Making Good Multiple Choice Problems at College Mathematics Classes
Kim, Byung-Moo ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 489~503
It is not an easy matter to develop problems which help students understand mathematical concepts correctly and precisely. The aim of this paper is to review the merits and demerits of three problem types (i.e. one answer problems, multiple choice problems and proof problems) and to suggest some points that should be taken into consideration in problem making. First, we presented the merits and demerits of three types of problems by examining actual examples. Second, we discussed some examples of misleading problems and the ways to make desirable ones. Finally, on the basis of our examination and discussion, we suggested some points that should be kept in mind in problem making. The major suggestions are as follows; i) In making one answer problems, we should consider the possibility of sitting a solution by wrong precesses, ii) In formulating multiple choice tests which are layered for their easiness of grading, we should take into account the importance of checking whether the students are fully understanding the concepts, iii) We may depend on the previous research result that multiple choice tests for proof problems can be helpful for the students who have insufficient math background. Besides those suggestions, we made an overall proposal that we should endeavor to find ways to implement the demerits of each problem type and to develop instructive problems that can help students understanding of math.
A study on derivation of root's formulas of cubic and quartic equation by method analogy
Lyou, Ik-Seung ; Shin, Hyun-Yong ; Han, In-Ki ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 505~514
In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.
Visual Cryptography Using the Number of
Kim, Moon-Soo ; Kang, Mee-Kwang ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 515~531
The visual cryptography scheme is a simple method which can be decoded directly the secret information in human visual system without performing any cryptographic computations. For some secret of image type, we scatter them to random n images and if any threshold (or more) of them are stacked together then original image is visible. In this paper we consider (2,n) visual cryptography scheme and show a construction method of the sample matrix using the rule of binomial coefficients
. This scheme can contribute interesting and effectiveness to the study of mathematics.
The educational models using enhanced mathematics ICT in the Korean IT environments
Kim, Duk-Sun ; Park, Jin-Young ; Lee, Sang-Gu ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 533~543
Recently, many advanced countries have used original ICT tools in their educational courses. But Korea didn't have any effective origin ICT tools in our mathematical education, compared with other countries which have developed various tools, for examples, Web-Mathematica and HP Calculator. Although we have the advanced IT environment, the educational environments in mathematics using ICT seems to be not promising. In this paper, we suggest a new mathematics education tools in ICT and the internet environments in Korea, and a teaching and studyingmodel for the teachers, students and classrooms. It is based on the Sage-Math and RPG. Sage-Math which is the software based on the web and RPG(Random Problem Generator) will give a good answer for the future of Korean mathematics ICT education.
A Study on Gergonne's Point and Its Adjoint Points of Triangle Using the Principle of the Lever
Han, In-Ki ;
Communications of Mathematical Education, volume 22, issue 4, 2008, Pages 545~556
In this paper we study Gergonne's point and its adjoint points of triangle using the principle of the lever. We prove existence of Gergonne's point and its adjoint points, suggest new proof method of a equality related with Gergonne's point. We find new equalities related with adjoint points of Gergonne's points, and prove these using the principle of the lever.