• East Asian mathematical journal
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• v.26 no.4
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• pp.447-461
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• 2010

Papert [17] introduced the LOGO environment in which we make a curve using LOGO commands (FORWARD, ROTATE). We call this geometry as turtle geometry. This environment has influenced many researchers and designers of computers and mathematics education. But the curve that we can make using LOGO command is elementary or too difficult. Polygon and circle is elementary and making other curves is difficult. In this paper, we introduce the method of drawing some other curves mediating new command. First, we study epicycloid and hypocycloid in the historical and the physical context. And we introduce the method of making epicycloid and hypocycloid using vector addition. Next we study the polygon patterns of this curve. Finally, we extend the method for making more general curve and we improve the computer environment using this metaphor.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.55-66
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• 1999

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, ′the process of the length of curve being equal to the sum of the vectors when intervals get smaller′ and ′the process of calculating volume of spinning curve by using definite integral.′ Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Also it can help students with solving mathematical problems intuitively. Consequently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the application of definite integral", which exists in mathematical curriculum the second and third grade of high school. When this study is used for students as assisting materials, it is expected the following educational effect. 1. Students will have precise concepts because they can understand what they learn intuitively. 2. Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 3. It is possible to change the teacher-centered instruction into the student-centered instruction. 4. Students will understand the relation between velocity and distance correctly because they can see the process of getting the length of curve by vector through the monitor. For the purpose of increasing the efficiencies and qualities of mathematics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, teachers have to use the CIA program carefully.

• The Journal of Korean Association of Computer Education
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• v.10 no.4
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• pp.51-59
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• 2007

There is the meager level of applying computers to mathematics education. It is because the effective mathematics educational softwares and the various contents that make students' spontaneous participation through the interaction with computers are insufficient. As a solution to solve it, we design and implement the graphic component, graphic entities and function types that are supported in the component was identified through analyzing the mid/high school curriculum, using a simple script language to invoke the functionality of the component improves reusability and extendability. The component can be used to produce the mathematics educational softwares and contents easily that need the facility to draw various functions and geometric figures.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.151-163
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• 1998

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

• The Mathematical Education
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• v.40 no.1
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• pp.113-123
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• 2001

We investigated an irrational constant e and compared its computational methods using spreadsheet. Such methods are based on classical definition, infinite series, continued fraction, infinite product exponential function and accelerated classical method. This kind of work is focused on experimental mathematics using computers in math class. This approach will be helpful for mathematics teachers to teach constant e in their classroom.

• The Mathematical Education
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• v.27 no.1
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• pp.15-23
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• 1988

We are at the onset of a major revolution in education, a revolution unparalleled since the invention of the printing press. The computer will be the instrument of this revolution. Computers and computer application are everywhere these days. Everyone can't avoid the influence of the computer in today's world. The computer is no longer a magical, unfamiliar tool that is used only by researchers or scholars or scientists. The computer helps us do our jobs and even routine tasks more effectively and efficiently. More importantly, it gives us power never before available to solve complex problems. Mathematics instruction in secondary schools is frequently perceived to be more a amendable to the use of computers than are other areas of the school curriculum. This is based on the perception of mathematics as a subject with clearly defined objectives and outcomes that can be reliably measured by devices readily at hand or easily constructed by teachers or researchers. Because of this reason, the first large-scale computerized curriculum projects were in mathematics, and the first educational computer games were mathematics games. And now, the entire mathematics curriculum appears to be the first of the traditional school curriculum areas to be undergoing substantial trasformation because of computers. Recently, many research-Institutes of our country are going to study on computers in orders to use it in mathematics education, but the study is still start ing-step. In order to keep abreast of this trend necessity, and to enhance mathematics teaching/learning which is instructed lecture-based teaching/learning at the present time, this study aims to develop/present practical method of computer-using. This is devided into three methods. 1. Programming teaching/learning method This part is presented the following five types which can teach/learn the mathematical concepts and principle through concise program. (Type 1) Complete a program. (Type 2) Know the given program's content and predict the output. (Type 3) Write a program of the given flow-chart and solve the problem. (Type 4) Make an inference from an error message, find errors and correct them. (Type 5) Investigate complex mathematical fact through program and annotate a program. 2. Problem-solving teaching/learning method solving This part is illustrated how a computer can be used as a tool to help students solve realistic mathematical problems while simultaneously reinforcing their understanding of problem-solving processes. Here, four different problems are presented. For each problem, a four-stage problem-solving model of polya is given: Problem statement, Problem analysis, Computer program, and Looking back/Looking ahead. 3. CAI program teaching/learning method This part is developed/presented courseware of sine theorem section (Mathematics I for high school) in order to avail individualized learning or interactive learning with teacher. (Appendix I, II)

• Communications of Mathematical Education
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• v.20 no.2 s.26
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• pp.215-230
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• 2006

In this paper, we performed research about the successful and unsuccessful factors for college math education. In addition, on the basis of the results from the comparative study on the Korean/foreign students' attitude toward the role of computers in math study, we tried to find out the ways to reflect the results on college math education. As the ways to improve college math education we propose that the professors should emphasize the significance of math and explain the successful and unsuccessful factors for math learning during the initial period of each semester. Furthermore, the professors should recognize the importance of computers in math study and ask for the university authority's support to provide necessary softwares and establish computer labs.

• The Mathematical Education
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• v.40 no.1
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• Research in Mathematical Education
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• v.1 no.1
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• pp.43-59
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• 1997

Now in Korea, the 7th curriculum reform is underway. The main difference of the seventh curriculum compared with former curricula is that it puts much emphasis on individual difference. It is a "differentiated" curriculum. The basic directions of the 7th mathematics curriculum are as follows: 1. Offer various mathematical subjects for "Selective Educational Period" (Grades 11 and 12). 2. 30% reduction of mathematical contents. 3. The reconciliation of domain names of school mathematics. 4. The use of computers and calculators in mathematics classrooms.

• The Mathematical Education
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• v.39 no.1
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• pp.71-80
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• 2000

As the new century begins, it is clear that K-l2 education is going through a major change. The increasing power and affordability of personal computers along with wide spread use of the Internet has not only changed the landscape for communication but it has opened up new and exciting opportunities for education. One of the ways that Internet could help improve education is to act as an interactive communication link to gather the knowledge and experience of all the teachers and to serve as an open forum for discussing and exchanging innovative ideas. But developing a successful site is not an easy task since the success of the site depends on the level of participation and cooperation of teachers. In this paper, learnings derived from the development of an interactive web based resource center for K-12 mathematics teacher are described and recommendations for developing an effective site for teachers are suggested. The development of an interactive resource center for mathematics teachers showed that while interest for a web based resource is very high, the main obstacle for effective teacher participation is lack of easy accessibility of internet by teachers, and lack of computer and internet training for teachers. The technical issues regarding hardware installation, software development and cost were minimal. Accessibility will improve in time as more and more schools are connected to the internet, but this alone will not be enough. The study suggests that in order to bring together teachers on the internet more effort needs to be made in training teachers on the use of computers and the internet.