• The Mathematical Education
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• v.61 no.4
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• pp.539-557
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• 2022

A research field develops by experiencing several turns of paradigms. Mathematics education research have experienced those turns as well. Still, the dominant perspective is that mathematics education research should be scientific and objective. In this article, I suggest that this need not to be the prime rule to follow and that the mathematics education field will fertile by discussing extraordinary cases which may seem controversal to be recognized as valid research work. To this end, I first briefly describe the necessity of open discussions among researchers for a field to develop. Then, I introduce fiction writing, a resesarch method derived from arts-based research, as an extraordinary case for open discussions. The benefit of Arts-based research is on that it takes an holistic approach to how we know by embracing emotion and emphathy as means for knowing. Because of this trait, arts-based research holds a powerful potential for influencing a wide range of people, both inside and outside of the resesarch field. Following this, I present a fiction about a prospective teacher who participated in an activity for designing educative curriculum materials. By doing so, I sought to provoke discussions among mathematics education researchers about what to include as a valid research work, possible standards for reviewing arts-based resesarch.

• 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)

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.397-408
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• 2005

This research developed self-directed teaming program for students who learn mathematics to improve their abilities for learning mathematics. A small-group cooperative teaming model was based on the self-directed loaming program which this research developed. The main target of this program was the second grade students of middle school. The program was consisted with three developing parts. The part 1 of program developing was consisted with analyzing and reconstructing mathematics curriculum, devising small-group cooperative learning program, and structuring teaching and teaming plans. The part 2 included the management of small-group cooperative Loaming and how to use the materials which this research developed. The part 3 provided various cooperative learning opportunities for students to improve their abilities for loaming mathematics.

• Research in Mathematical Education
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• v.6 no.2
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• pp.159-170
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• 2002

The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing developmental research effort to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the teaching and learning of differential equations at Ewha Womans University. The RME theory based on the design heuristic using context problems and modeling was developed for primary school mathematics. However, the analysis of this study indicates that a RME design for a differential equations course can be successfully adapted to the university level.

• The Mathematical Education
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• v.49 no.1
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• pp.67-83
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• 2010

The purpose of this study was to analyze the research trends of elementary mathematics education with regard to the topics, methods, subjects, and mathematical contents of such research. For this purpose, the papers published in domestic journals during the recent 5 years (2004-2009) were analyzed. A total of 383 papers from 8 professional journals were analyzed with the 4 criteria. First, the frequent research topics included instructional design and methods, learners' perspectives and abilities, and analysis of curriculum and textbooks in order. Second, qualitative research methodology was used twice as many as quantitative one. Whereas a survey was the most frequent quantitative research method, content analysis and case study were for qualitative methods. Third, research subjects included mainly typical students, specifically fifth and sixth graders. Papers dealing with lower graders or low-achievers as well as pre-service teachers were rare. Lastly, whereas the research on geometry as well as number and operations was active, that of measurement as well as probability and statistics was not. On the basis of these results, this paper includes several implications for the future research direction in elementary mathematics education.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.335-352
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• 2008

The purpose of this research was to investigate the descriptive evaluation method that focuses on the problem solving process of the student. The goal was to evaluate the students' understanding of the subject rather than the students' ability to find the final answer. The descriptive evaluation is being suggested as a way of examining the thought process of the student by performing a structured analysis of the problem solving process. Today, there are not enough descriptive evaluation resources available for teachers to effectively carry out this alternative assessment method in the elementary school mathematics curriculum. This research is a case study on the development of resources for descriptive evaluation in grade 4 mathematics. We designed the development process for descriptive evaluation and its rubric for all 8 units of the 4-Na level of mathematics in the elementary school curriculum. Three descriptive problems were developed for each of the 8 units for a total of 24 problems. The rubric consisted of three areas of assessment, 1) understanding of the problem, 2) problem solving, and 3) mathematical communication. The problems were first pilot tested in two 4th grade classes. Modified problems were then tested in a different 4th grade classroom. The study showed that the three defined areas of evaluation framework (problem understanding, problem solving and mathematical communication) were measurable and analyzable using the developed grading rubric. We then conclude that he descriptive evaluation could be used as an effective tool for improving teacher performance in elementary school mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.1
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• pp.1-18
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• 2005

The purpose of this study is to plan and apply the problem posing program to each unit of elementary mathematics 5-Ga stage, and to make an analysis of their effects on mathematics learning achievements, attitude and interesting. In order to achieve these purposes, the following research problems were set up for the present study: First, we design problem posing program which can be applied to the actual instruction with analyzing the curriculum of mathematics on 5-Ga stage in the seventh national curriculum. Second, we analyze the effect of applying problem posing program on students' mathematics learning achievements. Third, we analyze the effect of applying problem posing program on students' mathematical attitude and interest. The results of this study are as follows: First, the problem posing program developed in this study was more affirmative effects for improving the students' mathematics learning achievements. Second, the problem posing program also had affirmative effects on students' attitude and interest on mathematics. Third, after applying the problem posing program turned out to have a statistical significant correlation between mathematics learning achievements and attitude, and mathematics learning achievements and interest.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.453-474
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• 1998

This study is focused on the possibility if we can use graphic calculators in teaching and learning school mathematics. This study is consisted with four main chapters. In chapter II, the functions of the graphic calculator EL-9600 produced by Sharp Corporation was analyzed focused on the possibilities if the functions could be used in teaching and learning school mathematics. Calculating of real numbers and complex numbers, solving equations and system of linear equations, calculating of matrices, graphing of several functions including polynomial functions, trigonometric functions, exponential and logarithmic functions, calculation of differential and integrals, arranging of statical data, graphing of statistical data, testing of statistical hypotheses, and other more useful functions were founded. In Chapter III, a mathematics textbook developed by Core-Plus Mathematics Project was analyzed focused on how a graphic calculator was used in teaching and learning mathematics, In the textbook, graphic calculator was used as a tool in understanding mathematical concepts and solving problems. Graphic calculator is not just a tool to do complex computations but a tool used in the processes of doing mathematics, In chapter IV, the 7th mathematics curriculum for korean secondary schools was analyzed to find the contents could be taught by using graphic calculators. Most of the domains, except geometric figure, were found that they could be taught by using graphic calculators, In chapter V, a model of a unit using graphic calculator in teaching 7th mathematics curriculum was developed. In this model, graphic calculator was used as a tool in the processes of understanding mathematical concepts and solving problems. This study suggests the possibilities that we can use graphic calculators effectively in teaching and learning mathematical concepts and problem solving for most domains of secondary school mathematics.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.279-289
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• 1998

Main stream of ’90s mathematics education in the U.S must be the NCTM Standards. Since it was published in 1989, much focus has put on it and numerous research has been tried to apply it to real mathematics classes. But there hasn't always good fame. Some schools have already mathematics. NCTM(1998), Standards and Principles for School Mathematics: Discussion Draft taken the curriculum based on it and recently the negative results have been exposed. Not a few parents, teachers and experts became to be worry about that. In this situation, I suppose it is worth to review the original purpose of Standards, look into the recent problems related to it's application and think of improvement or alternatives. This article mainly includes first two issues and particularily considers what problems are to have to be reconsidered in Korea. The following four are what I draw as problem: Basic operations; constructivism;texts and work books;trial and error strategy and group activity.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.169-187
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• 2006

Ubiquitous errors in algebra like $(x+y)^2=x^2+y^2$ are a constant reminder that most students' manipulation of algebraic symbols has become detached from structural principles. The U.S. mathematics education community (NCTM, 2000) has responded by shying away from algebra as a structural study, preferring instead to ground meaning in empirical domains of reference. A new analysis of such errors shows that students' detachment from structural meaning stems from an inadequate structural curriculum, not from the inherent difficulty of adopting an abstract perspective on expressions and equations. A structural curriculum is outlined that preserves the possibility of students' engaging fully with algebra as both an empirical and a structural study.