• East Asian mathematical journal
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• v.30 no.2
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• pp.149-172
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• 2014

The problems of optimization addressed in the high school curriculum are usually posed in real-life contexts. However, because of the instructional purposes, problems are artificially constructed to suit computation, rather than to reflect real-life problems. Those problems have thus limited use for teaching 'practicalities', which is one of the goals of mathematics education. This study, by utilizing 'GeoGebra', suggests the optimization problem solving related to the quadratic curve, using the contour-line method which contemplates the quadratic curve changes successively. By considering more realistic situations to supplement the limit which deals only with numerical and algebraic approach, this attempt will help students to be aware of the usefulness of mathematics, and to develop interests in mathematics, as well as foster students' integrated thinking abilities across units. And this allows students to experience a variety of math.

• 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.

• School Mathematics
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• v.10 no.2
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• pp.181-197
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• 2008

Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.83-99
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• 2012

The conic sections are defined as algebraic expressions using the focus and the directrix in the high school curriculum. However it is difficult that students understand the conic sections without environment which they can manipulate the conic sections. To make up for this weak point, we have found the evidence for generating method of a conic section through a sundial and investigated the history of terms 'focus', 'directrix' and the tool of drawing them continuously.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.483-495
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• 2023

In his book "Exercitationum Mathematicalarum," a 17th-century mathematician van Schooten proposed linkages for drawing parabola, ellipse, and hyperbola. The linkages proposed by van Schooten can be used in action-based mathematics education and as a material for using mathematical history in school mathematics. In particular, students are not provided with the opportunity to learn by manipulating the quadratic curves in the high school curriculum, so van Schooten's linkages can be used for school mathematics. To this end, a method of implementing van Schooten's linkage in a dynamic geometry environment was presented, and proved that the traces of the figure drawn using van Schooten's linkage were parabola, ellipse, and hyperbola.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.49-70
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• 2002

There have recently been increasing exchanges between South and North Korea in many areas of society, involving politics, economics, culture, education. In response to these developments, research activities are more strongly demanded in each of these areas to help prepare for the final unification of the two parts of the nation. In the area of mathematics education, scholars have started to conduct comparative studies of mathematics education in South and North Korea. As a response to the growing demand of the time, in this thesis we compared the secondary mathematics education in South Korea with that in North Korea. To begin with, we examined the background of education, in North Korea, particularly predominant ideological, epistemological and teaching theoretical aspects of education in North Korea. Thereafter, we compared the mathematics curriculum of South Korea with that of North Korea. On the basis of these examinations, we compared the secondary school mathematics textbooks of South and North Korea, and we attempted to suggest a guideline for researches preparing for the unification of the mathematics curriculum of South and North Korea. As a communist society, North Korea awards the socialist ideology the supreme rank and treats all school subjects as instrumental tools that are subordinated to the dominant communist ideology. On the other hand, under the socialist ideology North Korea also emphasizes the achievement of the objective of socialist economic development by expanding the production of material wealth. As such, mathematics in North Korea is seen as a tool subject for training skilled technical hands and fostering science and technology, hence promoting the socialist material production and economic development. Hence, the mathematics education of North Korea adopts a so-called "awakening teaching method," and emphasizes the approaches that combine intuition with logical explanation using materials related with the ideology or actual life. These basic viewpoints of North Korea on mathematics education are different from those of South Korea, which emphasize the problem-solving ability and acquisition of academic mathematical knowledge, and which focus on organizing as well as discovering knowledge of learners' own accord. In comparison of the secondary school mathematics textbooks used in South and North Korea, we looked through external forms, contents, quantity of each area of school mathematics, viewpoints of teaching, and term. We have identified similarities in algebra area and differences in geometry area especially in teaching sequence and approaching method. Many differences are also found in mathematical terms. Especially, it is found that North Korea uses mathematical terms in Hangul more actively than South Korea. We examined the specific topics that are treated in both South and North Korea, "outer-center & inner-center of triangle" and "mathematical induction", and identified such differences more concretely. Through this comparison, it was found that the concrete heterogeneity in the textbooks largely derive from the differences in the basic ideological viewpoints between South and North Korea. On the basis of the above findings, we attempted to make some suggestions for the researches preparing for the unification in the area of secondary mathematics education.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.37-52
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• 2017

The purpose of this thesis is to analyze the current status of a program for an elementary math class for gifted students in Daegu and to propose a remedy. The main results of this thesis are as follows. First, goals of the gifted class and the basic operation direction were satisfactory, however plans for parent training programs and self evaluation of the classes were not presented. Therefore, it needs when and how to do for specific plan of gifted class evaluation and parent training programs. Second, The annual instruction plan has been restricted to the subject matter education and field trips and has not included specific teaching methods in accordance with the contents of learning program. The management of gifted classes, therefore, requires not only the subject matter education and field trips but also output presentations, leadership programs, voluntary activities, events and camps which promote the integral development of gifted students. Third, there is no duplication of content to another grade, and various activities did not cover the whole scope of math topics(eg. number and operation, geometry, measurement, pattern) equally. In accordance with elementary mathematics characteristics, teachers should equally distribute time in whole range of mathematics while they teach students in the class because it is critical to discover gifted students throughout the whole curriculum of elementary mathematics. Fourth, as there are insufficient support and operational lack of material development, several types of programs are not utilized and balanced. It is necessary for teachers to try to find the type of teaching methods in accordance with the circumstances and content, so that students can experience several types of programs. If through this study, we can improve the development, management and quality of gifted math programs, it would further the development of gifted education.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.