• Journal of Gifted/Talented Education
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• v.5 no.2
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• pp.37-54
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• 1995

The radical development of modern mathematics is due to the appearance of Collection Theory by George Cantor. The Set Theory is independent as an area and also closely interrelated with other areas. So its content becomes a common sense and a basic part across the whole area of modern mathematics. Accordingly, the basic element of modern mathematics is helping young children get familiar with set as early as possible. The thinking of set by which children can categorize, make partial sets and correspondences, understand the general characteristic, and conceptualize the discovered relationships is very important for young children. At this point where the Math education for young children is emphasized under the influence of the modernization movement of Math education, the systematic education for building up the set concept as the basic background of number concept during the early childhood is required. On current mathematics education for young children, graphs, the foundation of geometry, time, and patterns have been included in the traditional and practical content related to numbers. However, the education on collection which is the foundation of number concept is insufficient. A study shows that the level of young children's understanding on set is quite high, but the set concept isn't reflected in current Math curriculum for young children. And basic activities neccesary on building up the set concept, such as categorization, comparison, etc. are conducted in kindergardens but unsatisfactory because of those kindergarden teachers' premature understanding on the set concept. In conclusion, the curriculum for young children should be reorganized based on the set concept as the kernel concept. Also, the reappraisal of the training curriculum and the supplementary efucation for kindergarden teachers are urgent for raising the teaching ability of those kindergarden teachers.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.503-523
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• 2010

The current mathematics curriculum are consist of the following domains: 'Characteristics', 'Objectives', 'Contents', 'Teaching and learning method', and 'Assessment'. The mathematics standards which students have to learn in the school are presented in the domain of 'Contents'. 'Contents' are consist of the following sub-domains: 'Number and Operation', 'Geometric Figures', 'Measures', 'Probability and Statistics', and 'Pattern and Problem-Solving' (Elementary School); 'Number and Operation', 'Geometry', 'Letter and Formula', 'Function', and 'Probability and Statistics' (Junior and Senior High School). These sub-domains of 'Contents' are dealing with mathematical subjects, except 'Problem-Solving' at the elementary school level. In this study, the sub-domain of 'mathematical process' was suggested in an equal position to the typical sub-domains of 'Contents'.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.409-428
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• 2014

The purpose of this study is to examine the features of the curriculum of Chosun-Sanhak(朝鮮算學), the mathematics of Chosun Dynasty in the 17th to 18th century. The results of this study are as follows. First, the goal of education, teaching-learning method and assessment of Chosun-Sanhak in the 17th to 18th century had not changed since the 15th century. Second, the changes in the field of the organization of mathematical contents were observed. Chosun-Sanhak in that time was higher in the hierarchy than in the 15th to 16th century. The share of the equation and geometry had increased and various topics of mathematics had been studied as well. Third, in the field of the characteristics of mathematical contents, the influx of European mathematics and the uniqueness of Chosun-Sanhak had been observed. In conclusion, The 17th to 18th century was the time when Chosun-Sanhak had pursued the identity escaping from the effects of Chinese-Sanhak.

• East Asian mathematical journal
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• v.34 no.4
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• pp.403-427
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• 2018

The purpose of this paper is to reinterpret and visualize the medieval Arab's studies on the geometric methods of solving the cubic equation by utilizing Apollonius' symptom of the parabola. In particular, we investigate the results of $Kam{\bar{a}}l$ $al-D{\bar{i}}n$ ibn $Y{\bar{u}}nus$, Alhazen, Umar al-$Khayy{\bar{a}}m$ and $Al-T{\bar{u}}s{\bar{i}}$ by 4 steps(analysis, construction, proof and examination) which are called the complete solution in the constructions. This paper is available in the current middle school curriculum through dynamic geometry program(Geogebra).

• Research in Mathematical Education
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• v.4 no.2
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• pp.63-77
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• 2000

The purpose of this article is to devise the activities based on van Hiele levels of geometric thought using computer software, Geometer\\\\`s Sketchpad(GSP) as a tool. The most challenging task facing teachers of geometry is the development of student facility for understanding geometric concepts and properties. The National Council of teachers of Mathematics(Curriculum and Evaluation Standards for School Mathematics, 1991; Principles and Standards for School Mathematics, 2000) and the National Re-search Council(Hill, Griffiths, Bucy, et al., Everybody Counts, 1989) have supported the development of exploring and conjecturing ability for helping students to have mathematical power. The examples of the activities built is GSP for students ar designed to illustrate the ways in which van Hiele\\\\`s model can be implemented into classroom practice.

• East Asian mathematical journal
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• v.26 no.4
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• pp.535-551
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• 2010

In this paper, we investigate the methodology to calculate the volume of the pyramid and frustum of the pyramid that is found in Gu Jang Sel Hae and San Hak Jeong Ui(The first volume)text. Comparing and analyzing content in Korean and Chinese mathematics education textbooks that uses as a foundation the aforementioned methodology, it is proposed that in future development of mathematics education curriculum the area of solid geometry be taught in greater depth in basic study guides.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.431-450
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• 2007

A polygon is one of the main subjects of the geometry curriculum that is handled widely from the second-grade elementary school to middle school. In this research, we analyze second-grade middle school students' conceptions of the polygon that are revealed in the process of seeking the definition and the area of it given in a lattice worksheet.

• The Mathematical Education
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• v.49 no.3
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• pp.313-328
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• 2010

Mathematical modeling has been observed in the way of a possibility to contribute in improving students' problem solving abilities. One of the important views of real life problem context could be described such as a useful ways to interpret the real life leading to children's abstraction process. The problem contexts for the grade 6 with mathematical modeling perspectives were developed by reviewing the current 7th National Mathematics Curriculum of Korea. Those include the 5 content areas such as number & operation, geometry, measurement, probability & statistics, and pattern & problem solving. One of problem contexts, "Space", specially designed for pattern & problem solving area, was applied to the grade 6 students and analyzed in detail to understand student's mathematical modeling progress.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.125-136
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• 2008

There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.

• The Mathematical Education
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• v.52 no.1
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• pp.83-95
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• 2013

The purpose of this paper is to explain and reinterprets Apollonius' Symptoms on conic sections based on the current secondary curriculum of mathematics, present the historical background of Apollonius' Symptoms to teachers and students and introduce visualization proof of Apollonius' symptoms on a parabola, a hyperbola and an ellipse by a new method using dynamic geometry software(GSP) respectively.