• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.451-469
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• 2012

This research intends to examine how 6th graders (age 12) conceptualize the area of geometric figures. In this research, 4 problems were given to 122 students, which the 4 problems correspond to understanding area concept, finding the area of geometric figures-including rectangular, parallelogram, and triangle, writing the area formula for finding area of geometric figures, and explaining the reason why the area formula holds. As the results of the study, we identified that students revealed the most low achievement in the understanding area concept, and lower achievement in explaining the reason why the area formula holds, writing the area formula, finding the area of geometric figures in order. In based on the results, we suggested the didactical implication for improving the students' conception about the area of geometric figures.

• School Mathematics
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• v.10 no.3
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• pp.443-461
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• 2008

The purpose of this study was to provide teachers with suggestions on how to teach the unit of finding the area of plane figure by analyzing students' different solution methods. The solution methods were analyzed according to how the original area of the given figure was kept: partition, transformation, and elimination. The partition method was most used. With regard to transformation, students seemed to find it easy to use the area of rectangle. With regard to elimination, students were successful using elimination to find the area of a given figure but had difficulty in producing a formula from the method. The teacher played a key role to encourage students to employ different solution methods, and gave them opportunities to compare and contrast various methods. A cautionary note is that, with too much emphasis on 'variety', the mathematical efficiency may be lost in the process. It suggests that a teacher should be careful to establish appropriate sociomathe- matical norms with students in order that they can make their own judgment on which solution method is mathematically worth and efficient.

• School Mathematics
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• v.15 no.4
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• pp.847-866
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• 2013

The purpose of this study was to analyze students' various solution methods revealed in the lessons of finding out the area of plane figures, and to explore instructional implications on how to draw meaningful formalization out of such multiple methods. The teacher in this study tended to select a few solution methods that were easy for students to understand and to induce formalization. An analysis of students' solution methods and the process of formalization showed that students need to understand what parts of the length of the given plane figure they should know, and to identify the base, height, and diagonal line of the figure. The analysis also showed that it was effective to choose the solution methods that were used by many students and that could be easily transformed into a concise formula. Based on these results, this paper provides instructional suggestions for a teacher to orchestrate classroom discussion toward formalization based on students' multiple solution methods.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Journal for History of Mathematics
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• v.28 no.1
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• pp.31-44
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• 2015

The cycloid curve had been studied by many mathematicians in the period from the 16th century to the 18th century. The results of those studies played important roles in the birth and development of Analytic Geometry, Calculus, and Variational Calculus. In this period mathematicians frequently used the cycloid as an example to apply when they presented their new mathematical methods and ideas. This paper overviews the history of mathematics on the cycloid curve and presents proofs of its important properties.

• School Mathematics
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• v.8 no.1
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• pp.27-43
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• 2006

The objective of this paper is to design teaching units to foster secondary pre-service teachers' mathematising abilities. In these teaching units we focus on generalizing area of a 2-dimensional triangle and volume of a 3-dimensional tetrahedron to n-volume of n-simplex In this process of generalizing, principle of the permanence of equivalent forms and Cavalieri's principle are applied. To find n-volume of n-simplex, we define n-orthogonal triangular prism, and inquire into n-volume of it. And we find n-volume of n-simplex by using vectors and determinants. Through these teaching units, secondary pre-service teachers can understand and inquire into n-simplex which is generalized from a triangle and a tetrahedron, and n-volume of n-simplex which is generalized from area of a triangle and volume of a tetrahedron. They can also promote natural connection between school mathematics and academic mathematics.