• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.509-531
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• 2011

This study is to determine if teaching of measuring the area of plane figures in elementary school is successful. While they teach to measure the area of figures in elementary school, students don't measure the segment of the figure directly until now. The figures are presented with auxiliary line and numerical information. When students measure the area of such figure, they do only substitute the number and calculate it. This study found that such teaching is not successful and propose the new teaching method of measuring the plane 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.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.25-41
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• 2006

The purpose of this study was to analyze teachers' pedagogical content knowledge (PCK) about area of plane figure and how it was actualized in instruction. As an exploratory, qualitative, and comparative case study, 2 fifth-grade teachers were selected. Semi-structured interviews with the leachers were conducted in order to explore their PCK with regard to the area of plane figure. A total of 14 mathematics instructions were videotaped and transcribed. Teachers' PCK and classroom teaching practices were analyzed in detail into 3 categories: (a) knowledge of mathematics contents, (b) knowledge of students' understanding, and (c) knowledge of instructional methods. As such, this paper provided a detailed description on each teacher's PCK and her teaching practice. The results showed that teachers' PCK had a significant impact on instruction. The teacher who had rich knowledge about the area of plane figure was able to encourage students to understand the concept of area and to or explore the principles behind formula calculating various areas of plane geometry. The results demonstrated the importance of individual components of PCK as well as that of overall level of PCK. Different aspects of teaching practices were observed as to how the teachers had internalized PCK. On the basis of a close relationship between teachers' PCK and their teaching practice, this paper finally raised several implications for teachers' professional development for effective mathematics instruction.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.305-322
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• 2010

The epistemological obstacles in the area learning of plane figure can be categorized into two types that is closely related to an attribute of measurement and is strongly connected with unit square. First, reasons for the obstacle related to an attribute of measurement are that 'area' is in conflict. with 'length' and the definition of 'plane figure' is not accordance with that of 'measurement'. Second, the causes of epistemological obstacles related to unit square are that unit square is not a basic unit to students and students have little understanding of the conception of the two dimensions. Thus, To overcome the obstacle related to an attribute of measurement, students must be able to distinguish between 'area' and 'length' through a variety of measurement activities. And, the definition of area needs to be redefined with the conception of measurement. Also, the textbook should make it possible to help students to induce the formula with the conception of 'array' and facilitate the application of formula in an integrated way. Meanwhile, To overcome obstacles related to unit square, authentic subject matter of real life and the various shapes of area need to be introduced in order for students to practice sufficient activities of each measure stage. Furthermore, teachers should seek for the pedagogical ways such as concrete manipulable activities to help them to grasp the continuous feature of the conception of area. Finally, it must be study on epistemological obstacles for good understanding. As present the cause and the teaching implication of epistemological obstacles through the research of epistemological obstacles, it must be solved.

• Korean Institute of Interior Design Journal
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• no.41
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• pp.112-120
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• 2003

The purpose of this study is to review the plan composition characteristics of the super high-rise apartment. 20 cases were selected in Seoul and Kyunggi area that were planned or constructed since 1999, and 10 unit plans were analyzed to review such design characteristics as block type & entry access type, plane figure, opening layout, area distribution and spice composition of unit plan. The result of the study shows that the super high-rise apartment has more variant block types and plane figures compare with the conventional high-rise apartment, and it also has several design characteristics in plane composition such as the increase of the number of the walls with openings, the weakening of the spatial centralization of a living room and the dispersion of rooms with the increase of connection by corridors.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• The Mathematical Education
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• v.58 no.2
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• pp.283-298
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• 2019

Among the measurement attributes included in the elementary school mathematics curriculum, perimeter, area, volume and surface area are intensively covered in fifth and sixth graders. However, not much is known about the level of student performance and difficulties in this area. The purpose of this study is to examine the understanding and performance of sixth-grade elementary school students on some ideas of measurement and ultimately to give some suggestions for teaching measurement and the development of mathematics textbooks. For this, diagnosis questions were developed in relation to the following parts: measurement of perimeter and area of plane figure, measurement of surface area and volume of solid figure, and the relationships between perimeter and area, and the relationships between surface area and volume. The performances of 95 sixth graders were analyzed for this study. The results showed children's low performance in the measurement area, especially measurement of perimeter and surface area, and relationship of the measurement concepts. Finally, we proposed the introduction order of the measurement concepts and what should be put more emphasis on teaching measurement. Specifically, it suggested that we consider placing a less demanding concept first, such as the area and volume, and dealing more heavily with burdensome tasks such as the perimeter and surface area.

• 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 for History of Mathematics
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• v.34 no.4
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• pp.137-149
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• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• Journal of The Korean Association of Information Education
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• v.5 no.1
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• pp.33-45
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• 2001

In order to adapt ourselves to the Informationalization Society of twenty-first century, it is required to have ability to find quickly the necessary information and solve the problem of our own. In the field of school, it should be educated to develop learner's ability that can cope with the Informationalization Society. When a learner can study in such direction, he or she will be able to plan the learning of his own as the subject of education, and develop his ability to solve the problem by collecting and examining various information. It is self-leading learning that can make education like this possible. Through computer, especially Web site, self-directed learning can develop can develop the individuality and creativity of learners. They can collect and utilize autonomously information and knowledge. To do such an education, the program that can work out self-directed learning is needed. Therefore the program I want to develop is to reconstruct the 'figure' part of mathematics in elementary school into five steps by utilizing Web site. In the first step is to learn the concept of various shape. This step enable learners to know what figure is and how it can be utilized in our real life. The second step of dot, line and angle makes it possible that learners can consolidate the foundation of the study about figure and recognize the relation between angle and figure. In the third step of plane figure, we can study how to calculate the relation of plane figures and the area of figure with various shapes by cutting and adding them. The fourth step is about congruence and symmetry. Learners can learn to know the figure in congruence, reduction and enlargement and how it is used in our real life. In the fifth step of solid figure, we can learn the relation among the plane figure, solid figure, the body of revolution, corn and pyramid etc. controling the speed of learning on the basis of his ability. In the process of the program, it is also possible to develop learner's ability of self-leading learning by solving the problem by himself. Because this program is progressed on the Web site, it is possible to learn anytime and anywhere. In addition to it, a learner can learn beyond the grade as well as do the perfect learning by controling the pace of learning on the basis of his ability. In the process of the program, it is also possible to develop learner's ability of self-leading learning by solving the problem by himself.