• Education of Primary School Mathematics
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• v.17 no.3
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• pp.253-263
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• 2014

In this paper we review an axiomatic definition of the area of plane figures with area axioms, discuss what the area axioms mean, and analyze the contents about the area of plane figures in elementary school mathematics from the view point of area axioms. So we evaluate which aspects of the concept of area are emphasized or deemphasized in the current elementary school mathematics textbook.

• 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.

• Communications of Mathematical Education
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• v.12
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• pp.155-170
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• 2001

중등학교 수학교육 분야에서 기하 영역과 관련된 많은 연구들을 볼 수 있는데, 이들 중에서 도형에 관련된 다양한 개념 자체에 대한 심도 있는 논의는 많이 이루어지지 않았다. 예를 들어, 우리에게 가장 친숙한 개념들 중의 하나가 넓이임에도 불구하고, 왜 한 변의 길이가 a인 정사각형의 넓이가 a$^2$인가? 와 같은 물음은 그리 쉽지 않은 질문이 될 것이다. 그리고, 다각형의 넓이 자체는 다양한 수학 문제의 해결을 위한 중요한 도구이지만, 넓이를 활용한 다양한 문제해결의 경험을 제공하지 못하고 있다. 본 연구에서는 다양한 다각형들의 넓이를 규정하는 공식들을 유도하고, 유도된 넓이의 공식들을 활용한 다양한 문제해결의 아이디어를 제시하고, 이를 통해, 다각형의 넓이를 활용한 효율적인 수학 교수-학습을 위한 접근을 모색할 것이다.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.371-385
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• 2015

In this paper we investigate the axioms defining area and volume so that revisit area formula for triangle, volume formula for triangular pyramid, and related contents in school mathematics from the view point of axiomatic method and Hilbert's third problem.

• 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.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.181-199
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• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.167-191
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• 2014

In this study, we investigate the term-sets of 'base' or 'bottom': 'the bottom side of a polygon' and 'the base side (of a geometrical figure)'. And we study the concept of 'the base area' in the solid figures and the formula of 'the bottom dimensions'. We start from the 6th grade math problem: 'Find the bottom dimension of the rectangular.' The primary answer is that it does not use the term('the bottom dimensions') in the elementary mathematics. However, in the middle school mathematics, 'the base area' is used as means of 'the area of one bottom side', which is not explained anywhere from the elementary mathematics to middle school mathematics. In addition, the base is defined and 'the surface area' and 'the side area' is taught in the elementary mathematics, so we naturally think of 'the base area'. Therefore we first investigate the term-sets of 'base' or 'bottom' which has two elements: 'the bottom side of a polygon' and 'the base side (of a geometrical figure)'. Next we discuss 'the base area' through curriculum and textbooks, dictionary definitions and so on. In addition, we survey pre-service teachers and teachers about the solid figures and analyse the understanding of 'the base side' and 'the base area' comparatively. In particular, we compare the changes and the tendency of correct answers from the first question to the last question. As a result, we verify 'the cognitive gap' between the elementary mathematics and the middle school mathematics, we suggest the teaching of 'the base area' and succession subjects to teach figure domain in the elementary mathematics.

• School Mathematics
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• v.10 no.1
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• pp.123-138
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• 2008

The objective of this paper is to reveal the cause of failure of New Math in the field of the SMSG area education from the didactical point of view. At first, we analyzed Euclid's (Elements), De Morgan's (Elements of arithmetic), and Legendre's (Elements of geometry and trigonometry) in order to identify characteristics of the area conception in the SMSG. And by analyzing the controversy between Wittenberg(1963) and Moise(1963), we found that the elementariness and the mental object of the area concept are the key of the success of SMSG's approach. As a result, we conclude that SMSG's approach became separated from the mathematical contents of the similarity concept, the idea of same-area, incommensurability and so on. In this account, we disclosed that New Math gave rise to the lack of elementariness and geometrical mental object, which was the fundamental cause of failure of New Math.

• School Mathematics
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• v.16 no.4
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• pp.763-782
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• 2014

The purpose of this study is to investigate mathematics content knowledge(MCK) of pre-service teachers about the area of a circle. 53 pre-service teachers were asked to perform four tasks based on the central ideas of measurement for the area of a circle. The results of this study are as follows. First, pre-service teachers had some difficulty in describing the meaning of the area of a circle. Quite a few of them didn't recognize the necessity of counting the number of area units. Secondly, pre-service teachers had insufficient content knowledge about the central ideas of measurement for the area of a circle such as partitioning, unit iteration, rearranging, structuring an array and approximation. Lastly, few pre-service teachers understood the concept of actual infinity. Most students regarded the rectangle as the figure having the approximation error instead of the limitation from rearranging the parts of a circle.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.