• 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.

• 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 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.

• 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.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.43-55
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• 2011

The purpose of this study was to investigate the effects of inquiry oriented instruction on the learning of area formulas. For this purpose, current elementary mathematics textbook(2007 revised version) which deal with area formulas was reviewed and then the experimental research on inquiry oriented instruction in area formulas was conducted. The results of this study as follow; First, there was no significant effect of inquiry oriented instruction on the mathematical achievement in area formula problems. Second, there was no significant effect on the memorization of area formulas. Third, there was significant effect on the generalization of area formulas. Forth, there was significant effect on the methods of generalization of area formulas. Fifth, through inquiry activities, the students can learn mathematical ideas and develop creative mathematical ideas. Finally, implications for teaching area formulas through inquiry activity was discussed. We have to introduce new area formula through prior area formulas which had been studied, and make the students inquire the connection between each area formulas.

• 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.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.381-402
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• 2011

In this paper we study formulae of the triangle's area. We solve problems related with making new formulae of the triangle's area. These formulae is consisted of some elements of triangle, for example side, angle, median, perimeter, radius of circumcircle. We transform formulae $S=\frac{1}{2}acsinB$, $S=\frac{abc}{4R}$, $S=\sqrt{p(p-a)(p-b)(p-c)}$, and make new formulae of the triangle's area. Some formulas are received in the process of Research and Education program in the science high school. We expect that our results will be used in the Research and Education program in the science high school.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.10a
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• pp.79-90
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• 2006

새로운 것을 학습할 때 학생들은 자신이 어떤 지식 상태를 갖고 있는지에 따라 상당히 다른 이해의 정도를 나타낸다. 유의미한 이해를 이끌어 내기 위해서 교사들은 학생들의 사전 지식상태를 파악하고 그것에 근거하여 학습과제를 제시할 필요가 있으며, 어떤 단원을 학습한 후에 학생들의 지식상태를 파악해 보는 방법도 모색되어야 할 것이다. 본 연구는 충청북도 C도시 4개 초등학교 5학년 학생 285명에게 수학 5-가 6단원을 학습한 후 넓이 측정과 관련된 지식상태 검사를 실시하고 그 결과를 Doignon & Falmagne(1999)의 지식공간론을 활용하여 분석하였다. 학생들의 답안에서 평면도형의 넓이 측정과 관련된 지식의 상태를 파악하고 세 가지 범주-측정의 의미 파악, 공식 활용, 전략의 사용-에서 지식 상태의 위계도를 작성하였다. 첫 번째 범주인 측정의 의미 파악과 관련하여 학생들은 둘레나 넓이의 속성 파악에서 혼동을 보이거나 직관적으로 넓이를 비교해야 하는 과제에서도 계산을 시도하는 지식 상태가 반 이상인 것으로 드러났다. 두 번째 범주인 공식 활용과 관련해서는 학생들의 상당수가 부적합한 수치를 넣어 무조건 넓이 계산을 시도하고 있었다. 또한 세 번째 범주인 전략 사용에 관해서는 분할이나 등적변형 등의 전략을 알고 있는 학생 중에도 40% 가량은 문제를 표상하는데 어려움이 있어 해결하지 못하는 것으로 드러났다.

• 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.

• The Mathematical Education
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• v.59 no.2
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• pp.131-146
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• 2020

Regarding the formula for measuring the area of a circle, the Archimedes' constant is generally written in front of the square of radius length, but there were a few cases where the Archimedes' constant was written after that in Germany and France. In this study, two things are studied: First, how many students are writing the Archimedes' constant after that? Second, what do the students think about the written order of characters in the formula for measuring the area of a circle? In the online survey of 201 people aged 14 to 21 in Korea, there was a perception of more than 86% that both are possible or only after that are possible. In this study, it is suggested that there is a difference between the general written order of characters and the natural perception of students formed through school education. In addition, students aged 14 to 16 thought more that the Archimedes' constant should be written after that, and after that age, there was a greater perception that both are possible without confusion of meaning. It can be seen that the change in students' perception has emerged through school education on natural mathematical written order of characters after middle school courses. From this point of view, the most common perception can be that if there is no confusion in meaning, then both expressions are possible.