• Education of Primary School Mathematics
• /
• v.24 no.4
• /
• pp.247-264
• /
• 2021

The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

• The Mathematical Education
• /
• v.45 no.2 s.113
• /
• pp.177-189
• /
• 2006

This study focuses on the analysis of prospective elementary teachers' representation of trapezoid area and teacher educator's reflecting in the context of a mathematics course. In this study, I use my own teaching and classroom of prospective elementary teachers as the site for investigation. 1 examine the ways in which my own pedagogical content knowledge as a teacher educator influence and influenced by my work with students. Data for the study is provided by audiotape of class proceeding. Episode describes the ways in which the mathematics was presented with respect to the development and use of representation, and centers around trapezoid area. The episode deals with my gaining a deeper understanding of different types of representations-symbolic, visual, and language. In conclusion, I present two major finding of this study. First, Each representation influences mutually. Prospective elementary teachers reasoned visual representation from symbolic and language. And converse is true. Second, Teacher educator should be prepared proper mathematical language through teaching and learning with his students.

• East Asian mathematical journal
• /
• v.31 no.2
• /
• pp.167-188
• /
• 2015

Formula for the area of a trapezoid is an educational material that can handle algebraic and geometric perspectives simultaneously. In this note, we will make up the expression equivalent algebraically to the formula for the area of a trapezoid, and deal with the conversion of a geometric point of view, in algebraic terms of translating and interpreting the expression geometrically. As a result, the geometric conversion model, the first algebraic model, the second algebraic model are obtained. Therefore, this problem is a good material to understand the advantages and disadvantages of the algebraic and geometric perspectives and to improve the mathematical insight through complementary activity. In addition, these activities can be used as material for enrichment and gifted education, because it helps cultivate a rich perspective on diverse and creative thinking and mathematical concepts.

• Journal of Educational Research in Mathematics
• /
• v.23 no.2
• /
• pp.253-267
• /
• 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 of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.565-586
• /
• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• Fashion & Textile Research Journal
• /
• v.25 no.5
• /
• pp.615-625
• /
• 2023

This study aimed to analyze the characteristics of the lower-body shape of middle-aged males with abdominal obesity by type and consider dimensional distribution to present a suit-pants size. The criteria were having a waist circumference greater than 90 cm and a waist-to-hip ratio(WHR) greater than 0.90; a total of 566 middle-aged males were surveyed. The findings revealed that, first, compared to standard lower-body types, the average body size of abdomenobese middle-aged males was significantly larger, especially in the horizontal area than in the vertical ares. Second, through a cluster analysis, a total of three categories of abdominal obesity were defined: small oval, large cylinder, and trapezoid type. The coverage rates of each type were 93.8%, 75.9%, and 93.0%, respectively. Finally, the suit-pants size system established according to lower-body types indicated the basic body size and reference body size were different for each type and also for the KS K 0050 male adult's garments size system. According to the definition of abdominal obesity, the types of abdominal obesity and the dimensions of each area are different, even if they belong to the same obesity group, suggesting that it is necessary to develop a pattern based on the analysis of obesity types.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.24 no.11
• /
• pp.1411-1416
• /
• 2020

In this paper, we propose a method of extraction analysis of blood flow area on color doppler ultrasonography by using 4-directional contour tracking and K-Means algorithm. In the proposed method, ROI is extracted and a binarization method with maximum contrast as a threshold is applied to the extracted ROI. 4-directional contour algorithm is applied to extract the trapezoid shaped region which has blood flow area of brachial artery from the binarized ROI. K-Means based quantization is then applied to accurately extract the blood flow area of brachial artery from the trapezoid shaped region. In experiment, the proposed method successfully extracts the target area in 28 out of 30 cases (93.3%) with field expert's verification. And comparison analysis of proposed K-Means based blood flow area extraction on 30 color doppler ultrasonography and brachial artery blood flow ultrasonography provided by a specialist yielded a result of 94.27% accuracy on average.

• Journal of Internet Computing and Services
• /
• v.4 no.6
• /
• pp.57-67
• /
• 2003

The recent rapid development of multimedia and optical technologies brings great attention to application systems to process facial Image features. The previous research efforts in facial image processing have been mainly focused on the recognition of human face and facial expression analysis, using front face images. Not much research has been carried out Into image-based detection of face direction. Moreover, the existing approaches to detect face direction, which normally use the sequential Images captured by a single camera, have limitations that the frontal image must be given first before any other images. In this paper, we propose a method to detect face direction by using facial features such as facial trapezoid which is defined by two eyes and the lower lip. Specifically, the proposed method forms a facial direction formula, which is defined with statistical data about the ratio of the right and left area in the facial trapezoid, to identify whether the face is directed toward the right or the left. The proposed method can be effectively used for automatic photo arrangement systems that will often need to set the different left or right margin of a photo according to the face direction of a person in the photo.

• Honam Mathematical Journal
• /
• v.37 no.1
• /
• pp.41-52
• /
• 2015

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. Recently, it was proved that this property is a characteristic one of parabolas. That is, among strictly locally convex $C^{(3)}$ curves in the plane $\mathbb{R}^2$ parabolas are the only ones satisfying the above area property. In this article, we study strictly locally convex curves in the plane $\mathbb{R}^2$. As a result, generalizing the above mentioned characterization theorem for parabolas we present some conditions which are necessary and sufficient for a strictly locally convex $C^{(3)}$ curve in the plane to be an open part of a parabola.

• Journal of the Korea Fashion and Costume Design Association
• /
• v.16 no.2
• /
• pp.177-188
• /
• 2014

A fur has emerged as one of fashion staples. there has been a rising interest in fur industry. Therefore, this study investigated how to estimate the amount of raw materials consumed at the production of fur clothes, and the scope of the study was limited to mink clothes. For an empirical study, in addition, Koreans' favorable mink design was chosen based on previous studies and sales of fur clothes, and its consumption was estimated. The consumption of mink clothes depends on the special feature of natural resources such as place of origin, gender and variety. Therefore the method of consumption for mink clothes is inevitably different from it of fiber clothes. Considering the procedure of mink clothe's production as collect same kind of a fur and process though pattern placement, first is outfut work for consumption. At estimation of the consumption of mink clothes, the number of minks was counted by matching the area of mink skin with that of the mink cloth patterns. Then, the usable area of the patterns was calculated after splitting them into diverse figures such as triangle, quadrangle and trapezoid. If we divide area by using the similar in shape of pattern and calculate, We can find high efficiency by reducing extra space. Specially we can expect more efficient work system when we use computers for efficient division of area.