• Education of Primary School Mathematics
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• v.23 no.1
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• pp.45-61
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• 2020

The concept of equality is given as a way of reading the equal sign without dealing it explicitly in elementary school mathematics. The meaning of the equal sign can be largely categorized as operational and relational views. However, most elementary school students understand the equal sign as an operational symbol for just writing the required answers. It is essential for them to understand a relational concept of the equal sign because algebraic thinking in middle school mathematics is based on students' understanding of a relational view of the equal sign. Recently, the relational meaning of the equal sign is emphasized in arithmetic. Hence it is necessary for elementary school students to have some activities so that they experience a relational meaning of the equal sign. In this study, we investigate the meaning of the equal sign and contexts of the equal sign in elementary school mathematics to discuss explicit ways to emphasize the concept of equality and relational views of the equal sign.

• Research in Mathematical Education
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• v.18 no.4
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• pp.237-256
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• 2014

This paper reports findings from a written assessment which was designed to investigate Chinese primary school students' understanding of the equal sign and equation structure. The investigation included a sample of 110 Grade 3, 112 Grade 4, and 110 Grade 5 students from four schools in China. Significant differences were identified among the three grades and no gender differences were found. The majority of Grades 3 and 4 students were found to view the equal sign as a place indicator meaning "write the answer here" or "do something like computation", that is, holding an operational view of the equal sign. A part of Grade 5 students were found to be able to interpret the equal sign as meaning "the same as", that is, holding a relational view of the equal sign. In addition, even though it was difficult for Grade 3 students to recognize the underlying structure in arithmetic equation, quite a number of Grades 4 and 5 students were able to recognize the underlying structure on some tasks. Findings in this study suggest that Chinese primary school students demonstrate a relational understanding of the equal sign and a strong structural sense of equations in an earlier grade. Moreover, what found in the study support the argument that students' understanding of the equal sign is influenced by the context in which the equal sign is presented.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.643-662
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• 2017

The first appearance of the equations in elementary school mathematics is in the expression of the equal sign in the addition sentences without its definition. Most elementary school students have operational understanding of the equal sign in equations. Moreover, students' opportunities to have a clear concept of the properties of operations are limited because they are used implicitly in the textbooks. Based on this fact, it has been argued that it is necessary to introduce the properties of operations explicitly in terms of specific numbers and to deal with various types of equations for understanding a relational meaning of the equal sign. In this study, we use equations to represent the implicit properties of operations and the relational meaning of the equal sign in elementary school mathematics with respect to students' level of understanding. In addition, we give some explicit examples which show how to apply them to make efficient computations.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.459-475
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• 2022

The equal sign and equivalence are the most basic and core concepts in elementary mathematics, but there has been lack of research on how to teach these concepts with textbooks. Given this, this study analyzed elementary mathematics textbooks in terms of three instructional elements (i.e., emphasizing the meaning of the equal sign as a relational symbol, dealing with an equation as an object for reasoning, and using an equation with a missing value). In particular, this study analyzed 10 different mathematics textbook series that are newly used in 2022 and examined the overall trends and characteristics for teaching the equal sign and equivalence. The results of this study showed that the activities emphasizing the meaning of the equal sign as a relational symbol were most noticeable but the activities dealing with an equation as an object for reasoning or using an equation with a missing value were relatively rare. Based on the results of the analysis, this study provides textbook writers with implications on what to further consider in covering the equal sign and equivalence.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.39-55
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• 2024

Recently, the 2022 revised mathematics curriculum has established achievement standards for equal sign and equality, and efforts have been made to examine teaching methods and student understanding of relational understanding of equal sign. In this context, this study conducted a lesson that emphasized relational understanding in an introduction to equal sign, and compared and analyzed the understanding of equal sign between the experimental group, which participated in the lesson emphasizing relational understanding and the control group, which participated in the standard lesson. For this purpose, two classes of students participated in this study, and the results were analyzed by administering pre- and post-tests on the understanding of equal sign. The results showed that students in the experimental group had significantly higher average scores than students in the control group in all areas of equation-structure, equal sign-definition, and equation-solving. In addition, when comparing the means of students by item, we found that there was a significant difference between the means of the control group and the experimental group in the items dealing with equal sign in the structure of 'a=b' and 'a+b=c+d', and that most of the students in the experimental group correctly answered 'sameness' as the meaning of equal sign, but there were still many responses that interpreted the equal sign as 'answer'. Based on these results, we discussed the implications for instruction that emphasizes relational understanding in equal sign introduction lessons.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• School Mathematics
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• v.10 no.4
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• pp.537-555
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• 2008

The study aims to analyze elementary school students' understanding of the concept of equality sign in contexts, to reflect the types of contexts for equality sign which mathematics textbook series for $1{\sim}4$ grades on natural numbers and its operation provide, and to invetigate the effects of teaching methods of the concept of equality sign suggested in this research. In order to achieve these purposes, the origin, concept, and contexts of equality sign were theoretically reviewed and organized. Also the error types in using equality sign were reflected. Modelling, discussing truth or falsity of equations, identifying relations between numbers and their operation, conjecturing basic properties of numbers and their operations, experiencing diverse contexts for equality sign, and creating contexts for equality sign are set up as teaching methods for better understanding the concept of equality sign. The conclusions are as follows. Firstly, elementary school students' under-standing of the concept of equality sign varied by context and was generally far from satisfactory. In particular, they had difficulties in understanding the concept of the equal sign in contexts with operations on both sides. The most frequently witnessed error was to recognize equality sign as a result of operations. Secondly, student' lack of understanding of the concept of equality sign came from the fact that elementary textbooks failed to provide diverse contexts for equality sign. According to the textbook analysis, contexts with operations on the left side of the equal sign in the form of $a{\pm}b=c$ were provided excessively, with the other contexts hardly seen. Thirdly, teaching methods provided in the study were found to be effective for enhancing understanding the concept of equality sign. In other words, these methods enabled students to focus on relational understanding of concept of equality sign rather than operational one.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.211-236
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• 2014

The purpose of this study is to investigate teacher's knowledge of concept of equality and derive implications about proper teaching methods. To solve these study problems, three elementary school teachers are chosen for this study, and a pencil-and paper tests for comprehension of the equality concept targeting 72 students for elementary school that the teachers are in charge of the students was carried out. Also, The semi-structured interview(using a questionnaire) was conducted for analyzing of the teachers' knowledge of the equality concept. The findings are as follows. First, during the lesson, the teachers' reading of equal sign has a decisive effect on the students' the way of reading. Second, teachers tend to interpret the concept of equality as a systematic analysis rather than a relational analysis, and use a equal sign focusing on meaning of 'same result'. So, Students also can't interpret the concept of equality as a relational analysis. Third, under the influence of teacher's feedback or reaction, making the mistake of the using equal sign of students reoccurred continually. Fourth, teachers misjudged some of examples of the nonstandard context equation for teaching elementary school students. Furthermore, during the lesson, they usually used a limited equality context. So, students can't have a chance to learn equality in a plenty of context. Thus, the knowledge of teachers and their lesson has decisive influence on the comprehension of students about the equality concept. So, Teacher has to focus on the meaning of the equality as a relational analysis and teach them in a plenty of context. With this, lots of study and in-service training are needed to enhance knowledge of teachers. And more of lesson programs and materials have to provided on the instruction manual for teaching the meaning of the equality.

• The Research Journal of the Costume Culture
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• v.8 no.4
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• pp.562-576
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• 2000

The purpose of this study is to semiotically reinterpret the Korean beauty and symbol inhering in the modern clothing of Korean designers as the context of traditional culture through regarding the clothing including hegemony that is controlling the Korean society and culture as a sign. The theoretical framework for analysis was derived from the semiotically analytic methods of F. Saussure and R. Barthes. The results of the study are as follows ; Korean images reflected in the modern clothing designed by Korean designers are humanistic image, environmental-friendly image, totemic and mythlogical image, equal and peaceful image, and metaphorical and metonymical image. Conclusively, developing a creative design based upon the interpretation of our unique and traditional culture, the clothing could be newly made of historical and cultural resources in the modern lives. If so, I think that the clothing will be not only the visual and decorative art, but also an information which contains implication of our culture, and finally can be established.

• (The) Research of the performance art and culture
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• no.34
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• pp.277-313
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• 2017

This study is to find out the correlation with buddhist music after analyzing the rhythm of six pieces of PanYeombul sung by Kim Janggil out of Ogu exorcism of East coast the findings summarized are as follows. First, PanYeombul by Kim Janggil, performed on Oct, 16, 2016, was composed of , , , , , , , , , , and . Still, even if PanYeombul is performed by the same male shaman, the composition can be added or left out depending on some circumstances, which means the procedures are flexible. Seeing that there is common component of in additoin to compared with Kimyongtaek, it can be said that the component of is an important part in PanYeombul of Ogu exorcism of East coast Second, is usually referred to 'SinmyojangguDaedalani' in buddhist ritual, While Kim yongtaek accepts this practice in title, Kim Janggil uses 'YeomhwajangguDaedalani' as the title which makes his song different from others. Yeomhwa means "picking up flowers with fingers" which has been used in buddhism, not in common Considering this fact, the conclusion can be reached that by using the term 'Daedalani' from a buddhist chant, but making differentiation from buddhism, Kim Janggil is making the effort to be different from buddhist rituals. give some unique meaning to shaman rituals. Third, PanYeombul of Ogu exorcism of East coast may be divided into two main parts - the former part is PanYeombul and the latter part is Jiokga. In performing PanYeombul, male shaman sits singing alone and playing Jing himself, on the other hand, in case of Jiokga, he stands singing a solo with gwaeggwari in his hand accompanied by other musicians with the rhythm of Samgongjaebi. As the song and the accompaniment are in the form of giving and taking like duet. it is in peak in terms of music. Accordingly, PanYeombul can be divided into PanYeombul and Jiokga, But since it is performed by one male shaman and sung a solo, it is usually seen as one procedure. Jing, which is a kind of accompaniment in PanYeombul by Kim Janggil, has the role to distinguish a phrase and settle the musical paragraph. When the buddhist chant with one word-one note is performed. it requires the performer to catch his or her breath or clear throat. Just then, Jing comes out for filling out the intervals. Also, its role to distinguish a phrase and settle the musical paragraph helps make it clear to deliver words. The rhythm of Jing is mostly made up of small triple time except equal small binary time, comes out with overwhelmingly more frequency of Sutsoe(♪♩) than Amsoe(♩♪), and often shows syncopation. By often using Off Beat or short-long rhythm even in accompaniment of equal small binary time, he tris to give some variation to monotonous and equal rhythm for the musical vitality. These are similar to Sutsoe rhythm which can evoke tension and Kim Janggil makes these things his characierisiic of rhythm. Fifth, all the pieces consist of mi, sol, la, do, re and the descending melody like do'${\searrow}$la${\searrow}$sol${\searrow}$mi appears most frequently. The descending melody usually arouses the feeling of sorrow, so the sadness for the deceased is presented properly, which suggests his musical talent. Generally, pieces take on Menari-tori as a whole where the length of sol appears for a short time in descending la${\searrow}$sol${\searrow}$mi of perfect four degrees. Sixth, Even he accepts the lines of buddhist chant, he changes them in some degree. For example, he inserted some words between lines like 'Wonwangsaeng' and 'NamuAmitabul' and added Korean words like hapsosa to the lines of buddhist service written in Chinese character. Also, he inserted some words like 'iiiiiii~' to express the feeling of sadness. These are to maximize the desire of the deceased to go to the heaven and at the same time to diminish the sign of buddhism and strengthen the features of shamanism. Seventh, the effort to decrease the sign of buddhism is made in pasting lines of two songs. For example, Between the last words 'Wonsuaenapsu of Dage and the first words 'Jisimgwimyeongrye' of Chiljeongrye, there is usually a short pause to distinguish paragraphs, But he continues two songs without any pause to get rid of the feelings of buddhist chant. In terms of melody, he makes a distance from buddhist chant in an effort that he gives some traits to shaman rituals which are different from buddhist even if he uses the lines of buddhist rituals. Eighth, the analyzed pieces can be in four categories - no regular melody , , equal small binary time , eotmori melody of ten eighth time with 3+2+3+2 mixed small time . and Samgongjaebi melody 3+2+3 mixed small time . Each piece has its unique melody. Although of buddhist ritual is often performed, by using eotmori melody, he evokes the feeling of shaman and is another example of giving unique characteristic to the shaman of East coast by using Samgongjaebi melody.