• 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.

• 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.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.79-101
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• 2016

Understanding the equal sign is of great significance to the development of algebraic thinking. Given this importance, this study investigated in what ways a total of 695 students from second to sixth graders understand the equal sign. The results showed that students were successful in solving standard problems whereas they were poor at items demanding high relational thinking. It was noticeable that some of the students were based on computational thinking rather than relational understanding of the equal sign. The students had a difficulty both in understanding the structure of equations and in solving equations in non-standard problem contexts. They also had incomplete understanding of the equal sign. This paper is expected to explore the understanding of the equal sign by elementary school students in multiple problem contexts and to provide implications of how to promote students' understanding of the equal sign.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.287-307
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• 2003

This study analyzed the concept of equal symbol(=) that is the most symbol used in learning of mathematics and investigated students' understanding of that. The equal symbol is endowed with the 'same', 'equal', and 'equivalent' meaning, represented by =, but students interpret the meaning of equal symbol according to the mathematical con text. Thus, we analyzed the equal symbol on the basis of the theory of conceptual fields. In the theory of conceptual fields, concept is a three-tuple of three sets of situation, operational invariants and symbolic representations, and the operational invariants are the concept-in-action and the theorems- in-action. With the analysis contents, we investigated how students read = by korean, what equals in the expression containing = or by what meaning students used =, and which they could correct the error for =. This study imply that we should consider the symbol notation agreed by mathematical society, the meaning, and the situational context that it used, when we teach the mathematics symbols.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.365-384
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• 2010

This paper is an analysis study where we surveyed how well pre-service teachers understand the mathematical concepts taught in elementary school. We analyzed the results focusing on the following: First, what are the pre-service teachers' understandings of the equal sign and variables? Secondly, how exact are their understandings of other elementary school mathematical concepts? The survey was done on the students in Teachers College of Jeju National University. We hope that the results of this study will help the improvement of mathematical education for elementary pre-service teachers.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.207-223
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• 2013

Teachers unfold a series of timeless mathematical symbols such as 5+2=7 in time by verbalizing the symbols in classrooms. A number sentence 5+2=7 is read in Korean as '5 더하기 2는(five plus two) 7과(seven) 같다(equals). Unlike in English, 5+2 and 7 are read first before the equal sign in Korean. This sequence of reading in Korean conflicts with the conventional linguistic sequence of writing from left to right. Ways of resolving the discrepancy between reading and writing sequences can make a difference students' understanding of the equal sign. Students would be in danger of perceiving the equal sign as an operational symbol, if a teacher resolves the discrepancy by subordinating reading sequence to linguistic convention of writing. This way of resolving results in the undesired phenomenon of changing the reading expressions in Korean elementary math textbook which represent relational notion of the equal sign into other reading expressions that represent operational notion of it. For understanding of relational notion of the equal sign, the discrepancy should be resolved by changing writing sequence in accordance with reading sequence. In addition, teaching of verbalizing the equal sign should be integrated with teaching of verbalizing inequality signs.

• The Mathematical Education
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• v.61 no.1
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• pp.109-126
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• 2022

The purpose of this study is to explore how well teachers anticipate students to understand and solve equations. For this purpose, a questionnaire of the equal sign was developed, and 20 fourth-grade classes were selected as research participants. Teachers in each class were asked to predict various strategies on how their own students would respond to the questionnaire, and a total of 450 students from the 20 classes solved the questionnaire. As a result of the analysis, the teachers could predict students' computational strategies and relational strategies easily but did not fully understand that some students used both strategies or employed incorrect computational or relational strategies. The students tended to use relational strategies better than the teachers expected. They also employed operational strategies more often than the teachers expected. The teachers predicted that students' strategies would be influenced by the types of the problems such as equation-structure items and equation-solving items, whereas the students were more influenced by the forms of equations in the problems. Based on these results, several implications for the knowledge to which teachers needed to attend were discussed so that elementary school students could enhance the relational understanding of the equal sign.

• 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.

• The Mathematical Education
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• v.55 no.1
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• pp.1-19
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• 2016

Given the importance of understanding the equal sign in developing early algebraic thinking, this paper investigated how a total of 695 students in grades 2~6 understood the equal sign. The students completed a questionnaire with three types of items (equation structure, equal sign definition, and open equation solving) based on the construct map by four different levels of understanding the equal sign. The questionnaire was analyzed by Rasch model. The results showed that about 80% of the students were at least Level 3 which means a basic relational understanding of the equal sign. However, the success rates varied across grades and it was noticeable that about 70% of the second graders remained at Level 1 or 2 which maintains an operational understanding of the equal sign. The results of item types demonstrated that item difficulty for the advanced relational thinking was the highest and this is the same even for the Level 4 students. This paper is expected to investigate elementary school students' understanding of the equal sign and provide implications of how to deal with the equal sign in the elementary school.