• Title/Summary/Keyword: Equality sign

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The Analysis of Elementary School Students' Understanding of the Concept of Equality Sign in Contexts and the Effects of its Teaching Methods (등호 문맥에 따른 초등학생의 등호 개념 이해와 지도 방법 연구)

  • Ki, Jeong-Soon;Chong, Yeong-Ok
    • 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.

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Analysis of the Equality Sign as a Mathematical Concept (수학적 개념으로서의 등호 분석)

  • 도종훈;최영기
    • The Mathematical Education
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    • v.42 no.5
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    • pp.697-706
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    • 2003
  • In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

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A study on patterns shown in the process of solving a linear equation - Centering around the first grade of middle school - (일차방정식의 풀이 과정에 나타난 유형에 관한 연구 - 중학교 1학년을 중심으로 -)

  • Seo, Jong-Jin
    • Journal of the Korean School Mathematics Society
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    • v.12 no.2
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    • pp.281-308
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    • 2009
  • In the process of solving a linear equation, some questions had equal sign('=') relation properly, while other questions did not have equal sign('=') relation properly. Since whether students could express equal sign('=') relation properly or not is determined by questions, the direction for teaching should be instituted, and instruction and teaching should be conducted by comparing and analyzing after conducing tests on may items. Most of students who got the answer for items without the method of solving a linear equation solved the items using binomial. For questions asking to solve using the characteristic of equality, most of students solved the questions using binomial instead of using the characteristic of equality. Therefore, instruction and learning to solve equations using both the characteristic of equality and binomial have to be achieved.

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An Analysis of Elementary School Teacher's Knowledge of Concept of Equality (초등학교 교사의 등호 개념에 관한 지식분석 사례 연구)

  • Jeong, Ho Jeong;Choi, Chang Woo
    • 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.

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Discrepancy between Reading and Writing Equality Number Sentences in Korean Language (등호 해석의 두 시간적 차원인 읽기.쓰기의 불일치와 그 해소)

  • Yim, Jaehoon
    • 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.

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Some Remarks on the Sameness and the Meaning of the Equal Sign in Elementary School Mathematics Textbooks (초등학교 수학에서 같음과 등호의 의미에 대한 고찰)

  • Paek, Dae Hyun
    • 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.

다항식의 대수적 표현

  • 홍영희
    • Journal for History of Mathematics
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    • v.16 no.4
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    • pp.15-32
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    • 2003
  • Since algebra before the 19th century was the study of equations and equations are not differentiated from polynomials because of lack of the equality sign, the algebraic symbolism of polynomials plays very important role for tile history of algebra. We deal with the evolution of literal notations of polynomials in western and eastern worlds, and then compare their history.

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면류에 대한 고찰

  • 호문룡
    • Journal for History of Mathematics
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    • v.12 no.1
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    • pp.13-20
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    • 1999
  • Lee, Sang-Hyuk(1810-\ulcorner) explained application problems which can be represented as the equation of degree 1 or 2 in the chapter of 'Myun-Lyu' of his book 'Cha-Geun-Bang-Mong-Gu.' Mainly he dealt with the various questions which looks for the length of right triangle and square. After they are expressed in the equation, all of them has terms on both side of equality sign and they have solution as integer. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with few step to solve.

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Analysis of students' understanding of equal sign through equal sign introduction lessons emphasizing their relational understanding (등호 도입 단원에서 관계적 이해를 강조한 수업에 따른 학생들의 이해 분석)

  • Lee, Yujin
    • 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 Study of Response' Type according to a Position of Variable on Linear Equation - Centering around the First and Third Grade of Middle School - (일차방정식에서 변수의 위치에 따른 반응 유형에 관한 연구 -중학교 1학년과 3학년을 중심으로-)

  • Seo, Jong-Jin
    • Journal of the Korean School Mathematics Society
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    • v.12 no.3
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    • pp.267-289
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    • 2009
  • Students have difficulties in solving linear equation problems with a variable on the right side rather than linear equation problems a variable on the left side of the sign of equality. In order for students to overcome such difficulties, opportunities to experience many types of basic linear equation problems would have to be provided. Also, it is necessary to examine the process of students' problem solving process by constructing various types of evaluation item and test them in instruction and learning of linear equations, or grasp students' studying statues through individual interview and based on theses, error correction through feedbacks have to be achieved.

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