Middle-School Students' Understanding of the Equal Sign: The Books They Read Can't Help (2024)

Equal sign representations in curriculum and textbooks in middle schools and students’ understanding of equal sign

Scientia Paedagogica Experimentalis

The aim of the current study was to investigate fourth and fifth grade students’ equal sign conceptions in the light of the revised Turkish mathematics curriculum (MoNE, 2018) that includes newly added objectives related to the equal sign concept in fourth grade. A total of 53 students (30 fourth-grade students) participated in the study. Equal sign test (EST) was used for quantitative data collection. Semi-structured interviews were conducted to gain a deeper insight into the students’ equal sign conceptions. Moreover, the fourth and fifth grade students’ textbooks and other course materials were analysed in terms of equal sign contextual presentations. According to the quantitative analysis results, the average score of fifth-grade students was 11.21 whereas the fourth-grade students’ average score was 8.13 out of 13 in the EST. The analysis of the course materials displayed that standard contextual presentations of the equal sign, which are only helpful for teaching the operation...

An Analysis of the Introduction of the Equal Sign in Three Grade 1 Textbooks

The conception of substitution of the equals sign plays a unique role in students' algebra performance

Journal of Numerical Cognition, 2019

Students’ conceptions of the equals sign are related to algebraic success. Research has identified two common conceptions held by children: operational and relational. The latter has been widely operationalised in terms of the sameness of the values on each side of the equals sign, but it has been recently argued that the substitution component of relational equivalence should also be operationalised (Jones, Inglis, Gilmore, & Dowens, 2012, https://doi.org/10.1016/j.jecp.2012.05.003). In this study, we investigated whether students’ endorsement of the substitution definition of the equals sign is a unique predictor of their algebra performance independent of the other two definitions (operational and sameness). Secondary school students were asked to rate the ‘cleverness’ of operational, sameness, and substitution definitions of the equals sign and completed an algebra test. Our findings demonstrate that endorsement of substitution plays a unique role in explaining secondary school ...

The Effects of Instruction on Children's Understanding of the "Equals" Sign

The Elementary School Journal, 1983

Grade 9 Learners’ Understanding of the Concept of the Equal Sign: A Case Study of a Secondary School in

2016

This paper reports on 49 Grade 9 learners’ understanding and interpretation of the concept of the equal sign and how they transit from arithmetic to an algebraic equation. A case study using a sequential mixed method research design was conducted in a secondary school in Soshanguve, a township in Gauteng, South Africa. Out of the 49 learners who wrote a test on the concept of the equal sign, eight were chosen for an interview. The study reveals that Grade 9 learners in this school interpret the equal sign as a “do something” and unidirectional (one-sided) sign, not as the concept that represents an equivalent (concept of keeping both sides of the equal sign equal) of two quantities. The researchers attributed misinterpretation of the equal sign to how learners had been taught the concept of number sentences at lower grades, where greater emphasis was placed on rules rather than the meaning of a concept. It is thus recommended that learners should be encouraged to solve equations thr...

The Equals Signthe Problem of Early Algebra Learning and How to Solve It

Teaching Innovations, 2022

The equals sign is one of the most important concepts and symbols in mathematics, the understanding of which is crucial for learning and understanding all mathematical content, especially algebra. The paper will draw attention to the problems related to the formation and understanding of this concept, and present a methodological approach to learning based on the context modeling of real-life situations (modeling length, balance, etc.), with the aim of overcoming this misconception. In the empirical section of the paper, we examined the effects of the methodological framework of learning algebra on the understanding of the equals sign through an experiment with parallel groups, and on a sample of the fourth-grade students of primary school (N = 257). The obtained results show that the methodological approach based on the context modeling of real-life situations improves student understanding of the equals sign, as a symbol of mathematical equivalence and their ability to solve problems containing this sign. Keywords: contextual approach, equals sign, early algebra, Realistic Mathematics Education, student achievement

Revisiting the equal sign: Some Grade 8 and 9 learners' interpretations

Does understanding the equal sign matter? Evidence from solving equations

Journal for Research in Mathematics Education

Equal Sign Conceptual Understanding and Early Algebra Problem Solving

Master's Thesis, 1998

Students often encounter difficulties when transitioning from arithmetic to algebra, potentially due to an incomplete understanding of mathematical symbols like the equal sign. We assessed students' equal sign conceptual understanding and algebra problem-solving strategies before and after algebra instruction. Participants engaged in a 40-minute session comprising various segments: an Equal Sign Conceptual Understanding Assessment, an Algebra Problem Solving Assessment, an intervention, a post-test Equal Sign Conceptual Understanding Assessment, and a post-test Early Algebra Problem Solving Assessment, followed by a Transfer Algebra Problem Solving Assessment. The intervention consisted of either a lesson on doing the same thing to both sides, a move-and-change strategy, or a control condition involving additional problem practice. Results showed students experienced challenges with both algebra equations and the conceptual understanding of the equal sign. Only 37% of participants correctly solved both algebra pretest problems, and 42% employed invalid strategies. Additionally, 43% of students lacked a firm grasp of the distinction between relations and operations, scoring below 5 points on the Equal Sign Conceptual Understanding Assessment. A significant correlation was found between students' conceptual understanding and problem-solving abilities at the pre-test stage. Students who used more advanced strategies for algebra problems displayed higher levels of conceptual understanding. Further research is needed to establish causal relationships between conceptual understanding and problem-solving, considering factors such as instructional impact and potential bidirectional influences between these skills.

Students' Early Grade Understanding of the Equal Sign and Non-standard Equations in Jordan and India

Many students around the world are exposed to a rote teaching style in mathematics that emphasizes memorization of procedures. Students are frequently presented with standard types of equations in their textbooks, in which the equal sign is immediately preceding the answer (a + b = c). This exposure can lead to many misconceptions, such as thinking that the equal sign means “do something” or “the answer is.” This paper describes students’ understanding of the equal sign when solving nonstandard equations in Jordan on the Early Grade Mathematics Assessment (EGMA) and in India on a number sense screener. Common misconceptions are shared, as well as strategies for improving instruction with the equal sign and non-standard equations to prevent future errors.