Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings

Stephens, Ana C.; Knuth, Eric; Blanton, Maria; Işler, Işıl; Gardiner, Angela Murphy; Marum, Tim

doi:10.1016/j.jmathb.2013.02.001

Cited by 52 publications

(54 citation statements)

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“…Some have interpreted the equal sign as a 'dosomething' sign rather than as a symbol indicating equivalence (Essien & Setati, 2006;Hattikudur & Alibali, 2010;Stephens et al, 2013). The operational conception of the equal sign can be attributed to incorrect articulation.…”

Section: When Asked About the Meaning Of The Equal Sign L1 Said "Nomentioning

confidence: 99%

“…Much thought and research have gone into exploring learners' understanding of the equal sign in elementary and middle schools (Essien & Setati, 2006Hattikudur & Alibali, 2010Hohensee, 2017, Jones, Inglis, Gilmore, & Dowens, 2012Stephens, Knuth, Blanton, Isler, Gardiner, & Marum, 2013). Linchevski and Herscovics (1996) argue that teachers and learners should be made aware of the demarcation between arithmetic and algebra.…”

Section: Introductionmentioning

confidence: 99%

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Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve

Machaba

2017

EURASIA J MATH SCI T

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This article gives an account of Grade 9 learners' understanding of the concept of the equal sign and how they move from an 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 selected for an interview. The study revealed that Grade 9 learners in this school interpreted 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 in lower grades, where greater emphasis was placed on rules than on the meaning of a concept.

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Section: When Asked About the Meaning Of The Equal Sign L1 Said "Nomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve

Machaba

2017

EURASIA J MATH SCI T

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“…Several studies have documented that students in elementary, middle school, high school and college do not fully understand the equal sign (Jones, Inglis, Gilmore & Evans, 2013;Kaplan & Alon, 2004;Knuth, Alibali, Hattikudur, McNeil & Stephens, 2008;Knuth, Alibali, Hattikudur, McNeil & Stephens, 2007;Molina, Castro & Castro, 2007;Rittle-Johnson, Matthews, Taylor & McEldoon, 2011;Sherman & Bisanz, 2009;Stephens et al, 2013). Studies have determined that the development of the common student misconception about the equal sign as an operation sign or signal for "the answer comes next" (Carpenter, Levi, Franke & Zeringue, 2001, p. 2) may initially occur in the early years of elementary school (Baroody & Ginsburg, 1983;Behr, Erlwanger & Nichols, 1975;Carpenter & Levi 2000;Erlwanger & Berlanger 1983;Falkner, Levi & Carpenter, 1999;Kieran, 1981;Knuth, Stephens, McNeil & Alibali, 2006;Molina & Ambrose, 2008).…”

Section: Problem Statementmentioning

confidence: 99%

“…This incomplete understanding has been well documented across grades and ages prior to the release of the explicit standard regarding the equal sign in the CCSSM (Knuth, Alibali, Hattikudur, McNeil & Stephens, 2008;Molina, Castro & Castro, 2009;Rittle-Johnson, Matthews, Taylor & McEldoon, 2011;Stephens et al, 2013). Few studies have been conducted with elementary students since 2011 which was the year some states started to implement the CCSS (Rittle-Johnson et al, 2011;Stephens et al, 2013).…”

Section: The Current Studymentioning

confidence: 99%

“…To define the equal sign accurately, "the equal sign denotes the relation between two equal quantities" (Carpenter, Franke & Levi, 2003, p. 9). By administering a written assessment to 290 third, fourth and fifth grade students, Stephens et al (2013) found the operational definition of the equal sign to be the dominating conception.…”

Section: Students' Misconceptions About the Equal Signmentioning

confidence: 99%

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Understanding the meaning of the equal sign : an investigation of elementary students and teachers.

Bennett

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I would like to thank Dr. Karen Karp, my advisor and dissertation chair. Dr. Karp has long been a most supportive and encouraging mentor to me. As a student in her class and especially as her doctoral student, Dr. Karp inspired me to think critically and she has always expected me to succeed. I have the deepest respect and admiration for Dr. Karp.My words can never fully express the level of gratitude I have for the innumerable instances of guiding, supporting and teaching I have received from Dr. Karp. I thank Dr.Karp for the role she has played in my academic career. The purpose of this study was to investigate the impact of two different policies for implementing new mathematics standards in two schools, for grades two through five, on student understanding of the equal sign. The study also examined teachers' knowledge of the equal sign. The research used a mixed methods design to explore differences in student understanding of the equal sign as a result of how standards were implemented in two adjoining states with two different decisions as to when the standards would be implemented. This dissertation shares research that may be of interest to teachers, administrators, teacher educators and other stakeholders.The main constructs under investigation were student understanding of the equal sign, teacher knowledge regarding the equal sign including how it is taught and assessed, and the impact of different implementation schedules for new mathematics standards on student performance on their knowledge of the meaning of the equal sign -a standard that was not previously explicit in either state.The study was conducted in two adjoining Midwestern states in three separate schools (fifth grade students from one of the states are housed in a middle school building vii for overcrowding reasons and are equivalent to fifth grade students in an elementary setting). Each school as per their state mandates, followed the timeline for new mathematics standards implementation with one school in the fourth year of implementation and the other two (same district) in their first year.The sample was 1,182 students in second, third, fourth and fifth grade and their forty-two classroom teachers. Students and teachers from the three schools were given the Mathematical Equivalence Knowledge Assessment (MEKA) as a measurement of teacher knowledge and student understanding of the equal sign. Data from teacher interviews and surveys were used to complement findings related to their students' understanding of the equal sign and their classroom practices related to this topic. A hierarchical linear model was used to detect differences between student scores on the MEKA in each school in the two states.To determine the impact of teacher knowledge of the equal sign on student understanding of the equal sign an unconditional hierarchical linear model and a follow up ANCOVA were conducted using the MEKA results from both teacher and student participants. The same model was also used to detect significant differences found between student sc...

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Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective

Jeongsuk

Kim²

2017

Teaching and Learning Algebraic Thinking With 5- To 12-Year-Olds

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Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings

Cited by 52 publications

References 14 publications

Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve

Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve

Understanding the meaning of the equal sign : an investigation of elementary students and teachers.

Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective

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