Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

Asquith, Pamela J.; Stephens, Ana C.; Knuth, Eric; Alibali, Martha W.

doi:10.1080/10986060701360910

Cited by 96 publications

(86 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Though there is not significant influence, it is known that the number of students with operational conception is higher than that of those with relational conception. It is not surprising results, because the same results are also obtained by previous researchers (Knuth et al, 2008;Asquith et al, 2007;Alibali et al, 2007;McNeil et al, 2006;Knuth et al, 2005;Falkner et al, 1999) for students of elementary and secondary schools. Since relational conception plays important roles in the success in completing equation and reasoning in algebra, it is really necessary to provide students with this conception as soon as possible.…”

Section: Understanding Of the Equal Signsupporting

confidence: 78%

“…Analysis was made by coding each students' answer for each task like in Knuth et al (2008), Asquith et al (2007), Alibali et al (2007) and Knuth et al (2005). Then it is said that in order to have a validity in the coding procedures, the coding was made by two persons.…”

Section: Discussionmentioning

confidence: 99%

“…The instrument of this present research referring to Knuth et al (2008), Asquith et al (2007), Alibali et al (2007) and Knuth et al (2005) was used to describe mathematics education students' understanding of the equal sign and strategies they adopted in solving the equivalent equation.…”

Section: Instrumentmentioning

confidence: 99%

“…The understanding of the equal sign is an important matter in the mathematics language in general, especially in algebra and arithmetic. Researches showed that teachers really expected that there are many students who may understand the equal sign as relational, since it is a very basic problem for learning algebra (Asquith et al, 2007). But, students' difficulties in interpreting the equal sign are well documented Knuth et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Baiduri¹

2015

ASS

View full text Add to dashboard Cite

The objective of this paper is to analyse matemathics education students' understanding of the equal sign, their strategies in solving the equivalent equations and the relationship between the two. Data were collected through responses from 167 first year students of mathematics education in University of Muhammadiyah Malang, East Java, Indonesia to the assigned tasks and the data were descriptively analysed using a Chi-square statistics. The results of the analysis showed that their operational understanding of the equal sign is more dominant than their relational conception. In solving equivalent equations, they tended to adopt operational procedures by making solutions, comparisons and substitutions, instead of paying attention to the existing relations in equivalence, called a strategy to recognize equivalence. No significant relations exist between students' understanding of the equal sign and their strategies in solving equivalent equations. Then gender and repondents' origin of areas are also discussed.

show abstract

Section: Understanding Of the Equal Signsupporting

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Instrumentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Baiduri¹

2015

ASS

View full text Add to dashboard Cite

show abstract

“…For this reason, it is expected that students defined variables as unknown. Furthermore, students think that variables must stand for only one specific value as reported in the study of Asquith et al (2007). This may be another reason why students have difficulties with variables, which was also stated in the previous studies.…”

Section: Discussionmentioning

confidence: 89%

Middle Grade Students’ Concept Images of Algebraic Concepts

Sitrava¹

2017

JEL

View full text Add to dashboard Cite

This study investigates middle school students' concept images of algebraic concepts which are term, constant term, variable, and coefficient. Also, the study aimed to explore their performances in defining these concepts correctly. A phenomenological method was used to support methodological perspective and to reveal the findings of the study. Twenty seven 7th grade students completed a questionnaire, which aims to assess students' concept images of the algebraic concepts. Twelve of them were selected for semi-structured interviews on the basis of purposeful sampling method to clarify and expand on their responses to the questionnaire. The data was analyzed via the content analysis approach. The analysis of the data indicated that students have various concept images of basic algebraic concepts. More interestingly, this study showed that although students' performances on defining the algebraic concepts were above 50% for each concept, 7th grade students' concept images of the algebraic concepts is not so strong for learning algebra conceptually.

show abstract

Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge

Barbieri

Booth

2020

Applied Cognitive Psychology

View full text Add to dashboard Cite

Summary Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on algebraic feature knowledge and solving quadratic equations. Middle school algebra students (N = 206) were randomly assigned to four conditions. Two errorful conditions either displayed errors and asked students to explain or displayed correct solutions and primed students to reflect on potential errors by problem type. A correct example condition and problem‐solving control group were also included. Studying and explaining common errors displayed in incorrect examples improved equation‐solving ability. An aptitude‐by‐treatment interaction revealed that learners with limited understandings of algebraic features demonstrated greater benefits. Theoretical implications about using examples to promote learning from errors are considered in addition to suggestions for educational practice.

show abstract

Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

Cited by 96 publications

References 17 publications

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Mathematics Education Students’ Understanding of Equal Sign and Equivalent Equation

Middle Grade Students’ Concept Images of Algebraic Concepts

Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge

Contact Info

Product

Resources

About