The role of arithmetic structure in the transition from arithmetic to algebra

Warren, Elizabeth

doi:10.1007/bf03217374

Cited by 74 publications

(65 citation statements)

References 14 publications

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“…First, rather than assigning {I + 2{ $ = 22, Toyib assigned 20. This mistake is classified into the first category of difficulty, i.e., an arithmetical difficulty and applying additive inverse property in particular ( [9]; [13]). Second, rather than taking a square root for the equation {I + 2{ $ = 20, Toyib ignored the square and subtract both sides with 2 to get I = 18.…”

Section: Resultsmentioning

confidence: 99%

“…In [9], Jupri, Drijvers and Van den Heuvel-Panhuizen identified five main categories of difficulties in algebra learning. First, the difficulties in using arithmetical operations and properties include difficulties in adding like terms (e.g., [10]; [11]); in using commutative, associative, inverse, and distributive properties; and in using priority rules of arithmetical operations (e.g., [12]; [13]). Second, the difficulties in understanding the notion of variable concern understanding it as an unknown, a generalized number, a placeholder, or a varying quantity ( [10]; [12]).…”

Section: Difficulties In Initial Algebra Learningmentioning

confidence: 99%

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Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Jupri¹,

Drijvers²,

Heuvel–Panhuizen³

2016

AIP Conference Proceedings

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Abstract. The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students' thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital tool for algebra, the Cover-up applet for solving equations in particular. This case study was part of a larger teaching experiment on initial algebra enriched with digital technology which aimed to improve students' conceptual understanding and skills in solving equations in one variable. The qualitative analysis of a video observation, digital and written work showed that the use of the applet affects student thinking in terms of strategies used by students while dealing with the equations. We conclude that the effects of the use of the digital tool can be traced from student problem solving strategies on paper-and-pencil environment which are similar to strategies while working with the digital tool. In future research, we recommend to use specific theoretical lenses, such as the theory of instrumental genesis and the ontosemiotic approach, to reveal more explicit relationships between students' conceptual understanding and the use of a digital tool.

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Section: Resultsmentioning

confidence: 99%

Section: Difficulties In Initial Algebra Learningmentioning

confidence: 99%

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Jupri¹,

Drijvers²,

Heuvel–Panhuizen³

2016

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

“…Algebra is linked to the use of symbolic representations to express the variables and possibility of calculating on the basic of expressions involving the symbolic representations (Filloy & Rojano, 1989). Warren (2003) felt that understandings of basic arithmetic operations could assist successful transition from arithmetic to algebra. Her findings suggest that understanding of mathematical notion and arithmetic operations are basic criteria for the success in acquisition of algebraic knowledge.…”

Section: The Misconceptions In Algebramentioning

confidence: 99%

“…Research on the development of algebraic understanding by investigating the difficulties students encountered in solving algebraic problems has been well documented (Vlassis, 2002;Warren, 2003). However, most of these studies focused their attention on the topic of linear equations and the difficulties students encountered in solving linear equations.…”

Section: Introductionmentioning

confidence: 99%

An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

Lim

2017

EJREP

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“…Therefore, based on an earlier literature review study (Jupri et al 2014a), we identified five categories of difficulties in initial algebra. First, difficulties in applying arithmetical operations in numerical and algebraic expressions (abbreviated as ARITH) concern difficulties in adding or subtracting similar algebraic terms (e.g., Herscovics and Linchevski 1994;Linchevski 1995), difficulties in applying the associative, commutative, distributive, and inverses properties, and difficulties in applying priority rules for arithmetical operations (e.g., Booth 1988;Bush and Karp 2013;Warren 2003).…”

Section: Difficulties In Initial Algebramentioning

confidence: 99%

Improving Grade 7 Students’ Achievement in Initial Algebra Through a Technology-Based Intervention

Jupri

Drijvers

Heuvel–Panhuizen

2015

Digit Exp Math Educ

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Digital technology plays an increasingly important role in daily life, mathematics education and algebra education in particular. To investigate the effect of a technology-rich intervention related to initial algebra on the achievement of 12-13 year old Indonesian students, we set up an experiment. The experimental group's intervention focused on equations in one variable and is characterized by an alternated use of paper-and-pencil and digital work, and by the intertwining of word problems and bare algebra problems. The control group was taught in a regular way without digital tools. Students from eight classes in four schools took part in a pre-test and a post-test. The results showed that the experimental group's (n=131) gain score was significantly higher than the control group's (n=119) score, with a medium effect size. Also, a school factor was found to affect student achievement. The qualitative analysis of student written and digital work during the teaching experiment corroborated the quantitative results. Both results confirm the effectiveness of this type of technology-rich intervention for enhancing student achievement in algebra.

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The role of arithmetic structure in the transition from arithmetic to algebra

Cited by 74 publications

References 14 publications

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

Improving Grade 7 Students’ Achievement in Initial Algebra Through a Technology-Based Intervention

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