Young students learning formal algebraic notation and solving linear equations: are commonly experienced difficulties avoidable?

Hewitt, Dave

doi:10.1007/s10649-012-9394-x

Cited by 27 publications

(27 citation statements)

References 23 publications

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“…In this way abstract mathematics is experienced as a material activity of meaningful actions on symbols. Persuasive empirical examples consistent with this view can be seen in Empson and colleagues, and also in Hewitt (2012).…”

mentioning

confidence: 57%

Early algebraization: a global dialogue from multiple perspectives

Jones

2012

Research in Mathematics Education

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mentioning

confidence: 57%

Early algebraization: a global dialogue from multiple perspectives

Jones

2012

Research in Mathematics Education

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“…I have found that learners may question initially why something is written how it is, such as why division is written as a fraction rather than with the ÷ sign or why a multiplication sign is not used. However, there seems to be a quick acceptance that this is how the software writes things even though it is quite different to what they are used to seeing in their previous years of mathematics lessons (Hewitt 2012). I have sat in many mathematics lessons where teachers attempt to justify why they are not using the multiplication sign and rarely do I feel that the learners are convinced.…”

Section: Arbitrary and Necessarymentioning

confidence: 99%

“…Learners can shift between one world and the other whilst developing their confidence in working with the mathematical notation. The software has enabled relative young learners (9-10 years old) to go from never having met the use of brackets in a mathematical context, a division line in notation instead of the division sign ÷, nor a letter in an algebraic context, to solving linear equations within just three lessons (Hewitt 2012). At the end of the third and final lesson, learners were offered a choice of one of two sheets to complete; the first had a series of equations to solve as in Fig.…”

Section: Introductionmentioning

confidence: 99%

Designing Educational Software: The Case of Grid Algebra

Hewitt

2016

Digit Exp Math Educ

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To be successful educational software needs to be carefully designed in order to provide constraints and freedoms (Greeno 1994) which relate to its educational aims, restrict or enable learners and teachers to carry out certain actions, and be based upon a clear set of beliefs related to the complex dynamic of teaching and learning. This paper seeks to show the contraints and freedoms built in to the design of Grid Algebra; software which offers an intuitive and novel approach to early algebraic learning, and how they have been informed by a clear set of beliefs and frameworks. The paper shows how the design has taken into consideration known misconceptions that many learners exhibit with early algebra work and how the three frameworks of arbitrary and necessary, subordination and embodied cognition have been fundamental to the design of both the software and some of the activities used with the software. The paper finishes off with considering limitations of the software as well as some strengths that its design offers, and poses questions to consider about the design of this and other resources.

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“…In so doing, we focus not on studies that invoked atypical contexts to facilitate students' use of those strategies. For example, Hewitt (2012) exploited specialist software to facilitate children's informal approaches to the solution of linear equations. In similar vein, Pirie and Martin's (1997) teacher used arithmagons to provide a context for generating and provoking intuitive solutions to non-arithmetical equations.…”

Section: Approaches To the Teaching Of Linear Equationsmentioning

confidence: 99%

Polish teachers’ conceptions of and approaches to the teaching of linear equations to grade six students: an exploratory case study

Marschall

Andrews

2015

Research in Mathematics Education

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In this paper we present an exploratory case study of six Polish teachers' perspectives on the teaching of linear equations to grade six students. Data, which derived from semi-structured interviews, were analysed against an extant framework and yielded a number of commonly held beliefs about what teachers aimed to achieve and how they would achieve them. In general, teachers' aims were procedural fluency founded on students understanding the equals sign as a relational rather than an operational entity and the balance scale as a representation supportive of students' understanding of an equation as the equivalence of two expressions. The analyses also indicated that the ways teachers proposed to conduct their lessons, whereby they pose single problems for individual work before inviting whole class sharing of solutions, resonates with the didactical traditions found in other East and Central European countries previously influenced by the Soviet Union.

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Young students learning formal algebraic notation and solving linear equations: are commonly experienced difficulties avoidable?

Cited by 27 publications

References 23 publications

Early algebraization: a global dialogue from multiple perspectives

Early algebraization: a global dialogue from multiple perspectives

Designing Educational Software: The Case of Grid Algebra

Polish teachers’ conceptions of and approaches to the teaching of linear equations to grade six students: an exploratory case study

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