Learners' strategies for solving linear equations

[摘要] ENGLISH ABSTRACT:Algebra deals amongst others with the relationship between variables. It differs fromArithmetic amongst others as there is not always a numerical solution to the problem.An algebraic expression can even be the solution to the problem in Algebra. Thevariables found in Algebra are often represented by letters such as X, y, etc.Equations are an integral part of Algebra. To solve an equation, the value of anunknown must be determined so that the left hand side of the equation is equal to theright hand side.There are various ways in which the solving of equations can be taught.The purpose of this study is to determine the existence of a cognitive gap asdescribed by Herseovies & Linchevski (1994) in relation to solving linear equations.When solving linear equations, an arithmetical approach is not always effective.A new way of structural thinking is needed when solving linear equations intheir different forms.In this study, learners' intuitive, informal ways of solving linear equations wereexamined prior to any formal instruction and before the introduction of algebraicsymbols and notation. This information could help educators to identify thedifficulties learners have when moving from solving arithmetical equations toalgebraic equations. The learners' errors could help educators plan effective ways ofteaching strategies when solving linear equations.The research strategy for this study was both quantitative and qualitative. Forty-twoGrade 8 learners were chosen to individually do assignments involving different typesof linear equations. Their responses were recorded, coded and summarised.Thereafter the learners' responses were interpreted, evaluated and analysed.Then a representative sample of fourteen learners was chosen randomly from thesame class and semi-structured interviews were conducted with them From theseinterviews the learners' ways of thinking when solving linear equations, were probed.This study concludes that a cognitive gap does exist in the context of theinvestigation. Moving from arithmetical thinking to algebraicthinking requires a paradigm shift. To make adequate provision for this changein thinking, careful curriculum planning is required.

[发布机构] Stellenbosch University