Exploring ‘Non-Science’ Grade 11 Learners’ Errors in Solving Quadratic Equations
AbstractThis study investigates the errors that a class of grade 11 learners show when they solve quadratic equations tasks through factorisation. The research makes use of the constructivist perspective of learning to explain learners’ errors and misconceptions. The research took place at a high school in the East Rand of Gauteng Province, South Africa. Twenty two participants of both sexes regarded as below-average in mathematics performance were presented with four quadratic equations tasks which they were asked to solve. Learners’ scripts were scrutinised for errors. Selected learners were then probed and pressed about their errors so as to manifest their thinking thereof. Analysis of data indicated that most students’ errors arose from problems with factorisation; the pathway to solution. Some of the reasons why learners had errors are that they used inappropriate schemas to mediate their solutions. In the main, learners held on to the simple equation schema which they unsuccessfully used to assimilate solutions to quadratic equations when restructuring the schema was the only viable pathway. Also, most errors were due to mis-interpretation of what the tasks required. The study recommends that this topic may be taught using procedures with connections tasks (Stein, Smith, Henningsen, & Silver, 2000) to help students understand what they are doing.
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