Learners’ performance in arithmetic equivalences and linear equations
Date
2017
Authors
Sanders, Yvonne
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Abstract
This study investigates learners’ performance in solving arithmetic equivalences and arithmetic and algebraic equations and was influenced by the notion of the didactic cut (Filloy & Rojano, 1989). Data was collected from two township schools in Johannesburg using a written test. With a Vygotskian perspective on learning, learners’ performance was investigated in two ways: through a response pattern analysis of 106 test scripts as well as through an error analysis on 46 scripts. The response pattern analysis identified seven clusters of responses, each of which suggested a different performance pattern. Two clusters of responses suggest evidence of the didactic cut and that learners struggled with the concept of negativity. A purposive sample of 46 test scripts was analysed further to investigate the actual errors that learners made. Common errors within the two most relevant response pattern analyses were also investigated. Using a combination of typological and inductive methods to categorise learners’ errors, equality and negativity errors were most prominent. Findings revealed that there were very few learners who used arithmetic strategies to solve arithmetic equations and that instead, they used algebraic procedures. The most unexpected finding was that learners appear to memorise the structure of solutions and hence manipulate their procedures in order to obtain familiar structured solutions.
Key words: Equality, equal sign, solving linear equations, negativity, learner error, response patterns
Description
A research project submitted to the Faculty of Science, School of Education, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science by combination of coursework and research, 2017
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Citation
Sanders, Yvonne (2017) Learners’ performance in arithmetic equivalences and linear equations, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23587>