The effect of using Grade 9 learner errors and misconceptions when Explaining

Abstract

This qualitative error analysis research reveals the effect of using learner errors and misconceptions when explaining algebraic equations in a professional noticing intervention. The study was guided by the research questions: (1) What learner errors and misconceptions are identified by the teacher while attending to the grade 9 learners’ work on solving algebraic equations? (2) What learner reasoning and justifications are evident from the learners’ work of solving algebraic equations? (3) What possible learning advantages and disadvantages can result from providing explanations that are informed by the learners’ errors and misconceptions? (4) To what level can learning and learner achievement in solving algebraic equations be improved if explanations are informed by the learner errors and misconceptions? To answer the research questions, 40 grade 9 learners from a secondary school in Johannesburg voluntarily took part in the study by, firstly, writing a pre-test. The pre-test served as the instrument for establishing the type of errors that grade 9 learners elicit when solving algebraic equations as well as the misconceptions associated with these errors. These errors, which were categorized using Donaldson’s (1963) error classification and Hirst’s (2003) categorization framework, were used as a resource to guide the explanations offered as an intervention. Secondly, to understand the learners’ intuitive conceptions, the study used a purposive sampling of 8 learners which were interviewed based on their pre-test responses. Thirdly, the participants attended the intervention session where the mathematics teacher from the school offered explanations that were based on addressing the identified errors and misconceptions. The teacher explanations offered in the intervention lesson considered professional noticing intervention as a framework to guide the session. Lastly, the effect of offering these explanations on the performance of learners was comparatively analyzed by considering the pre-test and the post-test responses (which had questions of similar nature as the ones in the pre-test). It is evident from the findings that indeed offering explanations that are directed at the identified learner errors and misconceptions in a professional noticing context results in a substantial improvement on the learner performance. It is apparent from their responses to the post-test that there were traces of cognitive gains. As a result, this study remains a confirmation that indeed the errors and the misconceptions that learners encounter has the potential to serve as a resource to improve the learner performance in solving the grade 9 algebraic equation. In fact, such vi explanations offered in a professional noticing intervention are a general resource that can be considered by mathematical teachers throughout the mathematics discourse