Learners’ Graphical Efficacy When Solving Trigonometric Problems

Abstract

This study explored grade 12 learners’ graphical efficacy when solving problems involving trigonometric graphs. A structured test consisting of five trigonometric problems, with variations in context and structure, was administered to a purposefully selected group of 25 Grade 12 learners from the Sekhukhune District in South Africa. Insights into learners' graphing efficacy were obtained through task-based interviews. Data were analysed using direct interpretation which involved deductive thematic analysis of the task-based interviews and content analysis of the test scripts to match learners’ responses to the themes drawn from the Meta-Representational Competence (MRC) framework. The results showed that most learners lack invention and functioning, critiquing and reflection efficacies and hence this affected their drawing and interpretation of the graphs and consequently lead to incorrect solutions. Furthermore, the results show most learners have critiquing efficacy. This indicates that learners lack graphical efficacy for solving trigonometric problems involving trigonometric functions. This finding has pedagogic implications: the apparent lack of graphical efficacy in graphical solutions may suggest inadequate mastery of the concept. Therefore, this study recommends that the teaching and learning of trigonometric graphs should consider the development of invention, functioning, critiquing and reflection efficacies.