The role of mathematical tasks in providing grade 10 Learners an opportunity to learn trigonometry

Abstract

Poor mathematics performance in South African schools is a major concern (Reddy et al., 2014) and learners’ opportunity to learn is one of the concepts that needs to be explored in schools (Dowd, Friedlander & Guajardo, 2014). Several authors (Gür, 2009; Ebert, 2017; Rohimah & Prabawanto, 2019) state that learners believe that trigonometry is difficult and abstract compared with the other topics of mathematics. Opportunity to learn (OTL) is defined as the degree to which learners during instruction get exposed to the content of the mathematics intended curriculum (Reeves & Muller, 2005). The term “mathematical tasks” refers to classwork problems, homework problems, projects, investigations and assignments. These tasks play a vital role in effective teaching and learning. Learners’ OTL was explored according to the types and nature of tasks selected by the teacher, and the pedagogical approach and strategies used by teachers and the influence of these two aspects on the time spent on tasks and learner engagement. This study therefore aimed to answer the research question about the extent to which mathematics tasks provided Grade 10 learners an opportunity to learn trigonometry. A two-part conceptual framework was used: the first part focused on the task selection in terms of its nature and cognitive demand and the second part focused on the teacher-specific factors such as teachers’ approaches and strategies. The influence of these two parts on the implementation of the tasks by the learners in terms of time-on-task and learner engagement was then described. A qualitative approach was followed, and a descriptive case study was conducted with two Grade 10 mathematics teachers from two formerly disadvantaged public schools in Gauteng Province. A qualitative research approach was used in which document analysis and classroom observations served as data collection techniques. A deductive analysis approach was implemented. The study revealed that teachers mainly gave learners recall-type and routine procedure questions involving pure mathematics, which according to CAPS’ cognitive demands, are classified as lower order thinking tasks. There was a lack of higher order mathematics tasks that could have provided the learners with and OTL trigonometry effectively. The study further revealed that both teachers’ approaches were dominated by a teacher-centred approach where the focus was on the teachers and where teachers mainly used direct teaching as teaching strategy where learners were directed to learn through memorisation and recitation techniques. Although, due to the small sample, the study’s results cannot be generalised, I believe that the findings will contribute to pre- and in-service teacher training, where teachers come to realise the importance of appropriate mathematics tasks to contribute to learners’ OTL. Moreover, the study’s findings highlight the need to engage the four cognitive levels, namely knowledge (20%), routine procedures (35%), complex procedures (30%), and problem solving (15%) in the types of tasks. The value of teachers’ choices regarding the teaching approaches and strategies used should never be under-estimated. Future research could possibly build on this study by examining the implementation of tasks to enhance learners’ in-depth understanding of trigonometry.