An analysis of Grade 11 learners’ levels of understanding of functions in terms of APOS theory

Abstract

This article reports on a study of six Grade 11 learners’ levels of understanding of concepts related to the function definition and representation. Task-based clinical interviews were used to elicit the learners’ interpretations and reasoning when working with these function-related concepts. Indicators for Action–Process–Object–Schema (APOS) theory conception levels were formulated and used to categorise learners’ written and interview responses into conception levels of understanding of the function concept. According to the South African Curriculum Assessment Policy Statement (CAPS) curriculum, Grade 11 learners are expected to be operating at the object and schema levels after instruction. however, the results indicated that learners were operating at the action and process levels as their understanding was characterised by vague definitions of function-related concepts and memorisation of procedures for translating between symbolic and graphical representations.