An Exploration of Grade 12 Learners’ Misconceptions on Solving Calculus Problem: A Case of Limits

Abstract

This case study explored Grade 12 learners’ misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was adopted, and purposive sampling employed to select 35 Grade 12 learners (21 females and 14 males) who wrote a test on limits. From the 35 learners who wrote the test, five learners were interviewed guided by their written responses. Theoretically, the study was guided by the constructivism theory and used a systematic error conceptual framework to categories the learners` misconceptions according to extrinsic and intrinsic calculus misconceptions. The study sought to answer the questions: (a) What type of misconceptions do Grade 12 learners exhibit in responding to limit questions? (b) What are the possible sources of these misconceptions? The study found that Learners exhibited misconceptions on the limit concept and related symbolism. Learners who had a flawed understanding of algebraic concepts struggled to apply limits correctly. The weak foundation on algebraic skills impacted negatively on their learning of new concepts on limits. The study recommends that, educators should always check and make sure that learners have appropriate prior knowledge before the teaching of new concepts in calculus. It is recommended that that teaching and learning approaches need to be adjusted to give equal weight to both the procedural and the conceptual understanding of mathematical knowledge in learners.