Title: Grade 12 learners' understanding of differentiation: tracking first principle and power rule using the ACE teaching cycle

Authors: Wisani Hlangwani; Zwelithini Bongani Dhlamini

Addresses: Department of Mathematics Science and Technology Education, School of Education, University of Limpopo, Polokwane, South Africa ' Department of Mathematics Science and Technology Education, School of Education, University of Limpopo, Polokwane, South Africa

Abstract: This qualitative exploratory case study delves into learners' understanding of differentiation through the first principle and power rule. The study adopted the action, process, object, and schema (APOS) theory as a lens to track learners' understanding of these concepts using the activities, classroom discussion, and exercise (ACE) teaching cycle. The findings of the study highlight learners' algebraic conceptual obstacles in comprehending the first principle and power rule. Moreover, the study demonstrates the effectiveness of the ACE teaching cycle as a valuable tool for unveiling learners' conceptual obstacles. Overall, this research contributes to the advancement of knowledge and practice in mathematics learning by identifying critical issues, emphasising the significance of algebraic skills in differentiation, and showcasing the value of the ACE teaching cycle in supporting learners' understanding. As a result, the study suggests the need for further research to enhance learners' algebraic skills, which are essential for successful differentiation.

Keywords: activity classroom discussion exercises; action process object schema; differentiation; learner understanding; levelled; recursive.

DOI: 10.1504/IJLC.2024.141954

International Journal of Learning and Change, 2024 Vol.16 No.6, pp.678 - 694

Accepted: 22 Jan 2024
Published online: 03 Oct 2024 *

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