Unpacking pre-service teachers’ conceptualization of logarithmic differentiation through the APOS theory

Logarithmic differentiation is an effective method that aids the process of finding the derivatives of complex exponential functions. However, there has been a scarcity of studies, particularly in the South African context, that have provided evidence on pre-service mathematics teachers’ understanding of the concept of logarithmic differentiation. This study explored pre-service teachers’ conceptualization of logarithmic differentiation through action-process-object-schema (APOS) theory. We employed a qualitative case study design involving 90 first-year pre-service teachers enrolled in a mathematics teacher education program at a university in South Africa’s Eastern Cape Province. Overall, the analysis showed that 63.9% of the participants demonstrated a substantial understanding of logarithmic differentiation processes, including 46.1% who had reached the schema stage. Nonetheless, common misconceptions and errors persisted, particularly among those who operated at action and beginning process stages. Errors and misconceptions such as the misapplication of differentiation rules, calculation errors in combining derivatives, and conceptual misunderstanding were evident. These findings highlight the need for mathematics teacher preparation programs to emphasize both conceptual and procedural understanding of differentiation. Achieving this goal may involve targeted instruction on relevant foundational concepts, continuous professional development, and integration of active learning strategies, such as the activities, classroom discussions, and exercises (ACE) teaching cycles to address common misconceptions.