How Do Mathematics Teachers Utilize Their Specialized Content Knowledge In Teaching The Concept of Derivative?

Abstract

The Specialised Content Knowledge (SCK) is an important sub-domain under Mathematical Knowledge for Teaching (MKT) framework that describes the mathematical content knowledge that is unique to the profession of teaching and not necessarily required by other professions in which mathematics is used. Research on SCK in the context of secondary education is still underdeveloped while SCK of in service teachers have also received limited attention. The current study investigates the SCK of Sri Lankan in-service secondary mathematics teachers in teaching an important Calculus concept in G.C.E. (Advanced Level) combined mathematics curriculum: the concept of Derivative. Lessons of ten mathematics teachers from seven schools were observed. The data comprises of field notes and video recordings of lessons and these video recordings were transcribed verbatim for analysis. Transcripts of lessons were analysed through the lens of Ball’s MKT framework while placing more emphasis on SCK sub-domain. Analysis of data identified four different components that describe SCK in teaching the concept of derivative, namely: SCK-PK (Building new knowledge on prior knowledge), SCK-MR (Multiple Representations), SCK MJ (Mathematical Justifications), and SCK-ML (Mathematical Language). Teachers exhibited each SCK component in varying degrees of proficiency. Majority of teachers elicited their content knowledge under SCK-MR and SCK-ML components while gaps were noticed in SCK-MJ and SCK-PK components. This study sheds light on the current status of G.C.E. (Advanced Level) combined mathematics teachers with respect to SCK and provides insights for planning teacher education programs and workshops.