A case study of the development of in-service teachers’ concept images of the derivative

This research focuses on the development of the concept images of the derivative concept of five students enrolled in the in-service programme Advanced Certificate in Education (ACE) at the University of KwaZulu-Natal, Pietermaritzburg campus. For comparison, the concept images of two qualified teachers not enrolled in the programme were included. The findings show that of the five ACE students who were interviewed, only one had a profound concept image in all the three layers of the derivative, with multiple representations as well as connections among representations within the layers. This one student also passed the calculus module with a distinction. The other four students had the ratio layer and graphical representation in their concept images, while the other layers and representations were pseudo-structural with very few connections. Two of these students passed the calculus module, while the other two failed. All the students showed progression in their concept images, which can probably be credited to the ACE calculus module. However, it is clear that even upon completion of this module, many practicing teachers have concept images of the derivative which are not encompassing all the layers and more than one or two representations.  The research suggested that  historically disadvantaged students experience  continued inequalities in learning. The research also showed the need to expand the framework of Zandieh (2000), developed to describe concept images of derivative