Grade 10 Teachers' Example Selection, Sequencing and Variation during Functions Lessons

Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what opportunities for learning are created in mathematics classrooms. This qualitative multiple case study, using Sfard's commognitive theory, draws attention to mathematics teachers' classroom practices during functions lessons which is unexamined in the South African context. In this article, data sets include unstructured non-participant classroom observations on functions, which were videorecorded. Sfard's commognitive theory served as an appropriate lens in interpreting and analysing teachers' discourses and giving meaning to teachers' classroom practices during functions lessons. The findings demonstrate that the example selection and sequences teachers used during functions lessons either constrained or enabled the development of endorsed narratives about the effect of parameters on the different families of functions.