ABSTRACT
This chapter argues that key to becoming more disposed towards growing the habit of mind proposed here is deep engagement with mathematical ideas and concepts. Mathematics classrooms and teacher education programs thus need to be inspiring and innovative, both in growing mathematical content and problem-solving processes. Productive disposition is one of the strands of mathematical proficiency proposed by the Mathematics Learning Study Committee in 'adding it up'. The chapter explores case studies of South African educators purposively invited to respond based on our identification of them as being great mathematics teachers. Each has taught mathematics to school children for several years and, at the time of writing, is involved in mathematics development in various ways. Models of teacher knowledge comprise the domains of content knowledge; general pedagogical knowledge; context knowledge and pedagogical content knowledge.
