Notes about Reflection, Operative Knowledge, and Execution

If we want to capture the changes that Computer Algebra Systems (CAS) have brought into mathematics education, we need to have a global perspective regarding the process of teaching and learning mathematics. Mathematics educators have been challenged to identify and explore such global perspectives. We bring here several approaches on which we base our analysis of teachers solving problems in a CAS environment. Heid (2002) emphasized the role of automated production of representations and translations between them as a key to our thinking about the impact of CAS on mathematics learning. Peschek and Schneider (2001) introduced the didactical principle of outsourcing operative knowledge and operative skills as a didactical principle of CAS use. They regard operative knowledge as means to generate new knowledge (Peschek, 2005). An anthropological approach, based on the work of Chevallard, has bee