Mathematics for teaching: Observations from two case studies

We r eport on two c ase s tudies in whi ch we investigated m athematics for tea- ching. We were interested in the mathematical k nowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on t he t eaching of pr obability in Gr ade 8 a nd t he t eaching of functions in Grade 10. We discuss the mathematics for teaching probability and functions in terms of the mathematical 'problem solving' or 'mathematical work' demanded of the teachers as they taught the two topics. Among the findings are the interesting differences between the demands on the t eaching of f unctions and the demands on the teaching of probability in these two cases. We argue that mathematics f or t eaching needs t o be understood as shaped by the par- ticular topic being taught, as well as by how teachers select to introduce and approach the i deas and concepts t hey are t eaching. We conclude wi th a di s- cussion of questions raised for mathematics teacher education, together with implications for practice.