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## South African Journal of Education

*On-line version* ISSN 2076-3433

#### Abstract

KAZIMA, Mercy; PILLAY, Vasen and ADLER, Jill. **Mathematics for teaching**: **observations from two case studies**.* S. Afr. j. educ.* [online]. 2008, vol.28, n.2, pp. 283-299. ISSN 2076-3433.

We report on two case studies in which we investigated mathematics for teaching. We were interested in the mathematical knowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on the teaching of probability in Grade 8 and the teaching 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 teaching of functions and the demands on the teaching of probability in these two cases. We argue that mathematics for teaching needs to be understood as shaped by the particular topic being taught, as well as by how teachers select to introduce and approach the ideas and concepts they are teaching. We conclude with a discussion of questions raised for mathematics teacher education, together with implications for practice.

**Keywords
:
**mathematical knowledge; mathematics for teaching; mathematical work; problem solving; teacher education.