Subject content knowledge is an essential prerequisite for competent teaching in mathematics. However, in South Africa, many prospective teachers enter initial teacher education with substantial gaps in their mathematical knowledge. It is therefore important for teacher educators to identify and address these gaps as early as possible. This paper describes the first round of an intervention at a South African university, which aimed to improve preservice primary school teachers’ understanding of multiplicative relations (the knowledge of multiplication and division). The intervention used a design research approach, with the intention of refining the intervention strategy over the coming years, and ultimately formulating design principles to guide the effective teaching of multiplicative relations in initial primary teacher education programmes.

The study involved 143 students in their first year of primary school teacher training, and one teacher educator. The students wrote a pre-test which informed the contents of a two-week intervention module on multiplicative reasoning. After the intervention was complete, the students wrote a post-test and a delayed post-test. The tests showed a significant improvement between pre-test and post-test, with a large effect size (Cohen’s d = 1.01). No decline was evident: the improvements were still apparent in the delayed post-test six months later.

The paper ends with reflections on the first year of the intervention, and makes suggestions for improvement in subsequent iterations. It is suggested that the test instrument and teaching intervention could be refined, and that test scores could be supplemented with qualitative data such as student interviews and classroom observations to provide deeper insight into student thinking. Despite this room for improvement, however, it seems clear that targeted interventions like this one have the potential to substantially improve preservice teachers’ mathematical content knowledge. The improvement of multiplicative reasoning is important not only for the local space in South Africa but internationally as well because multiplicative reasoning is a difficult concept internationally as well.

Keywords: Teacher education, pre-service teachers, mathematics content knowledge, multiplicative reasoning.