Stimulating Pre-Service Teachers' Content and Pedagogical Content Knowledge on Rational Numbers

The transition from natural to rational numbers is difficult for most elementary school children. A major cause for these difficulties is assumed to be the "conceptual change" they need to undergo in order to see that several natural number properties do not apply to rational numbers. To appropriately handle pupils' difficulties, teachers need well-developed content knowledge (CK) and pedagogical content knowledge (PCK). In the present study, a lesson series to promote pre-service teachers' (PSTs) rational number CK and PCK was developed according to design principles to foster conceptual change. This lesson series was evaluated based on a comparison of the CK and PCK growth of PSTs in the intervention group (n = 138) with the knowledge growth of PSTs in an alternative teacher training course (control group; n = 135). Intervention group PSTs significantly outperformed control group PSTs on CK and PCK, indicating that the intervention was effective in stimulating PSTs' knowledge on rational numbers. Methodological, theoretical as well as practical implications of the present study are discussed.