This study focuses on the transition from additive to multiplicative (proportional) reasoning. In particular, it investigates simultaneously two phenomena that have been studied isolated during the last years: the development from primary to secondary school of the use of additive methods in proportional situations and the use of proportional methods in additive situations. Our findings indicate that while the over-use of additive methods in proportional situations increased during primary school and decreased during secondary school, the over-use of proportional methods in additive situations increased along primary and secondary school. The presence or absence of integer ratios strongly affects this behaviour but the nature of quantities only has a small influence in the use of proportional methods.
