Proefschrift 1. Introduction2. Theoretical background3. Learning for mathematical insight: a longitudinal comparative study on modelling4. Audrey's acquisition of fractions: a case study into the learning of formal mathematics5. The fraction learning process in low-achieving students:Shirley's choice and use of strategies in primary mathematics6. Effects of an experimental fraction programme in primary mathematics: a longitudinal analysis7. Theoretical reflection8. Conclusion and discussion