Learning for mathematical insight: a longitudinal comparative study on modelling

This paper reports on a longitudinal study of teaching and learning the subject of fractions in two matched groups of ten 9–10-year-old students. In the experimental group fractions are introduced using the bar and the number line as (mental) models, in the control group the subject is introduced by fair sharing and the circle-model. In the experimental group students are invited to discuss, in the control group students work individually. The groups are compared on several occasions during one year. After one year, the experimental students show more proficiency in fractions than those in the control group.