It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number…

Two studies involving 110 and 91 children aged 5 to 7 years show that children's knowledge of counting and addition facilitated their acquisition of a concept not taught in school, that every number has a natural successor (Successor Principle). Even the oldest children could not rank order correctly numbers that contained fractional notations.…

Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…

The research on conceptual change has so far mainly dealt with cognitive outcomes, but especially during the last few years there has been a growing interest in and discussion about the processes of conceptual change. The purpose of the article is to contribute to this discussion and to present a theoretical model of the dynamics among the…