Summary

1.) Reasoning and proof requires continuing development.
2.) Therefore we extend the spiral curriculum to mathematical activities.
3.) With the competence based four level model (Disposition, Comprehension, Communication, Autonomy) for arguing the complexity of tasks that demand reasoning and proof can be identified.
4.) GeoGebra-Applets support the continuing development of arguing, because they can visualize the arguments of a proof and refer to one or more different levels of the previous four level model.