[table] [tr] [td]1.) [/td] [td]Reasoning and proof requires continuing development.[/td][/tr] [tr] [td]2.) [/td] [td]Therefore we extend the spiral curriculum to mathematical activities.[/td][/tr] [tr] [td]3.) [/td] [td]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.[/td][/tr] [tr] [td]4.) [/td] [td]GeoGebra-Applets [br]support the continuing development of arguing, because they can visualize the arguments of a proof and [br]refer to one or more different levels of the previous four level model.[/td][/tr][/table]