Abstract
In the fi rst part of this chapter we discuss what mathematical ability is, what abilities can be developed in mathematics, in what pupils and under which circumstances. We characterize pupils into seven groups according to their approach towards mathematics.
This approach plays a key role in the development of various mathematical abilities. A pupil's relationship to mathematics is largely infl uenced by the teacher.
We list some qualities of teachers that can be reinforced or changed in order to support effi cient development of some pupil's math-ematical abilities. Some mathematical abilities are described and illustrated.
Finally, several tasks are offered to show the way from arithmetical experience from the lowest grades to algebra in higher grades.