A long-term project (2005-2012) was started to test the use of symbolic calculators (SCs) in Bavarian grammar schools (Germany) in Grade 10, 11 and 12. The results showed the necessity of having better diagnostics of the students' ability to understand the mathematics and their ability to work with the SC. How does a student understand particular content? Why were they unable to master a particular problem? Did she/he not understand the content sufficiently or has she/he "only" been unable to use the SC in an adequate way? Empirical investigations led to the development of a model of competence, which reveals information about the relation between understanding, tool competencies and different levels of cognitive activation.