The three-dimensional model of competence
- Evelyn Süss-Stepancik
In Austrians maths lessons the topic Reasoning and Proof is very important from grade 5 to grade 12. For this grades we have two different competence models. One for grade 8 and one grade 12. The model at grade 8 is a three-dimensional model (see below). One of these three dimensions is equal to the Process standards and includes Reasoning and Proof. The second dimension is equal to the Content standards and contains Numbers and Measurement, Algebra and functions, Geometry and Data analysis. The third dimension describes the complexity that students have to manage.
Process - Content - Complexity
Competences are defined as ...
"cognitive abilities which are available for a longer time and the readiness to make use of them" The competence model at grade 12 is only one-dimensional and describes 73 competences combining the content and the process. In this model only two competences refer to “reasoning and proof”. So for the final exam for the general qualification for university entrance „reasoning and proof“ seems not very important, but for the math lessons at secondary school reasoning and proof plays still an important roll. bifie (Hrsg.) (2011): Praxishandbuch für „Mathematik“ 8. Schulstufe. Graz: Leykam. IDM (2007): Standards für die mathematischen Fähigkeiten österreichischer Schülerinnen und Schüler am Ende der 8. Schulstufe.