Fostering the competence Reasoning and Proof across the grades by GeoGebra
The Austrian educational standards for Mathematics (IDM, 2007) at grade 8 define competences such as “cognitive abilities which are available for a longer time (and the readiness to make use of them)”. Moreover, they define four content areas and four types of mathematical activities/processes. One of these activities is, as with many other mathematical standards Reasoning and Proof. To be able to reason and prove requires continuing development. Extending the spiral curriculum with its main ideas (revisiting topics, increasing complexity) to typical mathematical activities enables a step-by-step acquirement of competence (cf. Süss-Stepancik & Götz, 2015). But what is the specific part of GeoGebra in this stepwise process? First of all GeoGebra supports the disposition to engage in mathematical tasks that demand reasoning. Secondly GeoGebra fosters the ability to understand, comprehend and explain prescribed reasons. Thirdly GeoGebra can also foster the ability to explain and argue a completed mathematical proof. And in the end GeoGebra supports the finding of reasons for a (mathematical) statement/conjecture autonomously. The four steps named above will be clarified with the content of the surface area, which leads from grade 5 to grade 12.
