The aim of this workshop was to show the (new) importance of task-based learning in school in acquiring general and specific knowledge of our world. By focusing on this, we have had to face a significant shift in task-based philosophies of teaching mathematics. Traditional operation-based teaching has been increasingly replaced by other approaches, especially methods stressing (new) prototypical aspects. Thus activities such as transferring, interpreting, and reasoning have gained a much higher importance in mathematics classes.

Hence, one of the underlying ideas of the workshop was to focus participants’ attention on these important parameters in ongoing national education reforms in the Austrian school system.

To elaborate this observation we presented a qualitative study that had focused on the development of teaching styles in Austrian secondary schools over the last 40 years: The shift to prototypical teaching approaches was fostered in at least two ways. In particular, young teachers and teachers with a thorough education in subject-specific didactics introduce a new understanding in learning mathematics that transcends the traditional analytical and algorithmic approach (transfer, interpretation, reasoning, etc.). Furthermore, new technologies have offered completely new possibilities in dealing with underlying principles of tasks. From the didactical point of view, the role of the genetic approach in its diversity, the concept of fundamental or universal ideas, and the multi-media approach change fundamentally. In brief, we referred to Geogebra as an example (interactivity, computer algebra, process orientation, and dynamical modelling possibilities).

All of these observations were discussed as significant tendencies and educational goals in an ongoing process in the context of a major educational reform in Austria’s school system. In the final part of the presentation, we questioned whether the tasks designed for attaining these goals by the Federal Institute for Educational Research, Innovation, and Development of the Austrian School System (BIFIE) satisfy the aims mentioned. The detailed discussion of two tasks from final exams showed that the pattern change that is needed in the design of individual tasks has not yet been realized. Most exam tasks rather follow the traditional task approaches mentioned above.