Thinking about – Making Sense. Reflecting in mathematics lessons – wh...

Reflecting is seen as an essential activity to be developed (also) in mathematics classrooms. There is a broad consensus in literature referring to mathematics education. Relevant regulations of educational policy such as syllabus, (national) educational standards, international tests like PISA also contain reflecting as required activity. In real mathematics lessons, on the other hand, there is little evidence of reflecting. So there seems to be a considerable problem of matching between claim and reality. This problem of fitting is a key issue in the project "Reflecting in mathematics classrooms” at the Institute of Mathematics Education at the University Klagenfurt. Interventions are developed and proposed for mathematics lessons.

In a first part, the lecture will give insight into the role and meaning attributed to reflecting by mathematics education. In addition to commonalities, various theoretical concepts also show more or less great differences - also with regard to what should be reflected on.

In a second part, conceptual definitions are presented which were made in the context of the project. On the one hand, it is a question of what should be meant by reflection in the project and, on the other hand, it is about suggestions, which types of reflection should be integrated into the teaching of mathematics. Thus, it is about the question of what should be reflected on and the question of which objects or relationships are at the center of reflections. These can be inner-mathematical relationships as well as relationships between mathematics and our world or even relationships between mathematics and us humans.

The focus of the third part of the presentation is on concrete tasks that are intended to stimulate reflections in mathematics lessons. As part of the project, a series of tasks were developed for different mathematical topics and different educational level (esp grade 5-12). The tasks also address all the types of reflections that are intended for use in the classroom. Some examples of such tasks stimulating reflections will be presented in the lecture. And it will be briefly reported on some experiences with the use of such reflections in secondary school mathematics lessons.