Séance Séminaire

From University Mathematics to Mathematics Education

Approaches in pre-service teacher education to counter Klein's double discontinuty - Thomas Bauer (University of Marburg) & Eva Müller-Hill (University of Rostock)

Abstract: Felix Klein's observation of double discontinuity poses several challenges at several stages of pre-service teacher education: 1) At the transition from school to university, how can students be provided with the experience that school mathematics and university mathematics are interrelated and useful for each other? 2) In mathematics content courses, how can students experience mathematics in such a way that they are both willing and able to make good use of academic knowledge later in their job? 3) And finally, how can students learn to make full use of their knowledge (math content and math education) when planning classroom implementations? In the talk we present approaches to these challenges from our teaching practice: With respect to the first discontinuity, we show how the concept of "interface tasks" in real analysis can help to strengthen the relationship between school and university mathematics. We present design principles and empirical results from the use of these tasks. Concerning the second discontinuity, we present math education course designs that relate proof and argumentation as core mathematical activities to implementations in the classroom. We use an activity theoretic framework to uncover and explain phenomena observed in students' classroom implementations.