(Re-)Konstruktion von Erfahrungsbereichen bei Übergängen von empirisch-gegenständlichen zu formal-abstrakten Auffassungen

Research in mathematics education on students’ transition from school to university
is as multifaceted as the transition itself. Most common research focuses on
two aspects. The first aspect is about an assumed lack of students’ knowledge
and competencies when they start at university. The second aspect deals with the
differences between school and university mathematics regarding their nature,
culture and way of doing mathematics.
My research can be associated best with the second research area. I reconstructed
student’s difficulties and his reflections upon them as well as the benefits of his
experiences regarding his transition, from the perspective of a change of belief
systems (Auffassungen). The student shared the information during an intervention
seminar addressing the transition. The perspective of reconstruction is based
on the distinction between empirical-concrete and formal-abstract belief systems
which were theoretically connected to the concept of subjective domains of experience
(Bauersfeld, 1983). The adequacy of this distinction is shown in two historical
case studies on von Mises’ (1931) “Wahrscheinlichkeitsrechnung und ihre
Anwendung in der Statistik und theoretischen Physik” and Kolmogorov’s (1933)
“Grundbegriffe der Wahrscheinlichkeitsrechnung” as well as a qualitative content
analysis of school and higher educational textbooks.
The conducted intensive case study research on one student showed, that the belief
changes students experience during their transition are crucial for a successful
transition from school to university. Their reflections upon belief changes
within the development of mathematics can be supportive.