“Is Mathematical Knowledge Certain? – Are You Sure?” Epistemological Beliefs of Pre-Service Teachers

Benjamin Rott (2020): “Is Mathematical Knowledge Certain? – Are You Sure?” Epistemological Beliefs of Pre-Service Teachers. Habilitationsschrift, Pädagogische Hochschule Freiburg.
Betreut durch Timo Leuders.
Begutachtet durch Timo Leuders, Lars Holzäpfel und Kim Beswick

Zusammenfassung

The research in this book deals with epistemological beliefs, i.e. beliefs on the nature of knowledge, its limits, sources, and justification. More precisely, studies dealing with epistemological beliefs in the domain of mathematics are presented. Being unsure about the validity of traditional instruments to measure be-liefs, a preliminary study was conducted. In this qualitative study, pre- and in-service mathematics teachers as well as mathematicians and mathematics educa-tors were interviewed. These interviews showed that – at least for the domain of mathematics – sophistication of beliefs is not correlated to the belief position (e.g., mathematical knowledge is certain vs. uncertain) a person represents. In a set of quantitative and qualitative preliminary studies, a test for mathe-matical critical thinking (CT) – as a component of students’ competencies – was developed. This test consists of several tasks that are supposedly easy to solve but whose results need to be checked, this way measuring a disposition to reflect upon results.