Understanding the Generality of Mathematical Statements

In this open access book Milena Damrau investigates the understanding of generality of mathematical statements in first-year university students and its relation to other proof-related activities. Through an experimental study, she particularly analyses the effect of different types of arguments (empirical, generic, and ordinary proofs) and statements (familiar and unfamiliar, as well as true and false ones) on several proof-related activities. The results reveal students' struggles with the concept of generality, how their understanding of generality is related to proof reading and construction and how different types of arguments and statements impact students’ performance in other proof-related activities. The findings offer valuable insights for improving mathematics courses at the transition from school to university and highlight the need for more experimental studies in mathematics education. The Author Milena Damrau completed her Master’s degree in mathematics at the University of Vienna in 2016 and received her PhD in mathematics education from Bielefeld University in 2023. Her main research interests are proof and argumentation, the transition from school to university, e-learning in higher education, as well as mathematics and arts.