Understanding the Generality of Mathematical Statements : An Experimental Study at the Transition from School to University

Hochschulschrift

Zusammenfassung: 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

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• ISBN: 9783658437633
• Extent: Online-Ressource, XXIV, 207 p. 50 illus., 25 illus. in color. Textbook for German language market.
• Edition: 1st ed. 2023
• Language: Englisch
• Notes: online resource.

References and Relationships

• Bibliographic citation: Bielefelder Schriften zur Didaktik der Mathematik ; 15

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Wiesbaden
• (who): Springer Fachmedien Wiesbaden, Imprint: Springer Spektrum
• (when): 2023
• Creator: Damrau, Milena
• Contributor: SpringerLink (Online service)

Further information

• DOI: 10.1007/978-3-658-43763-3
• URN: urn:nbn:de:101:1-2024020303135527288428
• Table of contents: Introduction -- Theoretical Background of Mathematical Statements and Proof -- State of Research -- Derivation of Research Questions -- Methodology -- Results -- Discussion -- Conclusions
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:30 AM CEST