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

• Ngôn ngữ: eng
• ISBN-13: 978-3658437626
• ISBN-13: 978-3658437633
• Thông tin xuất bản: Wiesbaden Springer Nature, 2023
• Mô tả vật lý: 1 online resource (207 p.)
• Bộ sưu tập: Tài liệu truy cập mở
• ID: 460485
• Chủ đề: 1. Experimental study; 2. Generality; 3. Proof reading and construction; 4. thema EDItEUR::P Mathematics and Science::PB Mathematics; 5. Transition from school to university; 6. Mathematics

Tóm tắt

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.