Understanding Convergence of Sequences

An Investigation of the Interplay between Concept Image und Concept Definition in Preservice Teachers‘ Work on Tasks
Erscheinungsjahr 2027
ISBN: 978-3-658-53611-4
Verlag: Springer

Buch, Englisch, 549 Seiten, Format (B × H): 148 mm x 210 mm

Using the concept of convergence of sequences, this book investigates the extent to which students refer on their concept image when solving tasks and how they connect their concept image with the formal concept definition and mathematical theorems. To describe such connections in content-specific terms, a qualitative study was conducted in which 26 university calculus students solved four exercises on convergence of sequences. The study identified several task-solving practices that indicate connections between students' concept image on the one hand and the formal concept definition and mathematical theorems on the other. The findings were incorporated into a practitioner-oriented summary for university teachers, which provides practical suggestions for teaching calculus courses and tasks on convergence of sequences. These tasks are designed to address common errors and, in particular, to support students in establishing connections between their concept image and formal definitions and mathematical theorems.

Zielgruppe

Research

Autoren/Hrsg.

Utsch, Nina

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Sozialwissenschaften Pädagogik Schulen, Schulleitung Universitäten, Hochschulen
• Sozialwissenschaften Pädagogik Lehrerausbildung, Unterricht & Didaktik Allgemeine Didaktik

Inhaltsverzeichnis

Analysis of the Tasks Used.- Analysis of the Task-Solving Processes Using Process Matrices.- Content-Based Description of the Practices.- Learners' Conceptions and Subject-Specific Characteristics Regarding Sequence Convergence.- Implications for Teaching.-Conclusion: Answering the Research Questions, Limitations, and Future Research.

Über Autor(innen)

Nina Utsch earned her doctorate in Mathematics Education at the Institute of Mathematics Education, Justus Liebig University Giessen. Her doctoral research was funded by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). Working with mathematically gifted children was another focus of her work.