In the last thirty years or so, the need to address the challenges of teaching and learning mathematics at university level has become increasingly appreciated by university mathematics teachers, and beyond, by educational institutions around the world. Indeed, mathematics is both a condition and an obstacle to success for students in many educational programmes vital to the 21st century knowledge society, for example in pure and applied mathematics, engineering, natural sciences, technology, economics, finance, management and so on. This breadth of impact of mathematics implies the urgency of developing research in university mathematics education, and of sharing results of this research widely. This book provides a bespoke opportunity for an international audience of researchers in didactics of mathematics, mathematicians and any teacher or researcher with an interest in this area to be informed about state-of-the-art developments and to heed future research agendas.
This book emerged from the activities of the research project INDRUM (acronym for International Network for Didactic Research in University Mathematics), which aims to contribute to the development of research in didactics of mathematics at all levels of tertiary education, with a particular concern for the development of early-career researchers in the field and for dialogue with university mathematicians.
The aim of the book is to provide a deep synthesis of the research field as it appears through two INDRUM conferences organised in 2016 and 2018. It is an original contribution which highlights key research perspectives, addresses seminal theoretical and methodological issues and reports substantial results concerning the teaching and learning of mathematics at university level, including the teaching and learning of specific topics in advanced mathematics across a wide range of university programmes.
Table of Contents
Viviane Durand-Gurrier, Reinhard Hochmuth, Elena Nardi and Carl Winsløw
Part I Achievements and current challenges
Chapter 1. Mathematics education research at university level: achievements and challenges
Chapter 2. Lessons for mathematics higher education from 25 years of mathematics support
Duncan Lawson, Tony Croft
Chapter 3. Current interactions between mathematicians and researchers in mathematics
Caroline Bardini, Marianna Bosch, Chris Rasmussen, María Trigueros
Part II Teaching and learning of specific topics in university mathematics
Chapter 4. Education and professional development of University Mathematics Teachers
Carl Winsløw, Rolf Biehler, Barbara Jaworski, Frode Rønning and Megan Wawro
Chapter 5. Challenging issues in the teaching and learning of Calculus and Analysis
Maria Trigueros, Stéphanie Bridoux, Ann O’Shea, Laura Branchetti
Chapter 6. Task design in calculus and analysis
Fabrice Vandebrouck, Erik Hanke, Rafael Martínez-Planell
Chapter 7. Discrete mathematics, computer science, logic, proof, and their relationships
Faïza Chellougui, Viviane Durand-Guerrier, Antoine Meyer
Chapter 8. Abstract and Linear Algebra
Thomas Hausberger, Michelle Zandieh and Yael Fleischmann
Chapter 9. Mathematics for engineers, Modelling, Mathematics in other disciplines
Alejandro S. González-Martín, Ghislaine Gueudet, Berta Barquero and Avenilde Romo-Vázquez
Part III Teachers' and students' practices at university level
Chapter 10. Transitions to, across and beyond university
Reinhard Hochmuth, Laura Broley and Elena Nardi
Chapter 11. Students’ in-class and out-of-class mathematical practices
Chris Rasmussen, Helge Fredriksen, Emma Howard, Birgit Pepin and Johanna Rämö
Chapter 12. Mathematics teaching practices at university level
Nicolas Grenier-Boley, Pedro Nicolás, Heidi Strømskag and Theresia Tabchi
Viviane Durand-Guerrier is Professor Emeritus of Didactics of Mathematics at the University of Montpellier, France.
Reinhard Hochmuth is Professor of Didactics of Mathematics at the Leibniz University Hannover, Germany.
Elena Nardi is Professor of Mathematics Education at the University of East Anglia, United Kingdom.
Carl Winsløw is Professor of Didactics of Mathematics at the University of Copenhagen, Denmark.