Research and Development in University Mathematics Education Overview Produced by the International Network for Didactic Research in University Mathematics

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 impactof 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.

IntroductionViviane Durand-Gurrier, Reinhard Hochmuth, Elena Nardi and Carl WinsløwPart I Achievements and current challengesChapter 1. Mathematics education research at university level: achievements and challengesMichèle ArtigueChapter 2. Lessons for mathematics higher education from 25 years of mathematics supportDuncan Lawson, Tony CroftChapter 3. Current interactions between mathematicians and researchers in mathematicsCaroline Bardini, Marianna Bosch, Chris Rasmussen, María TriguerosPart II Teaching and learning of specific topics in university mathematicsChapter 4. Education and professional development of University Mathematics TeachersCarl Winsløw, Rolf Biehler, Barbara Jaworski, Frode Rønning and Megan WawroChapter 5. Challenging issues in the teaching and learning of Calculus and AnalysisMaria Trigueros, Stéphanie Bridoux, Ann O’Shea, Laura BranchettiChapter 6. Task design in calculus and analysisFabrice Vandebrouck, Erik Hanke,Rafael Martínez-Planell Chapter 7. Discrete mathematics, computer science, logic, proof, and their relationshipsFaïza Chellougui, Viviane Durand-Guerrier, Antoine MeyerChapter 8. Abstract and Linear AlgebraThomas Hausberger, Michelle Zandieh and Yael FleischmannChapter 9. Mathematics for engineers, Modelling, Mathematics in other disciplinesAlejandro S. González-Martín, Ghislaine Gueudet, Berta Barquero and Avenilde Romo-Vázquez Part III Teachers' and students' practices at university levelChapter 10. Transitions to, across and beyond universityReinhard Hochmuth, Laura Broley and Elena NardiChapter 11. Students’ in-class and out-of-class mathematical practicesChris Rasmussen, Helge Fredriksen, Emma Howard, Birgit Pepin and Johanna RämöChapter 12. Mathematics teaching practices at university levelNicolas 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.