Practice-Oriented Research in Tertiary Mathematics Education

Rolf Biehler has been, since 2009, a full professor for didactics of mathematics at Paderborn University. Before, he was a professor for didactics of mathematics at the University of Kassel (since 1999). His research domains include: tertiary mathematics education, professional development of teachers of mathematics, didactics of probability, statistics, and data science.Michael Liebendörfer is Juniorprofessor of higher mathematics education at the University of Paderborn, Germany. His research focus is on students’ motivation and learning strategies as well as the evaluation of innovative teaching in higher mathematics.Ghislaine Gueudet has been, since 2009, a full professor in mathematics didactics at the University of Brest (France) and a member of the CREAD (Center for Research on Education, Learning and Didactics). Her research concerns university mathematics education, and the interactions between teachers, students and resourcesfor the learning and teaching of mathematics from preschool to university and in teacher education.Chris Rasmussen is Professor of mathematics education in the department of mathematics and statistics at San Diego State University. His research investigates inquiry-oriented approaches to the learning and teaching of undergraduate mathematics and the process of departmental and institutional change.Carl Winsløw holds, since 2003, the position as full professor in Didactics of Mathematics at the University of Copenhagen. WIth a background in pure mathematics, his research is currently mainly on university mathematics education, especially the teaching of analysis, and mathemathematics teacher knowledge.

• Part 1: Research on the secondary-tertiary transition.- Chapter 1. Self-regulated learning of first-year mathematics students.- Chapter 2. The societal dimension in teacher students beliefs on mathematics teaching and learning.- Chapter 3. The Organization of Inter-level Communities to Address the Transition Between Secondary and Post-secondary in Mathematics.- Chapter 4. Framing mathematics support measures: goals, characteristics and frame conditions.- Part 2: Research on university students' mathematical practices.- Chapter 5. “It is easy to see”- tacit expectations in multivariable calculus.- Chapter 6. University Students’ Development of (Non-) Mathematical Practices: A Theory and its Implementation in a Study of one Introductory Real Analysis Course.- Chapter 7. A theoretical account of the mathematical practices students need in order to learn from lecture.- Chapter 8. The choice of arguments: considering acceptance and epistemic value in the context of local order.- Chapter 9.Supporting students in developing adequate definitions at university: The case of the convergence of sequences.- Chapter 10. Proving and defining in mathematics - Two intertwined mathematical practices.- Part 3: Research on teaching and curriculum design.- Chapter 11. Developing mathematics teaching in university tutorials: an activity perspective.- Chapter 12. Conceptualizations of the role of resources for supporting teaching by university instructors.- Chapter 13. The rhetoric of the flow of proof – Dissociation, presence and a shared basis of agreement.- Chapter 14. Teaching Mathematics Education to Mathematics and Education.- Chapter 15. Inquiry-Oriented Linear Algebra: Connecting Design-Based Research and Instructional Change Theory in Curriculum Design.- Chapter 16. Profession-specific curriculum design research in mathematics teacher education: The case of abstract algebra.- Chapter 17. Leveraging Collaboration, Coordination, and Curriculum Design to Transform Calculus Teachingand Learning.- Part 4: Research on university students’ mathematical inquiry.- Chapter 18. Real or fake inquiries? Study and research paths in statistics and engineering education.- Chapter 19. Fostering inquiry and creatity in abstract algebra: the theory of banquets and its reflexive stance on the structuralist methodology.- Chapter 20. Following in Cauchy’s footsteps: student inquiry in real analysis.- Chapter 21. Examining the role of generic skills in inquiry-based mathematics education: the case of extreme apprenticeship.- Chapter 22. On the levels and types of students’ inquiry: the case of calculus.- Chapter 23. Students prove at the board in whole-class setting.- Chapter 24. Preservice secondary school teachers revisiting real numbers: a striking instance of Klein’s second discontinuity.- Part 5: Research on mathematics for non-specialists.- Chapter 25. Mathematics in the training of engineers: Contributions of the Anthropological Theory of the Didactic.- Chapter 26. For an institutional epistemology.- Chapter 27. Modeling and multiple representations: Bringing together math and engineering.- Chapter 28. The interface between mathematics and engineering in basic engineering courses.- Chapter 29. Modifying tasks in mathematics service courses for engineers based on subject-specific analyses of engineering mathematical practices. Chapter 30. Learning mathematics through working with engineering projects.- Chapter 31. Challenges for research about mathematics for non-specialists.- Chapter 32. Establishing a National Research Agenda in University Mathematics Education to Inform and Improve Teaching and Learning Mathematics as a Service Subject.- Chapter 33. Tertiary mathematics through the eyes of non-specialists: engineering students’ experiences and perspectives.

“I found myself, a research mathematician with an equal interest in mathematics education research, learning quite a number of new things. … it was an interesting read. Indeed, the book often lives up to its promise to deliver practice oriented research which I could try out in my own teaching. … the book endeavours to show what has worked in real university settings as well as suggest the way ahead for the field.” (Eng Guan Tay, International Journal of Research in Undergraduate Mathematics Education, Vol. 9 (3), 2023)