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

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. 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 Cover 1 Half Title 2 Series Page 4 Title Page 6 Copyright Page 7 Table of Contents 8 List of illustrations 10 List of contributors 12 Introduction 16 PART I: Achievements and current challenges 22 1. Mathematics education research at university level: Achievements and challenges 24 2. Lessons for mathematics higher education from 25 years of mathematics support 43 3. Current interactions between mathematicians and researchers in university mathematics education 62 4. Education and professional development of university mathematics teachers 80 PART II: Teaching and learning of specific topics in university mathematics 102 5. Challenging issues in the teaching and learning of Calculus and Analysis 104 6. Task design in Calculus and Analysis 125 7. Discrete mathematics, computer science, logic, proof, and their relationships 146 8. Abstract and Linear Algebra 168 9. Mathematics and other disciplines, and the role of modelling: Advances and challenges 190 PART III: Teachers’ and students’ practices at university level 212 10. Transitions to, across and beyond university 214 11. Students’ in-class and out-of-class mathematical practices 237 12. Mathematics teaching practices at university level 259 1 Mathematics education research at university level; 2 Lessons for mathematics higher education from 25 years of mathematics support; 3 Current interactions between mathematicians and researchers in university mathematics education; 4 Education and professional development of university mathematics teachers; 5 Challenging issues in the teaching and learning of Calculus and Analysis; 6 Task design in Calculus and Analysis; "7 Discrete mathematics,Computer science,Logic,Proof1,and their relationships"; 8 Abstract and Linear Algebra; "9 Mathematics and other disciplines,and the role of modelling"; "10 Transitions to,across and beyond university"; 11 Students’ in-class and out-of-class mathematical practices; 12 Mathematics teaching practices at university level 1 Mathematics education research at university level,2 Lessons for mathematics higher education from 25 years of mathematics support,3 Current interactions between mathematicians and researchers in university mathematics education,4 Education and professional development of university mathematics teachers,5 Challenging issues in the teaching and learning of Calculus and Analysis,6 Task design in Calculus and Analysis,7 Discrete mathematics, Computer science, Logic, Proof1, and their relationships,8 Abstract and Linear Algebra,9 Mathematics and other disciplines, and the role of modelling,10 Transitions to, across and beyond university,11 Students’ in-class and out-of-class mathematical practices,12 Mathematics teaching practices at university level