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Practice-Oriented Research in Tertiary Mathematics Education

  • Book
  • © 2022

Overview

Editors:
  1. Rolf Biehler

    1. Institute of Mathematics, Paderborn University, Paderborn, Germany

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  2. Michael Liebendörfer

    1. Institute of Mathematics, Paderborn University, Paderborn, Germany

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  3. Ghislaine Gueudet

    1. University Paris Saclay, Orsay, France

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  4. Chris Rasmussen

    1. Department of Mathematics and Statistics, San Diego State University, San Diego, USA

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  5. Carl Winsløw

    1. Faculty of Science, University of Copenhagen, Copenhagen, Denmark

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  • Presents current research paradigms in tertiary mathematics education
  • Analyses and support measures for the secondary-tertiary transition
  • Discuses practice-oriented research for teaching mathematicians

Part of the book series: Advances in Mathematics Education (AME)

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Table of contents (34 chapters)

  1. Front Matter

    Pages i-x
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  2. Practice-Oriented Research in Tertiary Mathematics Education – An Introduction

    • Rolf Biehler, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, Carl Winsløw
    Pages 1-20

  3. Research on the Secondary-Tertiary Transition

    1. Front Matter

      Pages 21-21
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    2. Emotions in Self-Regulated Learning of First-Year Mathematics Students

      • Robin Göller, Hans-Georg RĂĽck
      Pages 23-44

    3. The Unease About the Mathematics-Society Relation as Learning Potential

      • Johanna Ruge
      Pages 45-66

    4. Collaboration Between Secondary and Post-secondary Teachers About Their Ways of Doing Mathematics Using Contexts

      • Claudia Corriveau
      Pages 67-89

    5. Framing Goals of Mathematics Support Measures

      • Michael Liebendörfer, Christiane BĂĽdenbender-Kuklinski, Elisa Lankeit, Mirko SchĂĽrmann, Rolf Biehler, Niclas Schaper
      Pages 91-117

  4. Research on University Students’ Mathematical Practices

    1. Front Matter

      Pages 119-119
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    2. “It Is Easy to See”: Tacit Expectations in Teaching the Implicit Function Theorem

      • Matija Bašić, Ĺ˝eljka Milin Ĺ ipuš
      Pages 121-138

    3. University Students’ Development of (Non-)Mathematical Practices: The Case of a First Analysis Course

      • Laura Broley, Nadia Hardy
      Pages 139-161

    4. The Mathematical Practice of Learning from Lectures: Preliminary Hypotheses on How Students Learn to Understand Definitions

      • Kristen Lew, Timothy Fukawa-Connelly, Keith Weber
      Pages 163-180

    5. Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences

      • Laura Ostsieker, Rolf Biehler
      Pages 181-201

    6. Investigating High School Graduates’ Basis for Argumentation: Considering Local Organisation, Epistemic Value, and Modal Qualifier When Analysing Proof Constructions

      • Leander Kempen
      Pages 203-223

    7. Proving and Defining in Mathematics Two Intertwined Mathematical Practices

      • Viviane Durand-Guerrier
      Pages 225-241

  5. Research on Teaching and Curriculum Design

    1. Front Matter

      Pages 243-243
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    2. Developing Mathematics Teaching in University Tutorials: An Activity Perspective

      • Barbara Jaworski, Despina Potari
      Pages 245-263

    3. Lecture Notes Design by Post-secondary Instructors: Resources and Priorities

      • Vilma Mesa
      Pages 265-288

    4. Creating a Shared Basis of Agreement by Using a Cognitive Conflict

      • Mika Gabel, Tommy Dreyfus
      Pages 289-310

    5. Teaching Mathematics Education to Mathematics and Education Undergraduates

      • Elena Nardi, Irene Biza
      Pages 311-327

    6. Inquiry-Oriented Linear Algebra: Connecting Design-Based Research and Instructional Change Research in Curriculum Design

      • Megan Wawro, Christine Andrews-Larson, Michelle Zandieh, David Plaxco
      Pages 329-348
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Keywords

About this book

This edited volume presents a broad range of original practice-oriented research studies about tertiary mathematics education. These are based on current theoretical frameworks and on established and innovative empirical research methods. It provides a relevant overview of current research, along with being a valuable resource for researchers in tertiary mathematics education, including novices in the field. Its practice orientation research makes it attractive to university mathematics teachers interested in getting access to current ideas and results, including theory-based and empirically evaluated teaching and learning innovations.


The content of the book is spread over 5 sections: The secondary-tertiary transition; University students' mathematical practices and mathematical inquiry; Research on teaching and curriculum design; University students’ mathematical inquiry and Mathematics for non-specialists.

Reviews

“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)

Editors and Affiliations

  • Institute of Mathematics, Paderborn University, Paderborn, Germany

    Rolf Biehler, Michael Liebendörfer

  • University Paris Saclay, Orsay, France

    Ghislaine Gueudet

  • Department of Mathematics and Statistics, San Diego State University, San Diego, USA

    Chris Rasmussen

  • Faculty of Science, University of Copenhagen, Copenhagen, Denmark

    Carl Winsløw

About the editors

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. 

Bibliographic Information

  • Book Title: Practice-Oriented Research in Tertiary Mathematics Education

  • Editors: Rolf Biehler, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, Carl Winsløw

  • Series Title: Advances in Mathematics Education

  • DOI: https://doi.org/10.1007/978-3-031-14175-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-14174-4Published: 03 January 2023

  • Softcover ISBN: 978-3-031-14177-5Published: 04 January 2024

  • eBook ISBN: 978-3-031-14175-1Published: 01 January 2023

  • Series ISSN: 1869-4918

  • Series E-ISSN: 1869-4926

  • Edition Number: 1

  • Number of Pages: X, 736

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Mathematics Education, Mathematics, general, Higher Education, Curriculum Studies

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