Topic Study Group No. 2: Mathematics Education at Tertiary Level
The Programme
Research in mathematics education at the tertiary level has experienced tremendous growth over the last decades (Biza, Giraldo, Hochmuth, Khakbaz, & Rasmussen, 2016; Rasmussen & Wawro, 2017). Evidence of this growth includes the continued success of the Research in Undergraduate Mathematics Education conference in the United States, now at its 20th annual conference; the university mathematics research contribution to the Espace Mathématique Francophone since 2006; and since 2011 the working group on University Mathematics Education in the Congress of European research in Mathematics Education conference. In 2015 the Australian Mathematical Society established a Special Interest Group in Mathematics Education, which has among its goals the promotion of inquiry and discussion about tertiary mathematics education. The first biennial conference of the International Network for Didactic Research in University Mathematics took place in 2016. Furthermore, in 2015 the new International Journal of Research in Undergraduate Mathematics Education published its first issue.
Reflecting this growth, a total of 64 papers and 23 posters were accepted for presentation at TSG 2. There were four main sessions with 14 papers, including two invited talks, one by Elena Nardi and one by Greg Oates. There were 50 short oral presentations in eight different sessions. Session blocks were organized around more or less coherent themes, including mathematical practices, teaching, professional and curriculum development, connections to engineering, transition to university, preservice teachers, student thinking, and research related to specific courses such as calculus, differential equations, and linear algebra. All talks and authors organized by session type are presented below. As a whole, these talks represent a rich and diverse collection of interests and theoretical approaches characteristic of a maturing discipline.

Symbolizing and brokering in fostering inquiry, Megan Wawro, Michelle Zandieh, Chris Rasmussen

University students’ behavior working with newly introduced mathematical definitions, Valeria Aguirre Holguín

Learning how to axiomatise through paper folding, Dmitri Nedrenco

Teaching mathematics to nonmathematicians: what can we learn from research on teaching mathematicians? Elena Nardi

University mathematics lectures: teaching the same topics but different mathematics, Alon Pinto

Using a theoretical perspective to teach a proving supplement for an undergraduate real analysis course, Annie Selden, John Selden

Exploring lecturers’ perceptions of using technology to teach mathematics at tertiary level, Jayaluxmi Naidoo

Mathematicians and mathematics education: collaborating for professional development, Greg Oates, Tanya Evans

Holistic approach to curriculum review of undergraduate mathematics, Pee Choon Toh, Weng Kin Ho, Kok Ming Teo, Khiok Seng Quek, Tin Lam Toh, Eng Guan Tay, Romina Ann S. Yap

Using technology to develop formative assessment resources for first year undergraduate modules, Ann O’Shea, Sinead Breen, Conor Brennan, Frank Doheny, Fiona Lawless, Christine Kelly, Ciaran Mac an Bhaird, Seamus McLoone, Eabhnat Ni Fhloinn, Caitriona Ni She, Brien Nolan

The transition from secondary to tertiary mathematics education—a Swedish study, Christer Bergsten, Eva Jablonka, Hoda Ashjari

Students’ thinking modes and the emergence of signs in learning linear Algebra, Melih Turgut, Paul Drijvers

Exploring students’ interactions in an online forum that accompanied a course in linear Algebra, Igor’ Kontorovich

Mathematical argumentation of firstyear students: the influence of conceptual knowledge, Kathrin Nagel, Kristina Reiss

Difficulties in mathematics experienced by students in a transdisciplinary engineering study, Evangelia Triantafyllou, Olga Timcenko

Ideas of mathematical literacy for cultivating students’ understanding of concepts of linear Algebra, Ryuichi Mizumachi

A task design to introduce the concepts of eigenvectors and Eigen values. An embodied approach, María José BeltránMeneu, Marina MurilloArcila

Déjà vu in mathematics: what does it look like?, Robyn Pierce, Caroline Bardini

The art of mathematical chatter, Anne D’ArcyWarmington

Why students are not motivated to learn mathematics?, Seyed Hadi Afzali Borujeni, Azimehsadat Khakbaz

“What we need to show is that t is welldefined”: gesture and diagram in abstract Algebra, Andrew Francis Hare

Scripts in mathematics tutorials, Juliane Püschl

A case study on the impact of investigating multivariable calculus concepts through geometry and multiple representation, Aaron D Wangberg, Brian Fisher, Elizabeth Gire, Jason Samuels

Student reasoning about functions, limits, and rate of change in introductory calculus, Caroline Julia Merighi

Research and practice of college mathematics course assessment in Sichuan University, Jianren Niu, Liang Yang

How do students of economics understand the concept of marginal cost? Frank Feudel

About doing geometric approach in differential equations: difficulties and a coherent method, Younes Karimi Fardinpour

Instrumental action schemes in differential equations using a computer Algebra system, maxima, Fereshteh Zeynivandnezhad

The practice, guarantee and effect on the second classroom platform in university mathematics teaching, Chen Li, Chen Chaodong

A comparative study of university students’ math achievement of smallclass teaching and largeclass teaching, Chao dong Chen, Jian ren Niu

Using journals to support learning: case of number theory and proof, Christina M Starkey, Hiroko Warshauer, Max Warshauer

Knowledge of rational and irrational numbers of two undergraduate students, Geraldo Claudio Broetto, Vânia Maria SantosWagner

The activitybased learning of mathematics in a technical higher education institution, Elena G. Yevsyeyeva

Motivating university students to learn mathematics, Azimehsadat Khakbaz, Seyed Hadi Afzali Borujeni

The future of mathematics teaching: analysis of the expectations of undergraduates in the federal district, Brazil, Jéssica de Aguiar França, Regina da Silva PinaNeves, Raquel Carneiro Dörr

Principles for designing invention tasks for undergraduate mathematics, Ben Davies, Caroline Yoon, John Griffith Moala, Wes Maciejewski

Meaningful learning in mathematics education for the humanities and social sciences students, Mitsuru Kawazoe, Masahiko Okamoto

Lecturer education: a course design, Ignasi Florensa, Marianna Bosch, Josep Gascón

An investigation into the efficacy of flipped classroom for tertiary mathematics, Weng Kin Ho, Kok Ming Teo, Lu Pien Cheng, Puay San Chan

Interactive videos: a 21st century necessity for student engagement, Haitham S. Solh

Systemic integration of programming in undergraduate mathematics: from implementation to theory, Chantal Buteau, Eric Muller

Undergraduate math students’ interactions with programming: developing instruments in institutions, Laura Rose Margaret Broley

Development of diagnostic selfassessments as a base for individual support for firstyear students, Christoph Neugebauer, Sebastian Krusekamp, Kathrin Winter

Didactical elaboration of multimedia learning materials by recent technological advancements exemplified by computer aid, Tobias Mai, Silvia Becher

exploration of transfer of first year undergraduate mathematical learning to science, Yoshitaka Nakakoji, Rachel Wilson

The algebratocalculus transition, William Crombie

What first year university students’ recommendations for freshmen reveal about their learning strategies, Robin Göller

Issues in the transition from secondary to tertiary mathematics, Michael Surman Jennings, Merrilyn Goos, Peter Adams

Challenges involved when reforming traditional courses in mathematics for engineers, Frode Rønning

Analysis of typical mathematical competences required to solve tasks in basic engineering courses, Joerg Kortemeyer, Rolf Biehler

Treestructured online exercises in mathematics for engineering students: design and evaluation, Robert Ivo Mei

Learning behaviour, academic success in engineering mathematics, and lecturers’ ratings, Birgit Griese, Michael Kallweit

Mathematical selfefficacy of engineering students at the introductory phase of studies, Ronja Kürten

A preliminary analysis of the effectiveness of studentproduced videos on the relevance of mathematics in engineering, Birgit Loch, Wendy Scott, Michelle Dunn

Procedural knowledge as a predictor for success in German math exams for first year engineering students, Mike Altieri

Mathematics graduate teaching assistants’ longitudinal transitions in beliefs about mathematics teaching and learning, Mary Beisiegel

Algebraic thinking in the understanding and solution of geometric problems amongst year university students, Luis Weng San, Bhangy Cassy

Results of us national study on calculus, Jess Ellis and Chris Rasmussen

Studifinder: mathematical elearning materials for the transition from secondary school to university, Yael Fleischmann, Alexander Börsch, Rolf Biehler, Christoph Colberg, Tobias Mai

Concept and application of mathematizing to the process of classification, Alfonso J. GonzálezRegaña, Verónica MartínMolina, José María GavilánIzquierdo

How, when, where and why do students use lecture recordings?, Roland Gunesch

Digital media as motivating tool for learning descriptive statistics, Mathias Hattermann, Alexander Salle, Stefanie Schumacher, Daniel Heinrich

A commognitive perspective on students’ engagement with the concept of group: the case of students F and M, Marios Ioannou

Students’ perception of group discussions and presentations in a math education course, SeongA Kim, JeongGyoo Kim, Sunhee Lee

Perception vs reality: using tutorial videos to aid tutor reflection, Heather Lonsdale, Deborah King

A comparative analysis of three comprehensive initiatives to redesign developmental mathematics college curriculum, Carolyn Masserang

Supporting internalisation of mathematical syntax using blocks, Anthony Morphett

Revision activities of undergraduate mathematics students, Philip Walker, Eabhnat Ní Fhloinn

Autonomy in mathematics in the secondarytertiary transition, PierreVincent Quéré, Ghislaine Gueudet,

Mathematical competencies visible through assessment for engineering students, Kristina Raen

University teaching assistants’ teaching related beliefs, Johanna Rämö, Juulia Lahdenperä, Susanna Oksanen

Bremath—redesign and implementation of university maths courses for future high school teachers, Ingolf Schäfer

Assignments and written exams in an ICT learning environment, Karsten Schmidt

Explicating strategies—planning an intervention to increase the strategic knowledge of university freshmen, Thomas Stenzel

description and initial results of the preservice teachers seminar “Überpro_wahrscheinlichkeitsrechnung”, Gero Stoffels

Artin’s braid group as an introductory example for group theory approaches at the university of hamburg, Sophie Stuhlmann

Lecturers’ pedagogical routines and expectations on students’ engagement in closedbook examinations, Athina Thoma
References
 Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A., & Rasmussen, C. (2016). Research on teaching and learning mathematics at the tertiary level: Stateoftheart and looking ahead. In Research on Teaching and Learning Mathematics at the Tertiary Level. Berlin: Springer International Publishing.Google Scholar
 Rasmussen, C., & Wawro, M. (2017). Postcalculus research in undergraduate mathematics education. In J. Cai (Ed.), Compendium for Research in Mathematics Education. National Council of Teachers of Mathematics: Reston, VA.Google Scholar
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