Registration Deadline: September 20, 2026

Instructor: Dr. Francis Duah, Toronto Metropolitan University

Course Dates: September 9 - December 2, 2026
Mid-Semester Break: October 12 - 16, 2026
Lecture Times: Wednesdays | 3:00 PM - 6:00 PM (ET)
Office Hours: By Appointment

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 20 students

Format: Online via Zoom (Zoom link will be provided through the Fields LMS course page)

Course Description

This course aims to provide opportunities for Masters and Doctoral students who are interested in the science and art of learning and teaching undergraduate mathematics to explore the current research in the field. The course focuses on issues in learning and teaching undergraduate mathematics. Topics to be covered include: 

1. Issues in Learning and Teaching Undergraduate Mathematics;
2. Active Learning in Undergraduate Mathematics;
3. The Role of Definitions, Theorems, and Proof;
4. Theories of Mathematics Education;
5. Learning Outcomes and Assessment;
6. Undergraduate Textbook Research;
7. Qualitative Methods of Evaluation of Educational Interventions;
8. Quantitative Methods of Evaluation of Educational Interventions;
9. Resilience in Undergraduate Mathematics Education;
10. Statistics Education;
11. Teaching Mathematics for Social Justice; and,
12. Eye Tracking Research in Mathematics Education.

The undergraduate mathematics curriculum content that will be drawn upon for illustration and discussion on transformative and effective higher education pedagogy includes but is not limited to Calculus, Linear Algebra, Complex Variables, Mathematical Proofs, Probability Theory, and Statistics.

Course expectations: 

• Lectures are based on discussion, conversation, and debate and both students and instructor aim to learn from each other.
• Before each lecture, students are expected to read the assigned paper(s). This task is necessary for lectures to be productive. Reading should be active and brief summary about the paper's arguments are to be noted and posted to the Learning Management System as evidence that the reading has been done. This will also help the student to submit an annotated bibliography assignment on the topic timely.

Evaluation method: A literature review of a maximum of 25 empirical studies on a chosen  topic in undergraduate mathematics education.

Weekly Reading Before Class (Additional Reading may provided if needed):

Week 1 Issues in Learning and Teaching Undergraduate Mathematics

• Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A. S., & Rasmussen, C. (2016). Research on Teaching and Learning Mathematics at the Tertiary Level. Springer Nature. Available at https://library.oapen.org/bitstream/handle/20.500.12657/27729/1/1002276.pdf   

Week 2 Active Learning in Undergraduate Mathematics

• Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences. 111 (23), 8410 – 8415

Week 3 The Role of Definitions, Theorems, and Proof in Mathematics Education

• Abramovitz, B., Berezina, M., Berman, A., & Shvartsman, L. (2009). How to understand a theorem?. International Journal of Mathematical Education in Science and Technology, 40(5), 577-586. 
• Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In Advanced mathematical thinking (pp. 65-81). Dordrecht: Springer Netherlands.

Week 4 Theories of Mathematics Education, 

• Radmehr, F., & Drake, M. (2019). Revised Bloom’s taxonomy and major theories and frameworks that influence the teaching, learning, and assessment of mathematics: a comparison. International Journal of Mathematical Education in Science and Technology, 50(6), 895-920. 

Week 5 Learning Outcomes and Assessment,

• Osueke, B., Mekonnen, B., & Stanton, J. D. (2018). How undergraduate science students use learning objectives to study. Journal of Microbiology & Biology Education, 19(2), 10-1128.
• Mitchell, K. M., & Manzo, W. R. (2018). The purpose and perception of learning objectives. Journal of Political Science Education, 14(4), 456-472. 

Week 6 Undergraduate Textbook Research,

• Mesa, V., Suh, H., Blake, T., & Whittemore, T. (2012). Examples in college algebra textbooks: Opportunities for students’ learning. Primus, 23(1), 76-105.

Week 7 Qualitative Methods of Evaluation of Educational Interventions

• Michael Grove and Tina Overton (Eds)(2011). Getting started in pedagogic research within the STEM Disciplines, University of Birmingham and Higher Education Academy

Week 8 Quantitative Methods of Evaluation of Educational Interventions

• Michael Grove and Tina Overton (Eds)(2011). Getting Started in pedagogic research within the STEM Disciplines, University of Birmingham and Higher Education Academy

Week 9 Resilience in Undergraduate Mathematics Education

• Ricketts, S. N., Engelhard Jr, G., & Chang, M. L. (2015). Development and validation of a scale to measure academic resilience in mathematics. European Journal of Psychological Assessment. 
• Kooken, J., Welsh, M. E., McCoach, D. B., Johnston-Wilder, S., & Lee, C. (2016). Development and validation of the mathematical resilience scale. Measurement and Evaluation in Counseling and Development, 49(3), 217-242.

Week 10 Statistics Education

• Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report.
• Paul, W. (2017). An exploration of student attitudes and satisfaction in a GAISE- influenced introductory statistics course. Statistics Education Research Journal, 16(2), 487-510.

Week 11 Teaching Mathematics for Social Justice;

• Jong, C., Hodges, T., & Zhou, H. (2023). Teaching mathematics for social justice beliefs scale: psychometrics and practices in teacher education. International Journal of Mathematical Education in Science and Technology, 54(8), 1716-1730. 

Week 12 Eye Tracking Research in Mathematics Education

• Schindler, M., Simon, A. L., Baumanns, L., & Lilienthal, A. J. (2025). Eye-tracking research in mathematics and statistics education: recent developments and future trends. A systematic literature review. ZDM–Mathematics Education, 57(4), 727-743.
• Strohmaier, A. R., MacKay, K. J., Obersteiner, A., & Reiss, K. M. (2020). Eye-tracking methodology in mathematics education research: A systematic literature review. Educational Studies in Mathematics, 104 (2), 147-200. 

Background Reading:

1. Carlson, Marilyn Paula, and Chris Rasmussen, eds. Making the connection: Research and teaching in undergraduate mathematics education. No. 73. MAA, 2008
2. Kelton, S. (2020). A Beginner's Guide to Teaching Mathematics in the Undergraduate Classroom. Routledge.
3. Grove, M., Croft, T., Kyle, J., & Lawson, D. (2015). Transitions in Undergraduate Mathematics Education. Birmingham: Higher Education Academy and University of Birmingham.
4. Grove, M., & Tina, Overton, D. (2013). Getting Started in Pedagogic Research within the STEM Disciplines. Birmingham: Higher Education Academy and University of Birmingham.
5. Lerman, S. (Ed.). (2020). Encyclopaedia of Mathematics Education. Cham: Springer International Publishing. https://link.springer.com/referencework/10.1007/978-94-007-4978-8
6. Sriraman, B. & English, L. (Eds.) (2010a). Theories of Mathematics Education: Seeking new Frontiers. Heidelberg, DL: Springer.