Student-driven perspectives in the classroom – leveraging former student experiences to promote more effective learning and inclusivity

Cohort March 2023: Faculty of Science – Nahid Walji, Seckin Demirbas, Al Rahim Hossain, Mila Micovic, Nia Tzvetkova

Project background

Math 220 (Mathematical Proof) is a course in the Math Major program that is required for all students who have not taken Math 226 (Honours Calculus). It is also an eligible course for majors combining Mathematics with Chemistry, Computer Science, Economics, Physics, or Statistics. Its importance stems from typically being a student’s first introduction to proofs, and as such, it presents a considerable adjustment in thinking and learning practices for many students. The course is currently structured as a ‘flipped’ classroom where students watch short instructional videos on Canvas and then solve exercises during classes. It also has an OER textbook called “PLP” written at UBC by S.Demirbas and A.Rechnitzer.

Project details

There are many challenges that arise for students in this course. We describe and address each of these in turn. Additionally, from an EDI lens, the student partners will be role models to show that everyone has the potential to succeed in this course (and in mathematics in general).

Mathematics courses taken before Math 220 typically focus on presenting a procedure which students can use in assessments. In those courses, sometimes questions are made harder and non-procedural, but this rises to greater level in Math 220. This leads to the first challenge for students – procedural thinking no longer suffices. We address this with student partner creation of video solutions of difficult homework or past finals questions. These would provide a vehicle to share intuition and explain the thought process needed to obtain a solution. They will also emphasize the importance of conceptual understanding (rather than procedural thinking) to solve a problem.

The next challenge arises because students learn many different proof techniques without feeling like they have enough guidance on how to choose from among these options when problem solving. In response, we will create ‘decision trees’ for questions that will be presented in class – the goal being to start a discussion on the approach needed to solve a problem. The student partner perspective informs us on the possible approaches that students may try (that often an instructor would never consider, knowing that they will not work).

The level of precision expected from students in Math 220 is far greater than in prior courses. The paradigm shift of what constitutes a perfect proof is difficult to adapt to, and it is challenging for students to spot gaps in their solutions. To address this, we will create solutions with crucial gaps (representing common errors in student answers) and ask students to identify and fix them. We will integrate these into class material, to develop student understanding of what constitutes a perfect proof.

Due to the challenges mentioned above, there is a significant need for resilience in problem-solving – this issue is not usually discussed at present. The video materials that we create will present a diverse range of students showing their expertise in solving difficult questions, and demonstrating that being tenacious pays off. This gives concrete relatable examples of success in the course.