Identifying the Genius in your Math Course

As a math professor at McMaster University, Patrick Speissegger has seen the decline in interest for undergraduate math courses in recent years. Many of the undergraduate math courses are open for enrolment from students of STEM disciplines, specifically engineering and physics majors.The Mathematics department experienced difficulty in finding the students early in their undergraduate careers that were focused on purely mathematics as a major. Patrick was presented with a daunting task of finding those math-focused students in their first year of their degrees, so the department could provide resources to ensure these particular students can succeed in a degree focused in Mathematics.

Patrick decided to pilot a first-year calculus proofs class, which was met with skepticism. Proofs is an advanced mathematical concept that is introduced to senior level undergraduate courses, where students have had years of foundational math courses to develop their conceptual understanding of the material. The enrolment for this special class was capped at 20 and offered as an open elective to first year undergraduate students in STEM courses. This was Patrick’s first attempt to identify students who had a natural inclination towards math as a major.

Using Peer Assessment to Identify Student Talent

Patrick decided that Kritik would be instrumental in enabling students to lean on their peers for understanding of the topics at hand. These mathematical proofs were complex and diverse in their solutions, and students were inspired by some of the feedback they received on their logical approaches to questions assigned. Patrick’s methodology behind peer review in math courses was simple; if a student was able to provide strong feedback to their peers’ proofs, he would be able to identify which students understood the concepts well enough to evaluate, and which students needed extra help due to their inability to provide strong feedback.

After the first few activities in Kritik, Patrick noticed that two students in particular were performing above the rest of the class in their Creation Scores and their Kritik Scores. These two students succeeded in a quantitative / qualitative nature; the marks they received on their own work were near perfect, and the feedback they provided to their peers exemplified a deep understanding of the material.

Developing Soft Skills in STEM Courses

Patrick offered these first year students the opportunity to enroll in his 4th year advanced proofs class if they wish. This senior level course also had masters students enrolled, and he expressed the nature and difficulty of the course to the two students. The two first year students enrolled in his upper level course, and surprised Patrick and the whole Mathematics department by receiving the highest and second highest grades in the 4th year level course. The first year calculus proofs course was a success; enrollment has doubled for the Fall and Patrick continues to spread the work of Kritik to his colleagues. Kritik provides students in STEM courses with the ability to demonstrate the soft skills required in communicating concepts, further developing a student’s understanding of the course material.

Patrick Speissegger
Patrick Speissegger
McMaster University
Professor of Mathematics

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