By Andrew Uderian
One aspect of university all engineers experience is midterm tests and examinations. Generally, students tend to either be indifferent to these evaluations or despise them, and math midterms are often some of the most polarizing. However, progress has been made towards making math evaluations both more fun and more applicable to real world problem solving. Since 2011, the University of British Columbia has used two-stage evaluations on high-stakes math and science evaluations, leading to increased student engagement and averages. At the University of Toronto, Professor Bernardo Sousa has worked to implement two-stage examinations in mathematics courses, most notably in Calculus II (MAT187).
When asked about the genesis of group tests within Skule, Professor Sousa replied, “My personal effort began with tutorials, …[which] used to be hosted by one TA who solved problems on the board with little to no interaction from students. Now, students work in teams on problems that are open-ended and involve critical thinking and problem solving skills.” After the introduction of team-based tutorial problems, Professor Sousa moved to implement similar problems in a group problem-solving section on calculus exams.
Within the profession of engineering, it is incredibly rare for practitioners to work alone. The ability for engineers to work with their colleagues effectively is essential, yet difficult to develop. One of Professor Sousa’s primary motivations behind using two-stage evaluations was the desire to foster the skill of teamwork within engineering undergraduate students. Arguing for the alternative tests, he stated, “students get to see the social aspect of mathematics and engineering… engineers don’t work by themselves, they work in teams… they create a very dynamic feedback loop of ideas, bouncing off of each collaborator to get ideas that would be much harder to get to otherwise.”
Despite the benefits of group evaluations, the tests have remained controversial amongst the student body. Students often question the fairness of two-stage examinations, particularly due to the freedom given to students to choose their own groups. Many students assume that their high-achieving peers will cluster together, leaving those who struggle in the subject to struggle and fail together.
However, in the case of the two-stage mathematics examinations, that assumption is untrue. According to Professor Sousa, both random selection and self-selection were trialled in another course before the introduction of group examinations to MAT187, with self-selection leading to a greater correlation between the individual and group portions of the exam. Although the approach leads to a similar distribution of marks as the individual portion, if the individual portion is assumed to be fair then the group portion must be as well. Furthermore, random groups would simply be far more challenging logistically: “Assigning random groups means that we must organize students (250+ in some rooms) to find their own group/table quickly.”
Despite the controversy surrounding group evaluations amongst the student populace, the method appears to produce results, with a higher average on the group portion of midterms versus the individual portion. Furthermore, the group portion allows more students to enjoy their evaluation and mathematics. Speaking from the perspective of an instructor, Professor Sousa stated, “students laugh while writing this part of the test, so you just get the feeling that everyone can enjoy math if put in the right setting. As a mathematics instructor, it is incredibly satisfying to witness the group part of the test.” Although midterms bring stress for many students, being able to collaborate with friends on the same problem appears to relieve that stress and even make parts of the evaluation enjoyable.
The use of two-stage evaluations in subjects that have been traditionally individually evaluated, such as mathematics, seems counter-intuitive at first glance. Many students argue that such tests are less fair; however, the results from the midterms, both anecdotal and otherwise, have suggested that a group portion improves student learning and enjoyment of evaluations. Due to the results, group midterms will continue to be a part of the mathematics curriculum at UofT, and will continue to be refined in order to change midterm evaluations from a source of stress into a more pleasant learning experience.