By Kevin Cheung, Associate Professor, School of Mathematics and Statistics
About midway through the first time I taught MATH 3801, Linear Programming, I found out that many of my students did not remember what the rank of a matrix was. The rank of a matrix is a basic concept covered in first-year linear algebra. It is as basic as the derivative in first-year calculus. To avoid losing a third or more of the class, I had to give a review.
After this experience, whenever I taught MATH 3801 again, I would clearly list the linear algebra concepts heavily used in the course and I would test the students on these concepts early on in the term. Such actions turned out to be effective as I no longer had to deal with too much trouble arising from students’ lack of proficiency in basic linear algebra.
So, in response to Alison Sandstorm’s post on final exams, I would say that final exams are probably not as necessary as beginning exams.
I remember that as a student, I would forget a lot of what I had studied not long after writing the final exam. But I also remember that much of the course material would finally make sense as I studied for the final exam. Studying for the final definitely helped me improve my command of the material. The only problem was that I could not make the improvement last.
One of the major challenges of teaching courses with prerequisites is that students don’t always remember what they have learned. However, is it always reasonable to expect students to be proficient at what they have learned after a long break?
One way to address students’ deficiencies in prerequisite knowledge or skills is to spend the first week or so on review. Unfortunately, most courses have more than enough material to fill the entire term, leaving practically no time for doing a proper review. Besides, students don’t necessarily show up for the first few lectures.
The main purpose of a final exam, for most courses anyway, is to do a check on students’ command of the course material. If there is a time when such a check is really needed, it is at the beginning of a course that depends on it. Hence, if students are required to pass an exam on the prerequisites before the course registration deadline, perhaps they will be better prepared to take on the new material!
As switching from final exams to beginning exams won’t happen any time soon, we will have to continue to come up with ways to make it stick when we teach and hope for the best.