Dr. Goodaire swooped down the stairs of the Auditoria style classroom two wide steps at a time to deliver his first lecture of the morning for a Calculus I class. It was the first week of September 1992 and this was my first class of a six-year long engineering program at Memorial University.
I was well prepared for the course. While I didn’t have the option of taking AP courses in high school, I did a pre-calculus course in Grade 12 in addition to the usual geometry and algebra topics. I did well in these courses, though I have no reason to believe I have a particular talent in this topic— I just did the assigned homework consistently (I recall spending perhaps an hour most nights on math homework). I would have considered math one of my favorite subjects, though I never had a passion for the topic.
It wasn’t long, however, before I felt like I was in over my head with university level math. Where I once felt mastery of the material, I now felt defeated. Grades in the 90s were replaced by 60s and low 70s on my assignments and mid-term.
I felt that Dr. Goodaire was a very good lecturer, but the course was intimidating. I didn’t keep up with him. He covered multiple sections of the text per class sometimes, a blistering speed compared with high-school pace. I don’t think I missed any lectures, but most of the time I barely understood the material; sometimes not at all. The text was hard to read (I never learned how to read a math text in high school). I didn’t know how to persist when encountering difficult problems. Even the course number, “Math 1000”, was a little chilling.
I recovered somewhat by the end of the course, thanks to some lengthy tutorial sessions which included practice exams. But I never fully recovered. I never really learned how to study math, and throughout my program I never regained the confidence that I could obtain grades comparable to those I received in high school.
Fast forward to 2019 when I enrolled in the B.Sc. Applied Mathematics program at AU, originally with the intent of taking a few courses to learn more about a subject called machine learning. I managed to bring my grades up to the level I achieved in high school, maybe even better. This was a pleasant surprise as I had once convinced myself that it was not possible to achieve 90s in university level mathematics. I am no smarter than I was, no more able to learn the material. What made the difference? While I employ several different study tactics, I believe that a genuine interest in the topic, coupled with confidence and persistence are at the root of my improved results.
Over time I had developed a greater appreciation for the contribution of mathematics to daily life. It probably goes without saying that space exploration wouldn’t happen without some of the mathematical discoveries since the Renaissance, however you are probably not aware that much of today’s comforts would not exist without certain discoveries in the mathematical sciences. GPS and cellphones—gone. Internet—wouldn’t have been invented. Commercial aircraft—we wouldn’t have gone much further than the Wright brothers. Electricity—it likely would be more expensive and less reliable. Even in the research community there are many crossovers with various branches of mathematics. Biology, climate science, economics, cryptography and encryption, and social sciences to name a few areas, all make use of complex mathematics. To my surprise, I have learned since my first university courses that mathematics research (both pure and applied) is alive and well, though the work in pure mathematics often takes many years to be applied by business or research outside of mathematics.
Activities in my work and personal life have also illustrated the applicability of mathematics in everyday experience. At the office, I once encountered some product pricing problems that required algebra and calculus to solve (note that I wisely excluded the math component in my presentation to the executive!). In my personal life, I noticed the importance of math in understanding personal finance. If the equation y = p * (1+i)x means nothing to you (hint: your high-school text will cover a simplified version of this for sure), then you are missing out on very important information concerning your future finances.
Consider the plight of students or recent graduates looking at some furniture options. They might be forced (as I once was) to make a purchase with a credit card or go without. They might also have the option to purchase furniture through a retailer on credit (in the form of a weekly or monthly payment). This option may seem attractive as it typically comes with a low weekly payment in comparison with a credit card charging nearly 20% interest. Exploring these options, as part of writing this article, I found a sectional sofa which could be purchased from one retailer on credit for $24 per week for 156 weeks (3 years) vs. $1560 from a 2nd retailer. If students were to put their high school or early university math skills to work with the equation above, they might be shocked to learn that this pleasant weekly payment conceals an interest rate of 70%!! Ouch. And I am not cherry-picking examples here—this was the first example I reviewed.
So the integral (pun intended) of these experiences, related to the applications of mathematics, opened my eyes to the benefit of a mathematics education, for both society and the individual. The other part of this story is about developing confidence and tenacity.
Confidence comes from application, which is easier when coupled with genuine interest. So, to start, I read non-technical books outside the curriculum on the subject. In Pursuit of the Unknown: 17 Equations That Changed the World, and Love and Math: The Heart of Hidden Reality were among the books I read. I also began listening to science and math podcasts and reading popular science journalism from sources such as Quanta Magazine. This material made the topic interesting and more relatable—some of my readings were less about the math but rather about the people behind discoveries, and some of the authors have a style that is quite infectious.
I also read Lara Alcock’s How to Study as a Mathematics Major soon after starting my first course at Athabasca (she is a university professor specializing in mathematics education). The book described many of the problems I encountered as a math student and indicated that they were quite common. As stated earlier, I struggled to read math texts. I didn’t understand the vernacular of mathematics (e.g., definitions, axioms, lemmas, theorems, and some symbols). I was terrified of proofs. I didn’t know how to get ‘unstuck’ on a problem. And as silly as it may sound, I didn’t know how to get help or ask the right questions or speak to the professor. Of course, I also had the added problem that university social life can be very distracting (Alcock doesn’t help with that one!).
Alcock’s book also helped with terminology and study skills: how to read math, how to write math, how to deal with proofs. For example, it helped normalize the fact that I often had to read a section 2 or 3 times before I really got it. “Sleeping on it” is another valuable technique. I learned to spend days or weeks on hard assignment problems; nudging toward the solution with a little bit of effort here and there, aided by the confidence that I would eventually find an answer.
I wish I had this book when I started my undergrad in 1992. The validation I felt would have helped me through the transition to university, while the advice and general description of the subject would have made the topic more accessible and would have helped me move forward in the lectures more confidently. Validation may seem an odd thing to help you study, but when you realize that so many people taking calculus and stats courses are going through the same experiences, you don’t feel so bad about your own struggle. It provided me with confidence that I could improve.
In the end I cultivated a passion for the topic (I’m not exaggerating—if someone would volunteer to pay my bills, I would love to do a Ph.D. in applied mathematics). Math studies have ceased to be ‘work’, but rather have become an intellectual play.
So there you have it; a strategy to tame this subject that seems the bane of so many students. It would be too optimistic of me to think you could come away from this article with the interest I have for the subject, but I do hope, if you are in the “I suck at math”, or “I hate math” camps, that you give it a chance. If nothing else than for self-interest. Math is kind of like a superpower, or maybe a superpower-lite. While you may not use most of your learned math skills directly, anything that you do in life that involves problem solving, logical thinking or numeracy, be it inside or outside of academia, will benefit from math studies.