I think graduate studies tend to attract a fairly specific subset of students, especially those who enter directly from undergrad; namely, graduate studies have an uncanny ability to find the students who enjoy school and are generally good at conforming to certain academic expectations.
Since I have always been a super-nerd, I thought it would be fun to share the experiences of Baby-Shu and high school math. American high schools are infamously obsessed with extracurriculars. There are good reasons why Glee has a certain verisimilitude, and why football stars continue to dominate the popularity (and, more importantly, the Prom King) scales. I was very heavily involved…. in nine different clubs (give or take a few casual meetings in a scattering of others). Including the infamous Mu Alpha Theta (ΜΑΘ), or the United States mathematics honor society for high school–whose members were colloquially known as “Mathletes”, as in “athletes, but in math”. The requirements for the club were a minimum grade average, a number of competitions, and several hours of community services in the form of math tutoring. It was a traumatizing experience for all involved.
Here’s the problem: Brookfield was absolutely correct when he asserted that the best students made for the worst teachers. Perhaps more than any other subject, math is not just about practice but relies upon a foundational, intuitive understanding of theory–about shapes and planes and numbers, changing slopes that change a cross-section from an ellipses to a hyperbola. Mathematical concepts nearly impossible to explain, let alone describe, without a model. Mathematical concepts that we Mathletes understood but could not articulate. I think that was the very first time that I experienced pedagogical failure. I tried to use the same language my teachers used when teaching me the quadratic formula, but even 16 year old me knew there was something futile about repeating instructions until someone breaks. It wouldn’t be until my senior year that I would recognize their frustration toward the mathematical problems. Because while I had remained in Mu Alpha Theta, I was a member in name only. I had given up on AP Calculus in favour of AP Statistics–a course that taught you how to program a graph and download Mario Cart onto a TI-nspire calculator.
I now recognize that I dropped out of calculus because of a lack of motivation; more specifically, a missing piece in terms of efficacy. Perhaps more than even English, math suffers from an efficacy problem. If English’s outcome expectancy suffers because of students say things like, “I can’t do well in an English class because English grammar is too difficult”, math’s problems is “I can’t do well because mathematical equations are too difficult. In English, efficacy expectancies suffer because students argue they can’t construct arguments; in math, students often pigeonhole themselves in the belief they cannot correctly enter an a logarithm. But unlike with English–which will be used as long as the student is forced to engage with Anglo-Euro-western society–a person could severe themselves from math more successfully, deepening the gap between math literacy and math avoidance. Despite once being an advanced math student, I now avoid it as much as possible and rely on my calculator when it nevertheless returns to my life.
If I were to trace my own trajection, I would wonder when I went from motivated to rejecting. And whether fragility or evasion came first. I doubt there are any easy answers, but in our teaching it may be a good idea to focus on that uneven ground, and finding ways to keep students motivated even during moments of doubt.
See you on Friday.