School and the Academy – Some Thoughts on Math Education

Last Friday, I had the pleasure of sitting on the student panel at the “School and the Academy” conference on math education. In the 40-minute panel discussion, high school teachers, TAs, and professors posed some great questions about the transition from high school to university mathematics to us students. I really enjoyed the session and thought I would expand upon my answers a little more in this blog post. I don’t remember all of the questions, so if you would like another question answered, post it in the comments or e-mail me (this is not restricted to the people at the conference!). Unfortunately, I don’t have inputs from the other 3 members of the panel. Nonetheless, I hope my comments will provoke some interesting thoughts.

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Q: Did high school math prepare you for university math? Why or why not?

A: Yes and no. There are really two types of preparedness – academic and mental. Being prepared academically entails having a good enough grasp on the fundamentals to handle the contents of university courses. Being prepared mentally involves adjusting to the university learning environment, orienting oneself on campus, redefining the role of teacher and student, and figuring out how to study. I was academically if not mentally prepared (though that was my own fault as I really dragged my feet). I think that a high school teacher can realistically prepare students academically, but not necessarily mentally. Mental preparation is really up to the students to do (though see below for some suggestions).

Q: What is the biggest difference between high school and university math? What’s the most challenging part of university math?

A: High school math is cookie cutter math. One learns a concept, follows the steps, and arrives at the answer. Everything is black and white. University math is a lot more conceptual and a lot less plug and chug. Someone in the room during the conference used an elephants analogy that I really liked, so here is my car analogy. In high school, students are presented with a blue Toyota, a purple Toyota, and a red Toyota. On an exam, they would be asked about one of the three, or if the teacher is daring, about a yellow or a green Toyota. In university, students are presented with Toyotas, Hondas, Volvos, and Fords. On an exam, they would be given a Mazda. Students would have to realize it’s a Japanese car, figure out which car they learned in class is most similar to it, and then solve the problem using the steps to learned (if they exist). As one gets into more difficult math, things either become a lot more specific (the different types of tires on one brand of a car) or a lot more abstract (throw in buses, trains, and boats).

In high school, it’s easy to recognize where one should start – it’s the how, the steps – that are truly challenging. In university, the steps are the easy part. It’s the starting – realizing that a Mazda is the most similar to one of the Japanese cars – that is most difficult.

Aside from seeing the connections to what is learned in class, students are also introduced to more concepts they haven’t seen before (Fermat’s Last Theorem, differential equations, matrices, graph theory, etc.) and that can be overwhelming. If possible, I would encourage grade 12 teachers to even just name some higher level math concepts in their classes along with some of the most famous questions in mathematics. Sure students would have no idea what they are, but when they are exposed to it in the future, they are better off than than their classmates (who would be going “huh??? What the heck is that? I’ve never even heard of it before”). That extra boost of confidence may encourage them and make math seem less daunting.

Q: What were some things that your high school teachers told you about university that were true, but that you didn’t believe?

A: So many things, here are some that I remember: (italics are my notes)

  • Getting into university is easier than staying there
  • No hand-holding:
    • No one cares if you show up to class and no one will chase after you for your homework
    • No spoon-feeding information and exams that require straight regurgitation
    • Mark grubbing won’t get you anywhere
  • Grades will drop 10 to 15% across the board, providing you don’t fail
  • Not all professors are created equal and not all are understandable. Professors are not paid to teach and some are absolutely terrible at it though there are some great professors. Professors probably won’t know your name.
  • Some courses are taught by TAs and not all TAs can teach. I’ve found that TAs are consistently better across the board than profs – I’ve yet to have a terrible TA but I’ve had some abysmal profs
  • Classes can be really large and it’s easy to feel like a number

Q: What more can high school teachers do to prepare their students? What about professors/TAs in university?

A: High school teachers could prepare students academically and maybe mentally. Teach the topics as thoroughly as possible and really hammer home the fundamentals (I believe the professor panel had some suggestions of what they would like incoming students to know). On the mental side, say some of the things from the answer to the question above. Students won’t believe you when you tell them that they have to take charge of their own education, but they will be able to orient themselves faster than other students once they do get to university. If possible, bring in a few recent graduates and have them tell the students these things. Students may take what their peers say more seriously. As for TAs and professors, I’m not sure. Aside from teaching to the best of your abilities, the rest is really up to the students. Perhaps you could stress that you’re always there to support them and that there are other resources available, such as academic coaching and tutoring, if they are not comfortable going to their profs.

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I hope this post is somewhat helpful to the teachers and students reading it! If you have any more questions, please write them in the comments! Happy Canada Day!

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