Mathematical Teaching Methods

Snake Lemma, via Wikipedia

Snake Lemma, via Wikipedia

I

It seems to me quite logical on how math classes should proceed. The professor presents some theory, with theorems and their demonstration, as well as definitions and propositions, before venturing into a slew of examples. For some reason, this is completely absent from my classes in Taiwan. The examples. I don’t know what these profs are thinking, but examples are paramount for students to understand some of the theory. OK, my complex analysis prof is good. he gives examples and answers questions well¹.

Limit of a commutative diagram, via wikipedia

Limit of a commutative diagram, via wikipedia

II

I was extremely pissed at my modern algebra prof today. He took a lot of time explaining trivial things and concepts to the math education people⁴, which were in a majority⁵, and then proceeded to go to warp speed while going through the last hour in order to catch up. Class ended 14 minutes late and he finished his slides. Yes, he uses Powerpoint presentations⁶. Of course, since he does that, he’s got no idea how long it takes for students to note things down. Almost all of the students have stopped taking notes. It seems that I’m the only one that has trouble with this. Naturally, the presentations are made available on his website, but I like understanding the subject matter and taking the time to note stuff down.

This is how the last hour went in my class. The prof went through a dozen slides very quickly. I barely had time to note stuff down before it was already gone and he had moved onto the next slide³. The presentation and explanations were so quick that while I was still noting down a theorem, the prof had moved onto examples, having already finished the proof. I was livid and raised my hand towards the end, stating that it was going too fast and that I hadn’t gotten anything in the last half hour. Actually I had, but it was deplorable.

This had me fuming after class². I vented in my office to other students. They managed to calm me down a bit, but I was still pissed. It’s only right now, 7 hours later that I’m no longer that annoyed with it. An algebra student told me that what we saw wasn’t really that important later in the course. It’s still made me upset.

What were we seeing? Section 7 in Chapter 1 in Hungerford’s Algebra. The theory wasn’t really hard, it was just a simple introduction to category theory. However, at the speed that the subject matter was presented, no one had time to understand much, unless they had taken this class in the past. Since I was struggling in English, I wonder how much the Taiwanese students were struggling, as the class was in English, as well as the slides.

Oh and I just checked, the slides from her latest lecture aren’t available on her website yet. Super-annoying!

III

It’s past 1AM here, and I’m listening to Glee Cast, Ep. 6, Halo/Walking On Sunshine. It’s really soothing because it’s so beautiful. I’ve never been a big fan of Beyoncé, but Halo is an incredible song. I like Diana Argon⁷.

It’s rare to see such beauty on network TV. Vitamin D, Ep 6 of Glee was incredible. The Halo/Walking on Sunshine mashup was amazing. It’s beautiful to watch and to listen to. It’s probably the best number of the series up to date. This show is one of the rare happy shows on TV. It makes you feel good watching this. It’s amazing to see that Ryan Murphy was able to so adequately distill happiness and provide it to us in Glee.

I was never a fan of musicals, though I could always appreciate good singing and good choreography. I really loved the pilot episode of Glee and find myself actually looking forward to the musical numbers. The storylines are predictable, yet engaging. There is so much talent on that show, it’s quite amazing.

That Halo/Walking On Sunshine mashup, I must have watched it about a dozen times tonight. It made me really feel good. The perfection is almost overwhelming.

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Relevant Posts

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[¹]: My real analysis professor spends 3hrs a week copying Measure and Integral by Wheeden and Zygmund onto the whiteboard.
[²]: A lot of swearing was involved on my part. I was careful not to say anything bad about the professor, just his methods. My colleagues encouraged me to go see him to bring this up, but I know better. In Asia, as a student, it’s best not to make any waves, not to disturb the order of things, and give face to your seniors.
[³]: I was already grumbling while this was happening, behind the yes-girls†.
[⁴]: Basic analysis and set theory. It was mind-numbing.
[⁵]: 22 students in total in this class. Between 5-8 are pure math students.
[⁶]: In math, powerpoint presentations aren’t bad, but they are terrible if not used properly. If text disappears in a swirl of animation, it’s bad because students don’t have time to note stuff down. This was never a problem in Canada, but seems like a big problem in this class.
[⁷] Argon isn’t the best singer, hasn’t got the vocal range of Lea Michelle, but she’s an incredible performer. I like seeing her perform in the musical numbers.

[†]: These are the two girls sitting in front of the class, who nod and laugh at the right time. It’s ultra-annoying.

4 Responses to “Mathematical Teaching Methods”


  1. 1 antoine October 17, 2009 at 00:18

    I can definetly understand the frustration. Its just too bad, because after a while, it just transforms into carelessness and turns a few potentially useful hours in class into a lot of work at home.

    I have always had a very hard time understanding math for some reason. I did not suck at it, but I was mostly relying on memorized examples to do tests and homeworks; this technique works well until you hit the last math courses of undergraduate engineering, at which point you come to realize that all those years of memorization were pretty much a waste. I remember very little of all my math class because I did not understand anything, I just blindingly applied what I was taught.

    That’s until I figured out I actually needed to use concepts to internalize them. For a personnal project, I had to program a 3D engine, which was a lot of fun, but mostly gave me an opportunity to relearn basic linear algebra (3D is just operations on matrices). Applying math in a meaningful context creates intrinsinc motivation and makes all the difference in the world with regards to the quality of the learning process. So much that I am now really confident with my understanding of basic linear algebra and have a solid ground onto which I could progress to study more complex stuff.

    Of course, that only applies to undergraduate mathematics, which is mostly taken by people who do not give a damn about it or just fail to see the usefulness because it fails to inspire them. For you and other graduate students, I suppose finding the motivation to learn is really not a problem, because after all, your field of study is testament to your genuine love of math.

  2. 2 range October 17, 2009 at 00:28

    I’ve always enjoyed abstract math. Yep, I totally agree that memorization basically doesn’t work at a certain level in math. This is especially true in the pure math classes that mathematicians take. It’s basically just a bunch of exercises that you have to do. If you don’t, you can’t do well.

    Before, I was really into numerical analysis, but my end of studies project in math ended that interest. I hate numerics. I like abstract algebra and analysis. Algebra is the foundation on which calculus can work.

    I used to really love linear algebra, but you could only go so far in that field. After a certain point, there isn’t much more to learn.

    It’s cathartic to write about these issues on my blog. It relieves the anger and frustration. Basically, today I’m totally chillaxing. I’m no longer angry with the prof. Maye that’s because I listened to that Glee musical number quite a few times last night. :)


  1. 1 Categorically Yours & Typographical Musings† « memoirs on a rainy day Trackback on October 24, 2009 at 17:54
  2. 2 Categorically Yours & Typographical Musings† « memoirs on a rainy day Trackback on October 24, 2009 at 21:28

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