Queen's University

Lessons up in smoke

You can lead students to the classroom, but you can’t always make them think. Prof. Peter Taylor's bold experiment to find a new way to teach mathematics didn't turn out quite as he'd hoped...

Not long ago I was in Toronto to visit my new grandson, Dawson, Arts 2027, and I chanced to drive past a restaurant called Phil’s Original BBQ on College Street. Underneath the big sign above the front door was the slogan: “REAL SMOKE, REAL SLOW, REAL GOOD.” I pulled my car over to the curb and stared reverently at the red neon writing.

“Real smoke.” education theorist Alfred North Whitehead’s critical first stage of learning (romance) is widely interpreted as lighting the fire, but for me the real driver is the smoke – that shroud of mystery that ­assaults my senses and sends the students fleeing to the clear haven of pen and paper.

In the Winter issue of the Review, I wrote optimistically about a somewhat innovative teaching approach for my first-year math classes. My article (“A new way of teaching”) listed four objectives – independent student learning, peer teaching, a simpler, leaner curriculum, and, ­finally, an assessment system with more integrity, that is, with a better fit to my learning objectives.

“If it were solely for interest and learning mathematics I would choose your approach; however, when it comes to getting marks I require a more systematic approach. So I am attending Prof. X’s class.”

My point was that while the first stage of this approach is essentially my job (as teacher), the second stage (precision) ­really belongs to the students. That’s what independent learning is about, and the point of the leaner curriculum is to allow us to go “real slow” and get in some good pen-and-paper time. In the event, however, they did indeed flee from the smoke, but not to pen-and-paper, rather than ­another section of the course.

I started the term in fine form, challenging my students to invent a multi-dimensional version of the derivative. But by the start of Week Two I’d already lost a good chunk of my class (pun intended), and on Tuesday of Week Three, attendance hit an all-time low of 20. I expressed my alarm to those remaining and announced that I would administer a survey on Thursday.

Word got around, and I received about 60 great responses. A dominant theme was the matter of marks.

“If it were solely for interest and learning mathematics I would choose your approach; however, when it comes to getting marks I require a more systematic approach. So I am attending Prof. X’s class.”

“Your approach teaches us understanding but we can’t afford it.”

“You don’t go fast enough. We need traditional lectures to cover all the material.”

And finally this wonderful observation: “I get confused.” (smoked!) Of course, there were also a number who found my approach to their taste.

In addition there were a few good organizational comments. For example, the students explained that there was almost no problem-solving happening in my small-group work. “Sometimes someone in the group already knows what to do and explains it to the rest of us, but not very well. Otherwise we get nowhere.” And, “You should keep control more.”

Half of our first-year students are not really ready for universityc . . . their learning objectives (and their learning skills!) are weak and fragmentary. . . .  They might well be better off doing other things for a few years,

Keep control. Well I did that. I moved more into presentation mode, still asking questions, but often answering them as well, and I paid more attention to the technical stuff that would appear on the exam. And my post-doc Ami gave me weekly feedback. The class settled down to a steady contingent of some 30 students. They were an awesome group to work with and very responsive. Unintentionally, I’d found a way to “stream” my class.

What have I gained so far from this experience? I believe that I have renewed faith in and a better grasp of the lecture as a fundamental vehicle for teaching. But there are significant provisos.

I perceive three systemic challenges to the lecture as it ought to be. The first is that most first-year courses (perhaps especially in science and engineering) seem overly packed with material, and even the best intentioned lecture will collapse under a heavy information load.

Secondly, half of our first-year students are not really ready for university. For ­example, their learning objectives (and their learning skills!) are weak and fragmentary. In particular, they have no idea what to do with a lecture and why the pen-and-paper refuge is so significant. They might well be better off doing other things for a few years, but for now we have them with us, so we have to rebuild their learning skills, which were in good shape when they were children.

That’s not an easy task. It takes precious class time, and it is removed from our zone of professional comfort. We also need to do a better job of matching our exams to our pedagogy. These are the aspects I will be working on next year. Only then can my slow smoke be “real good.”

Queen's Alumni Review, 2010 Issue #2Queen's Alumni Review
2010 Issue #2
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