Saturday, October 01, 2011


Yesterday I ran into one of my Precalc students outside of class. I was on my way back to Robinson Hall after teaching my Abstract class over in Karpen; Becky was en route to the library with the rest of her LANG 120 class. There they'd be discussing the use of library resources in conducting research.

We chatted briefly, and I asked her if she was still considering a math major. (She was one of two in that section who, without prompting by me, indicated interest in the major at the outset of the semester.) "I definitely am," she said excitedly, and then a look of worry spread over her face, "do you think I still should?" I was a bit thrown off and only after a few seconds managed to reply with something like "of course!" She went her way and I went mine, but our encounter stuck with me. Why had she asked what she had?

I suspect it may be because she may not feel as confident in her math ability as she did at the start of the semester. Though she's done well on every homework set and on every quiz, like everyone else in the class she's made her share of mistakes and hasn't presented complete understanding of everything we've talked about. Might she believe that only those who can complete Precalculus with flawlessness and perfection are worthy of pursuing a degree in mathematics? (Only later did I think of an apt analogy: as I'm highly unlikely to ever run a four-minute mile, might I just as well give up on one of my favorite hobbies?)

After thinking it over, I found that I could understand Becky's belief, given the traditional structure of mathematics education, home to bell-curve-based grades, punctilious point-based assessment, and lecture-based teaching. There's an air of elitism to the way students are often ranked and ordered, made to fight with one another for a scant few As. The unsaid assumption in classrooms where deep and steep curves guarantee a normal distribution of grades is that only the best need move on, and that the others' services will not be needed. Detailed rubrics with single-percentage-point resolution signal to the student that mastery of fine detail takes priority over authentic understanding. (No wonder students clamber after every point, wondering what it is that separates a score of 8/10 from a score of 9/10!) Fast-paced lectures make sure sure the students who start off slowly get little chance to get ahead; the quickest students (who are often, but not always, the brightest) control the pace in these classes.

All of these factors discourage students who are excited or intrigued about math, but who are put off by the way in which it's often taught. We can't afford to turn these students away. The fact of the matter is we, as a society, need more mathematicians than we can possibly prepare, and we do no good in discouraging anyone who's passionate about the field from pursuing it further. We do well to let as many students through the gate as we can, and to give them all of the support and encouragement they need to develop their skills fully. We do well to eliminate curves and to downplay in-class competition between students. We do well to "coarsen" our grading scales to accommodate "big-picture" thinkers who might miss a detail or two but who grasp complex systems in their entirety. We do well to step away from our classroom's center stage and let students take our place, so that it's not to the top ten percent that we teach, but to the class as a whole.

The bad news is that these practices are not universal; the good news is that they are more popular than ever. They're in use throughout my department and many like it. The youngest math teachers (at every level) are more adept at applying them than their older peers. These teachers are daily developing new tricks and techniques to make these practices more effective, and they're not shy about sharing these tricks and techniques with their colleagues and with their students. The future is bright for math education.

Stick with it, Becky! Welcome to the team. You're in good company. You'll do wonderfully.


Gillian said...

I have a confession to make. I'm getting an engineering degree which is essentially an applied math degree, but I don't know my times tables and I still have to add numbers on my fingers. The nice thing is once you get into higher math, it's mostly letters, pi, or the number zero! And my calculator is my new bff. I think people psych themselves out of pursuing a math degree because they don't fully grasp the concepts or the mechanics, but there is plenty of time to learn and master those. I've had 3 levels of calculus and still need to review the simple concepts I learned in Calc I. Each time I re-encounter these concepts, they get easier to understand.

DocTurtle said...

Thanks, Gillian! I'm glad you chimed in. Your words remind me of the Calc I class you were in last fall, in which several people were completely unafraid of asking questions, with no fear of "looking dumb." These questions unfailingly drive us toward deeper understanding.

Becky's class this term is similar: there are a handful of people in there who ask fantastic questions. Kendall's questions are often pragmatic ones that help us discover the inner workings of the computations we're plowing through, and Thomasina's often offer guidance and ways of reflecting on the computations once we've done. (She'd be a great teacher.) Then there are Oswaldo's questions, which always seem to straddle the line between mathematics and philosophy. I'll need to meet up with him outside of class sometime.

I love that class! I never know where we're going to go on a given day.