The little gifts

It's the little gifts I get that make this job worthwhile.

Yesterday one of the hardest-working of my second section's Calc I students came in to ask for help with a few of the related rates problems we've been working on for the past few days.

She didn't need much help, really: she understood most of it quite well already.

In fact, she's needed little help for the past few weeks. She's redoubled her efforts in our class, and despite not having had calculus before (whether or not that's a liability is a topic for another post) she's clearly picking up on the new ideas far more readily than most of her peers, many of whom are much more experienced with these topics.

I was particularly pleased by what I saw on the rough draft of her homework: "Know:" and "Need:" appeared ubiquitously on her paper. In response to my constant exhortation "to identify what you know and what you need," a number of my students are making their responses to this exhortation explicit in their writing, just as I've done on the board before them. The sooner they appreciate how crucial those two simple bits of information (the needed and the known) are in solving a mathematical (or, for that matter, any) problem, the better.

This evening's review session brought me another little gift: little more than a week ago maybe one or two of a class of thirty students would have remembered to include the "dy/dx" at the end of the implicit differentiation of y², nearly every person present at the review called out for its presence in unison, as though their intonation might mark the coming of a mathy god.

I remarked: "did y'all notice that? A week ago almost no one understood what the Chain Rule meant us to do right here. By now it's old hat to most of you."

It's the little gifts.

I've learned to be more patient in waiting for these little gifts, but to be more mindful of them, to expect them and appreciate them, to know that they're bound to come.

It's only every now and then we're likely to win awards for our teaching, no matter how outstanding our teaching is.

It's only every now and then our students are liable to approach us once a course is done and say "I truly appreciate all that you've done for me" or "you've touched my life, in a good, good way."

But if we're doing right and we're doing well, nearly every day will bring us little gifts: one student finally grasps the difference between "equals" and "implies"; another (unaided) drafts a beautiful document in LaTeX; a third, in the middle of an in-class group activity, helps a fourth through an application of logarithmic differentiation. Elsewhere, a colleague borrows a thing or two from your teaching toolbox or asks to use a version of the rubric you'd written for assessing the quality of students' writing, while another asks you to come and have a talk with their faculty: "maybe you can show them a few of the things you're doing in your classes, and they'll understand that there are alternatives to the way they've been doing things for years now."

What little gifts will tomorrow bring?