I'm not particularly "good" at drawing. My kids and wife are definitely artistic souls, and my wife has had some training. I teach at an independent school that is known for its spectacular arts programs. I shudder to think about letting my students see my drawings. When I have to draw things on the board, I tend to intentionally do blocky things so the (bad) drawing won't be the focus. I self-deprecate in front of them. I make jokes about it.
Does all that sound familiar? Sound at all like math, physics, or computer science students? Surrounded by "mathematical" minds and triggered by impostor syndrome? Making self-deprecating jokes and embarrassed to be exposed?
It's not that I have zero experience in drawing. When I was around ten I spent a lot of time copying comic book drawings (mostly by tracing). In high school I took two semesters of drafting and one of architecture, so I know a little bit about line drawings from flat angles and I can kind of still do perspective for really simple objects. I took photography for a couple of semesters (back when it was still all chemical dark room work).
But I haven't practiced, and I don't have a broader toolkit of skills and approaches like I would have gotten from a visual arts class. Ask me to draw something that's made of lines, and a little shade, and I might be able to do a passable job. I can occasionally do something that looks pretty good, but it's inconsistent. I don't really know how to use the tools, I don't have a vocabulary for describing the work. I don't know how to transfer what little I do know into new situations.
So when I looked at today's drawing in my #draweveryday challenge, "Bubbles", I'm like, "But I don't know how to draw bubbles!"
"But I don't know how to factor a quadratic when there's a number in front of the squared term!"
I feel like I'm at the "I don't even know how to start stage". What do I teach my students to do when they don't even know how to start?
I teach them to make a guess. In physics, making a good guess will help in figuring out the right units and the right order of magnitude. It will help them develop intuition, and it gives them a target to work toward through calculation and a fixed point to iterate from. A guess is a focusing device.
So I just started making guess sketches. They're not good. But now I've got questions. How do I make things look spherical when they don't have features? How do I indicate a light source? I was imagining a bunch of bubbles in a semi-dark room, with a light streaming in from the side making one side of the bubbles reflect brilliantly and the other side in darkness. I was imagining a bubble on the point of popping, when the film has gotten very thin on the top and the thin-film interference makes the top dark, with iridescent streaks running down the sides. And I was imagining a face blowing into a bubble wand, with the bubble stretching out away from the wand, billowing as it prepares to pop loose.
One thing I notice is that in drawing, while I have no idea how to accomplish any of those things, I do have a sense of how technically proficient (or even artistic) products might look when complete.
Do math students have a similar sense of what a technically proficient math product might look like when it's done?
How do we teach them to self-direct their iteration, when they don't understand the target?