I am a programmer.
Here are some of the things that I love.
- I love programming.
- I love abstraction and purity.
- I love complexity, and fiddly details.
- I love math.
- I love knowing that I have powers and knowledge that other people don’t.
I want to talk about that last one. It’s the one I’m least comfortable talking about, and I think it’s somewhere near the center of a number of discussions I’ve had with others and with myself about motivation, teaching, and the future of Computer Science.
A few days ago, I picked up G.H. Hardy’s A Mathematician’s Apology again. He is, to be blunt, an unreconstructed bigot in the area of Native Mathematical Ability. He believes that either you got it or you ain’t, and if you do, it is a thing that sets you apart from other men. (Not from other women, because in the 1920s, everyone was a man. Look it up.)
On the one hand, I can see the appalling lack of mental rigor in some of his arguments. I won’t go point by point, but it appears to me that the nailed-down-mathematical-argument part of his brain simply wasn’t engaged when he made arguments like the assertion that in general those with mathematical talent aren’t likely to have any other useful one.
Nevertheless, much of his thinking pervades mine. I think that thinking such as his fuels much of my own drive (such as it is), and indeed is relatively close to my central joy in life.
Let me put it differently, and more positively: Richard Feynman writes about the simple joy of discovering things for oneself. I completely subscribe to this. Yesterday, of my own accord, I examined the notion of continuity on functions from the reals to the reals and the more general one of continuity on topological spaces, and convinced myself that they’re perfectly aligned (on the functions from reals to reals). That’s a really beautiful thing, and I wanted to run around and tell everyone about it (and here I am doing that). I got to figure that out for myself, and that was a beautiful thing.
Let’s dig a little deeper, though, and try to understand why that should be a beautiful thing. Why is it thrilling to know things, or even better to discover them for ourselves?
Ultimately, I think that it comes down to this: it gives us power, and fuels our egos.
That doesn’t sound very nice, does it?
Well, in many ways it’s the same thing that drives us to work hard at anything. Why do we run races? Why do we compete at Golf? Why do we work hard for promotions, or try to explore new lands? Why do we … do anything?
Well, on a basic level, we’re trying to survive as a species. In order to do this, every individual is programmed to pull hard, to do her very best work, to train harder than the other guy.
When we put it that way, it doesn’t sound so bad. Survival of the species, and more locally, survival of our own DNA. I want to be the best at something, in order to give my DNA a competitive advantage. This is locally visible as an advantage over other people, but manifests itself globally as a path toward improving the survival of the species.
Looking at it in the global context, though, tempers the drive for individual success; my success benefits the species only when it doesn’t come at the expense of the species as a whole. If I try to ensure the success of my genes by eliminating those around me, I’m not benefitting the species, I’m hurting it, and I won’t be around very long.
So, what do we have? We’ve developed a system where we compete—to a point. We compete in venues where our individual success leads to improvement for our families, our communities, and our species.
But enough about you.
What does this mean for me?
When I was a child, I did well at math. I understood things easily, and none of the concepts gave me trouble. When there was an interesting new concept, I spent a bit of time thinking about it, and then I understood it. I got the same kind of satisfaction from math that you might from a video game: a bit of work, and lots of instant gratification. To be sure: I had a privileged upbringing, and lots of attention from teachers to help me succeed. I have relatively few illusions about the part that my background made in my success.
It’s no surprise, then, that I chose to focus on math; Math class was my favorite, and until college, I could convince myself that I was the best in every class (following Hardy here, I’ll suggest that some mild egotism is not out of place here—it’s helpful to believe that you’re the best, even when the evidence is weak).
In college, I discovered lots of folks that were better mathematicians than I was.
Hmm… I can see that I’m going astray here; from a discussion intended to be about the motivations of programmers and programming students, I’m drifting over into nature-vs-nurture.
Further Editing Required.
Or, as Piet Hein put it,
Things Take Time.
One of my children is in third grade. As part of a “back-to-school” night this year, I sat in a very small chair while a teacher explained to me the “Math Practices” identified as part of the new Common Core standards for math teaching.
Perhaps the small chair simply made me more receptive, taking me back to third grade myself, but as she ran down the list, I found myself thinking: “gosh, these are exactly the same skills that I want to impart to beginning programmers!”
Here’s the list of Math Practices, a.k.a. “Standards for Mathematical Practice”:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with Mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Holy Moley! Those are incredibly relevant in teaching programming. Furthermore, they sound like they were written by someone intimately familiar with the How To Design Programs or Bootstrap curricula. Indeed, in the remainder of my analysis, I’ll be referring specifically to the steps 1–4 of the design recipe proposed by HtDP (as, e.g., “step 2 of DR”).
Let’s take those apart, one by one: