I don’t think we get it yet.
I thought we were close. But today’s article in TeachThought (a normally fabulous site) just crushed my optimism.
They write:
In mathematics, instead of focusing on correct answers, focus on correct process. If students are learning and following the correct process, then they will eventually also produce the correct answers. A good automated tutoring program can help by honing in on the exact step a student struggles with when attempting a challenging problem.
It’s not about the process!
The article is about changing from a fixed mindset to a growth mindset.
(A fixed mindset means you’ve already decided if you’re good or bad at something. With a growth mindset, you know that you can be good at something if you take on the challenge and give it effort.)
When someone says, “learn the process,” it means “learn the steps.”
Indeed you can do much of math with steps. But the “steps” that we teach are merely the shortest route to a final right answer.
If we teach the process, or the steps, we’re still depriving students of growth mindset activities!
Processes enforce a fixed mindset.
Using a growth mindset means learning through thinking, taking on challenges and learning through failure.
Processes are steps. Discrete things to memorize. Processes that are handed to you aren’t thought about. They aren’t challenges.
And processes certainly do nothing for failure – unless you mean failing to do the process right.
Teaching processes enforces a fixed mindset – if you can learn the processes, then you’re good at math. If you can’t learn the processes, then you’ll assume you aren’t good at math.
And if math were processes, you’d be right!
It’s about thinking!
Instead of processes, we should teach – or facilitate – thinking about what each math concept means.
If a student understands what it means to be the graph of an equation, he can graph anything.
He’ll know what it means for a point to be on a line. He’ll figure out that the tilt of a straight line shows up in the equation. He’ll notice that the intercepts show themselves in various forms of an equation.
And he’ll get it.
So, teachers – let’s get it!
Stop the madness! Quit answering questions and start asking questions back.
If a student can do the process, can she extrapolate it to the next concept? Or is she stuck with running a computer program in her brain on only one thing?
If a student can’t do the process, can he think about the underlying meaning? Does he know a workaround?
And can you tell the difference between students who are running programs and really getting it?
Share your thoughts in the comments – and don’t forget to tweet too!
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Very well said. I just covered solving equations and inequalities, and the whole time the process was thought about in terms of figuring out what was happening to the variable and what should be done to get it by itself.
What frustrated me to no end was to hear students recite rules related to graphing in equalities on a number line that did not work when the variable is on the right.
Going to share this article with my department as we have been focusing on transitioning students to a growth mindset.
Thanks.
Chris – it sounds like you are doing sort of what I was doing! I did a short video of it here.
When they start spouting rules senselessly just kills me!
I look forward to hearing how your transition goes – please share anything, as I’m in that transition too.
This is actually something I’ve been struggling with lately…
Perhaps a year ago, I would have responded to this post with an enthusiastic “yes”, but right now, a year into grad school, I’m a little less sure.
I’ve always learned by intuition, and rarely proceed with something until I “understand” it, even if I “know the process”, but lately I’ve seen that sometimes I just need work through something blindly, before going back and understanding what’s “really” going on.
A particular example is something called “path induction” (or “identity elimination”) in type theory–it’s a notoriously difficult concept (amongst type theorists, anyway), and I beat my head against it for over a month. I then worked through about a dozen exercises and simple proofs blindly using the rule, and then went back to try to understand what it meant, and suddenly, it was almost completely clear.
Certainly, at school, process is (devastatingly) over-emphasized, but I’m less sure that teaching process is necessarily bad–it has routinely helped me gain intuition for concepts I’m struggling with.