The Teaching and Learning of Mathematics is NOT About “Right Answers”
Yesterday, I posted this on Twitter in response to our governor’s opinion on math instruction and curricular materials.
And, as expected, this pissed some folx off. I mean if you like to watch people get angry on twitter...read through those replies.
But, seriously. Here is what I meant:
The teaching and learning of mathematics is NOT about answers. It’s about ideas.
If you're like me, you learned math in a way that suggested that the answer was the most important part of the process. Now that I've been teaching for over 20 years, I’m no longer convinced that’s true. For me, the teaching and learning of mathematics is more about the ideas that students have than it is about the answer they provide.
See, I want to listen to my students. I want to know what mathematical ideas they have. I want to know them as mathematicians. And to do all of that, I MUST look at how they are thinking about the problem, and not just whether their answer is right or wrong.
Yes, the answer is important. But, it is not always interesting, and it usually gives me very little insight into what the student actually understands.
Now – the application of mathematics in life provides important times where the answer matters. Yes. I want my bridges to stay up and I want my doctor to get dosage right (see the comments). But, this is NOT what we are doing as teachers. Learning is messy. Teaching is messy. The process is messy. Not just in mathematics.
When my students are learning mathematics, the answer is less critical. It only tells me one thing. How a student arrives at that answer tells me LOTS of things.