My 9th graders have been learning right triangle trigonometry. We decided to include this topic in the 9th grade math curriculum because they are also taking physics. An understanding of trig will help with analyzing two dimensional motion and also with analyzing forces.
So, we did a bunch of problems and they mostly got it. But not all of them and not all the time. I used Kelly O’Shea’s Whiteboarding with Mistakes idea and had them produce solutions with common mistakes that students might make when solving these kinds of problems. Then the other groups had to identify the mistakes in a given solution. It led to some interesting discussion.
“Why would you want us to deliberately make mistakes?”
What a great question, I responded. Why do you think? Here’s a sampling of their responses:
- To make us aware of mistakes that we can make.
- To make us pay closer attention to our work.
- To have fun.
- To challenge each other.
- To teach us how to analyze work.
- Because without mistakes there can be no learning.
A little side note.
The 9th graders at my school also take an engineering class where they practice and practice the engineering design cycle. They identify a problem, design a solution, test it out, see where it fails, make improvements, and begin again. The teacher is very clear about learning from mistakes. Apparently, that message is being heard as evidenced by the last comment.
“Because without mistakes there can be no learning.”
I’m not sure that I agree with that exactly; I don’t think that mistakes always have to present for learning to happen). I do know that I tend to learn more from situations that give me unexpected results. But the better thing here seems to be that we are helping our students to understand that their work doesn’t have to be perfect the first time. They are kind and curious and smart – and not afraid of making mistakes.