It’s Okay To Be Wrong
Continuing on the theme of mathematical thinking this week, I was reflecting upon an thought I had pondered a few weeks ago. (Yes, I realise that there is a lot of reference to thinking in that previous sentence. I do that. A lot.) I have been trying to figure out how to help my students learn how to successfully fail so that their mistakes become stepping stones to improvement instead of stumbling blocks that hinder them. I think we are making progress in this, although even the process has had its own ups and downs.
Teaching my students different ways to express their mathematical thinking led us to an interesting conversation today. I have repeatedly expressed that I want them to write down everything they are thinking as they are working through a problem so that I can see their thought processes. As we worked through a problem today, I asked students to tell me how they would solve it and why they would do the things they did. The first step a student suggested turned out to be incorrect. Instead of erasing everything and starting again, as another student suggested, I just noted that a step was incorrect and continued to record what was said to me. Later I had to cross something out as a student realised that what she had said was not really what she meant. We ended up filling the entire whiteboard easel with the various attempts at solving the problem before finally reaching a solution that met all of the parameters given.
Before setting the class free to work on their own, I asked them if the work shown was acceptable, even with the mistakes. They agreed that it was. I repeated what I have been saying throughout the year: It is absolutely okay to make a mistake and fix it later! It is absolutely okay to record all of your attempts at solving a problem! Doing so shows me that they are thinking about the problem, not just solving it. Problem solving, on its own, is simply not enough for our 21st century learning. It must be combined with critical thinking. And we are getting better at it!