By Jamie Walker, posted February 27, 2017 —

What is it that we really want our students to gain from learning mathematics in our schools? By the time they graduate from high school, we would like them to have learned to solve linear equations, to apply the properties of special right triangles, and to prove trigonometric identities. However, are these lasting lessons? I expect that most of the formulas my students diligently memorize are forgotten shortly after their tests. Yet I believe that most of the skills and lessons we teach are invaluable. We teach so much more than these formulas. We teach our students logic and reasoning. We teach them the value of a good argument and why having a valid proof matters. We teach our students to ask questions to help them see flaws in the arguments of others or to strengthen their own conjectures.

Stop and think about your lessons over the last few weeks. Was there a point when you were able to sit back and let your students discuss possible solutions until they came up with one that they were pleased with? Did this perhaps happen during a whole-class discussion that you facilitated? Maybe it was like the quiet discussion two of my students engaged in recently when working on this problem:

Student 1:      Wait; why did you get 9? I got 5.

Student 2:      I added 7 and 2.

Student 1:      No. Aren’t you supposed to subtract? It’s dividing. That means subtract exponents.

Student 2:      I did subtract. If you take 7 minus a –2, that’s the same as 7 plus 2.

Student 1:      Oh yeah. Minus a negative. I forgot. Thanks.

From small mistakes regarding the properties of negative integers, two students were able to clarify their arguments and gain a deeper understanding about the rules of exponents.

I do my best to foster an environment in which these little discussions are encouraged. The more these conversations occur, the more often my students can practice their ability to reason and critique.

I teach the lowest level algebra 1 offered at my school. For a variety of reasons, my students come in having the belief that they are not good at math, and the last thing they want to do is be called on or ask a question. They certainly don’t want to discuss a problem openly. They are afraid that they might say something wrong or that they might not have anything of value to offer to the conversation.

I stand firm in the belief that everyone has something of value to offer. Don’t worry if you make a mistake. Mistakes are great. We learn more from our mistakes. It’s all about how we treat those mistakes. We don’t laugh at them; we question, we help, and we learn. By not only making room for mistakes but also by valuing them, I am able to show my students that every thought is worth exploring.

How have you made your classroom a safe place for arguments and debates? I would love to hear your stories.

Jamie Walker, walker.jamielynn@gmail.com, is a mathematics teacher at Providence Catholic High School in New Lenox, Illinois, where she teaches algebra 1 and geometry in a 1:1 environment. She shares literacy strategies on her webpage http://mathematicsplusreading.weebly.com/ and tweets from @walkerjamielynn. Walker has a passion for increasing literacy in mathematics and works to collaborate and share on the Twittersphere.