“What you do speaks so loud that I cannot hear what you say.” ― Ralph Waldo Emerson
Since the first day of school, I’ve been working hard to try to establish a classroom culture where students feel comfortable taking risks, asking questions, sharing and building on each others’ fully-formed and partial ideas, and acknowledging and correcting their mistakes; where all students feel that their contributions and questions are valuable and worthy of consideration. I have tried to do so by pointing out (less often than I should) when a student or a group is exemplifying one of these norms, by waiting (again, less often than I should) after questions and contributions to give more students the time they need formulate and share their ideas, by giving tasks that are accessible to a wide range of students and can be tackled with a variety of strategies, by eliciting and celebrating different solution paths, by highlighting different kinds of mathematical smartness (h/t Ilana Horn)…
And then, I proceeded to potentially sabotage it all with an inexcusable split-second decision.
On Friday, my Grade 9 class was working in small groups on finding different symbolic representations for a variety of images and situations involving fractional amounts. I brought the whole class back together again and invited different groups to share their representations. This was one of the images:
Different students explained why they chose to represent the image as 4/10, 2/5, 6/10, 3/5, 0.4, or 0.6. I carefully recorded their reasoning and their names for all to consider. Then, another student raised his hand and said he had another way of looking at it: “You can also look at it as 0. There are 0 red, or blue, or purple slices colored in. So it could also be 0/10.” I chuckled, acknowledged that this was another way of seeing things, and moved on to the next question. I did not add his explanation to the list, nor his name. For what it’s worth – which is nothing – we were running out of time, and I wanted to, you know, get to the point.
“Words cost nothing. Actions can cost everything.” ― Aleksandra Layland
I could have easily forgotten about this incident had the student not came up to me after class and asked, in a hurt voice, “Why didn’t you write my explanation, too?” He explained his thinking again which was, of course, perfectly reasonable. The instructions did not explicitly suggest that students describe how many slices were grey or how many were white. What an interesting, out-of-the-box interpretation! I had specifically chosen these images because they were ambiguous, because I wanted students to see that things in mathematics aren’t always black and white… and truly, I did not realize until after I wrote the previous line just how ironic it is.
What did my decision to not write the student’s contribution communicate to him and to the other students? That some ideas are, in fact, not valuable or worthy of consideration, even if I have prattled on about the contrary point many times since the beginning of the school year. That indeed there is a correct answer to a problem that can be interpreted in several ways, and that my apparent curiosity in hearing about different solution strategies and interpretations is just a thinly-veiled attempt to hone in on the right one – perhaps, some students had already suspected this, and this incident provided the necessary proof. This split-second decision may very well have discouraged other students from taking a risk and sharing their own divergent line of thinking – and why should they have, if I was just going to blow it off and get back on track to meeting the objective/outcome/target of the lesson?
I fear that I may have done some real damage to the classroom culture and to the students’ conception of mathematics – after all, it’s often the little things that have the biggest impact in teaching. And what if the student in question hadn’t so bravely chosen to confront me about it after the lesson? I may have done it again, and again, and again.
So on Monday, I will start with an apology to my class, as well as a thank you to the student who called me out on my mistake. We will re-consider the problem, and I will listen carefully and record diligently all of my students’ contributions, even if it takes up a little too much time and takes us astray from the path that I had anticipated. After all, in Nat Banting’s words,
“Teaching is a fluid movement through a landscape of lived curriculum. Not a mechanical movement through a planned one.”