Two great posts recently got me thinking about the quality of questions we ask students. I feel like I have a large and growing library of rich tasks that are worth exploring and provide my students opportunities to learn meaningful math. Figuring out what questions to ask students to facilitate learning through these tasks is much tougher for me.
Then, he asks students which tools would be helpful to answer the question, and which tools would be unhelpful. I love this question. It really gives life to Math Practice 5: Use appropriate tools strategically. Here’s a great image of his whiteboard:
I was impressed with the variety of tools that Andrew’s students were familiar with — it was a long list, including functions, lines of best fit, tables, Desmos, quadratic equations, and more. There’s definitely a barrier to entry here in that Andrew set this question up by providing his students with a huge number of tools. That said, it’s one different way to provoke high-quality student thinking about math, and I’m excited to give it a shot.
Second, from Jennifer Wilson, a description of a fascinating task and her facilitation of it, around finding the amount of water in this tank:
You should check out the entire post, because it’s excellent and full of great questions, but one question in particular struck me: she asked her students what they saw that wasn’t pictured — and then asked them to name more and more that wasn’t pictured.
This strikes me as a key conceptual skill in geometry — drawing auxiliary lines, seeing structure, and breaking down large objects into smaller, manageable ones. I like it because it draws student attention to non-routine ways of solving problems, and seems to lend itself to the kind of insights that math class should be about, instead of practicing procedures and repeating steps.
It’s easy to fall into the trap of finding great tasks on the internet and getting excited about how rich and interesting and open middle and everything else the tasks are, without thinking of how to facilitate them. I’m still trying to settle on what I want to focus on improving this year, and the quality of my questions, and task facilitation techniques more broadly, might be a good area to work on.