Thoughtful Problem Solving

1) Thinking tasks: The goal in giving students a thinking task is to present them with a problem where the path to the solution isn’t laid out for them within the problem. By giving students problems where they are having to think about not just the answer to the question(s) they’ve been asked, but also what approach(es) would allow them to find the answer(s), it helps them to think creatively about the work, rather than simply imitating a procedure they’ve been shown. At the start of the year, we practiced this with a series of non-curricular tasks, and as we’ve moved into the curriculum, I’ve been working on introducing new concepts through thinking tasks. Illustrative Math often starts with tasks such as these, so it’s been a great curriculum to tailor to this approach. We start most classes with the students joining me at a whiteboard where I explain what their challenge is that day. I try to give them just enough that they have the information they need, but leave it cryptic enough that they may need to work together in order to make sure they’re clear on exactly what they’re being asked. Those conversations happen when I put them into…

2) Visibly random groupings: One of the goals in building a thinking classroom is to instill in students the idea that everyone is both able to and expected to contribute to the work. A natural corollary of that premise is that students should be able to work with anyone in the room, and that I believe they are all capable of contributing to the work. By taking my decision making out of the group making process, it takes away the ability of students to say things like “oh, Scot put those two together because they’re so smart” or “You must be working with me so you can help me,” and hopefully leads them to see themselves and each other as people who can contribute to the work, as they work through that day's problem(s) at…

3) Vertical non-permanent surfaces: Another goal of building a thinking classroom is to get kids to dig into the work without getting hung up on trying to immediately get to the correct answer. Through his research, Liljedahl found that when given a thinking task, the shortest time between getting the task and writing down their first idea happened when students were working at whiteboards. (The reason for the longer descriptor is to emphasize that the work can happen at other surfaces as well, such as a window.) Because what they are writing doesn’t feel like as much of a commitment as writing an idea down on paper, students are more willing to try things out even if they are unsure of whether their initial ideas are going to work. Over the first month of school, I’ve definitely seen the impact that working at the whiteboards has had on students as they’ve been more willing to dig in quickly as they approach new tasks. Having students working at whiteboards has other advantages: It allows me to more quickly see which groups are on track and who might need a thoughtful hint or question in order to help them to move forward. It also allows for the mobility of knowledge between groups. Both by checking in with nearby partnerships and by simply noticing what other groups have done, groups who are feeling stuck can get an idea about how to move forward.

What I appreciate about these approaches, and what I hope is evident in them, is how they dovetail nicely with the educational frameworks we’ve built at Fayerweather. As opposed to “traditional” approaches to teaching math, this structure meets students where they are, honoring their own curiosity and encouraging them to seek out pathways of their own to find answers to their questions. And they do all of this not in isolation but in community, learning from, teaching, and relying on one another to solve problems and build something bigger. If we want students to see math as something with practical, everyday significance – and I do! – then it starts by modeling the kinds of creative and thoughtful ways they’ll engage with it throughout their lives.