I’ve spent some time in the last year experimenting with principles of a Thinking Classroom. Laura Wheeler’s sketchnote seems to have become the go-to summary of the Thinking Classroom framework:

Peter Liljedahl, the researcher behind these ideas, has a short piece on it in Edutopia here, and a longer paper here. I had the chance to meet him and experience the framework at PCMI this summer. I had two big takeaways:

First, Thinking Classrooms are often oversimplified. On the surface, you put students in random groups, send them to vertical whiteboards, and give them problems. In reality, there are a ton of micro-moves much more subtle than having students do problems at whiteboards in random groups that ensure every student is learning and that the class can reach meaningful mathematical goals. Second, each element of the framework has a purpose — it’s not some magic system that causes learning by itself; it requires constant monitoring and feedback to make sure the intent of the Thinking Classroom comes through. As a teacher, my role is to look for specific things, and make adjustments as necessary.

I’m not totally sold on the Thinking Classroom framework. But something I realized this summer is that last year, experimenting with different elements piecemeal, I never really understood how they all fit together. Seeing these connections has helped me to understand why I often felt frustrated with the results, and has me reconsidering my approach for this year.

These don’t feel like groundbreaking ideas, but it’s been helpful for me to step back and think about how the different elements of the framework fit together. Liljedahl advocates for implementing the framework one “level” at a time, and each level focuses on different ideas. Here’s where my thinking is right now, summarizing the big ideas of a Thinking Classroom and what I would need to look for to make sure it’s working effectively.

**Renegotiating Norms **

The first three elements of the framework are all about setting norms for thinking. Students are used to certain norms in schools, in particular in math class. They come in, sit down, face front. They copy things down that are written on the board. They solve simple problems after being shown how to do so. Liljedahl’s hypothesis is that these norms actually prevent thinking, and in some ways assume that students can’t think, by doing so much mathematical thinking for them. The first three elements of the framework try to reset those norms in ways that encourage thinking, to create a baseline of engagement in the classroom higher than what students are used to.

1. Begin with problems. Students are used to coming to class and being shown how to do a problem before solving it. Beginning class with a problem gets students thinking from the beginning, and uses student thinking to launch any instruction. At first these are just engaging problems; later they become curricular. Liljedahl’s site has some good problems on it, and Jo Boaler’s resources are useful as well. I’m looking for students to become more willing to try a problem that they haven’t seen before, rather than giving up at the first sign of difficulty.

2. Use visibly random groupings. Students are used to picking their own partners or being assigned partners or groups. In those spaces, students fall into predictable roles; some students are the “smart kids” who explain things, some rely on copying others’ work. Visibly random groups disrupt those roles, helping students become willing to work with anyone in the room and share ideas openly. I’m looking for students to move between groups flexibly, and for students to fill multiple roles in the group, sharing ideas, recording thinking, and generating new approaches.

3. Work at vertical non-permanent surfaces. Working at desks or tables makes it much easier for students to hide their thinking. Getting them standing and working vertically creates opportunities for collaboration, using erasable surfaces facilitates risk-taking, and orienting the work vertically allows groups to share ideas more easily. Each group should have only one pen to facilitate conversation, rather than a few students working in parallel. I’m looking for students to attempt problems right away, share ideas between groups when they get stuck, and look to each other for help when necessary.

**Helping Students Use Each Other As Resources**

The next five elements of the framework all focus on creating an environment where students look to each other for help, rather than exclusively to the teacher. Liljedahl spoke a lot about learned helplessness — one of the biggest things students learn in school is that they cannot rely on themselves to reason through challenges. These five strategies work together to create a culture of collaboration that empowers every student to own their learning.

4. Oral instructions. This one feels controversial to me — what if a student has trouble understanding ideas verbally? But the purpose isn’t to make sure every student understands every part of a problem instantly. Contrast giving directions verbally with handing each group or student the problem on a piece of paper. Giving the problem verbally encourages groups to make sense of it together, starting conversations and clarifications that lead to more thinking. Giving the problem on paper encourages silent reading and slows the collaboration of the group. I’m looking for groups to try to answer questions about a problem themselves before coming to me, and asking each other questions right after receiving a problem.

5. Defront the room. Students are habituated to look to the front of the room for knowledge and answers. Defronting the room — orienting desks in different directions, standing at random locations around the room, and using the whole room flexibly — breaks that habit. The less students look to the front of the room for answers, the more they rely on each other. I’m looking for students to become comfortable seeing their peers’ work as the most valuable resource for their learning.

6. Only answer “keep thinking” questions. When a student asks a question, it can serve one of two purposes. A “stop thinking” question might be, “is this right?” or “how do I do this?” and might only be asked because the teacher is close by. These questions short-circuit potential learning. On the other hand, a “keep thinking” question is one that allows a student who is stuck to keep working — maybe I tell them the formula for something they’ve seen before that will let them access a more complex problem, or I clarify something ambiguous in the problem to point them in a useful direction. I’m looking for students to persist in asking each other questions and using peers as resources when they get stuck, rather than trying to get the answer from the teacher.

7. Meaningful notes. Rather than having students copy things I write on the board, after a problem and debrief, I ask them, “what do you want to make sure you remember from this problem?” Students need to figure out, themselves or with peers, what the important learning was, and record it in ways that are useful to them. I’m looking for students to step back and consider the connections between ideas and problems and their implications, rather than relying on me for all of their knowledge.

8. Build autonomy. I want students to be able to visit other groups when they are stuck and create their own extensions to continue their thinking. I need to narrate and give feedback on these behaviors to make them a part of the class culture. I’m looking for students to interact less and less with me and more and more with each other as the year goes on.

**Meeting Mathematical Goals**

Elements nine to eleven of the framework are where the learning really happens. The first two conditions could be satisfied — setting new norms where students are doing more thinking, and creating a culture where students look to each other as resources –without anyone actually learning math. These teacher moves focus thinking on specific mathematical goals, and hold students accountable for those goals.

9. Give hints and extensions to manage flow. First, I always want students to be in the sweet spot between frustration (too hard) and boredom (too easy). Hints and extensions help to keep them in that zone. But second, hints and extensions focus students on specific goals. I don’t want to give extensions at random; as students solve problems, I want to keep moving them toward my goals for the lesson. Hints can help to manage the complexities of many groups working simultaneously; if there’s something I want everyone to get to, I can use hints to move slower groups in that direction. I’m looking for students to be constantly engaged rather than frustrated or bored, and for student thinking to zero in on larger goals of a class.

10. Level to the bottom. After a problem or series of problems, we step back to debrief and consolidate understanding. My goal in these conversations is that every student has engaged with the big ideas we’re summarizing (the bottom). If they haven’t, they might as well not have worked on the problem. So I time my debriefs after every group has reached a minimum threshold, and I design tasks, hints, and extensions to help every group get there. I’m looking for students to be able to actively make sense during debriefs, rather than receiving knowledge that feels unfamiliar, confusing, and disconnected from what they were just working on.

11. Assign check for understanding questions. After a task, I want to know what students learned. Check for understanding questions give me information about where to go next, and help students to monitor their own learning. Students can choose to do these problems alone or in a group, on whatever space they like. I’m looking for students to take ownership of their learning and advocate for themselves when they don’t understand something.

**Assessment & Reporting **

Liljedahl minimized the value of assessment — while assessment is a necessary evil in schools, it’s not where much of the learning happens. That said, some practices are better than others to promote thinking and learning. Very quickly:

12. Tell students where they are and where they are going. Formative assessment should help students understand what they know and what they don’t know, and position learning as part of a larger trajectory.

13. Evaluate what you value. Summative assessment communicates to students what is important in class. If collaboration and process skills are important, then they should play a role in summative assessment.

14. Report out based on data, not points. What does an 87 mean? What does 46/54 mean? Reporting should emphasize what students can and can’t do, rather than an aggregate score without meaning.

**Classrooms as Systems **

One interesting argument Liljedahl made was that small changes are often ineffective. His argument is that classrooms are like systems at equilibrium; students find a space where they are compliant but don’t have to think too hard, and teachers enforce norms to keep class organized and moving through curriculum. Small changes are likely to revert back to the status quo. Only large changes will disrupt the system enough that it finds a new equilibrium, one that pushes students toward higher levels of engagement.

It’s fascinating food for thought. Big change vs small change. Disruption vs evolution. I’m still not sure where I stand, but I’ve really enjoyed coming to understand the framework and its application better.

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