Thinking Classrooms and Formative Assessment

I recently read Peter Liljedahl’s paper “Building Thinking Classrooms: Conditions for Problem Solving” (available for free on ResearchGate!). It’s a pretty quick read, and has been really thought-provoking for me. I had been familiar with Peter’s work primarily through Alex Overwijk’s writing and presenting on vertical  non-permanent surfaces and visibly random groupings. I thought that was all there was to it — vertical non-permanent surfaces were a useful tool to get students collaborating on problems, and visibly random groupings were a useful tool to break down status barriers. Cool. Done.

But Peter’s work is much less interested in the specific tools of vertical non-permanent surfaces or visibly random groupings than some broader goals around what a math class should look like.

I wanted to build, what I now call, a thinking classroom–a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals thinking collectively, learning together and constructing knowledge and understanding through activity and discussion (362).

Peter’s article outlines how his work led to nine principles of thinking classrooms. They are divided into three stages in this table:

Screenshot 2016-08-02 at 12.53.10 PM.png

I have questions about several of these elements that I want to explore in the future — the diagram is certainly insufficient to describe the practices that lead to a thinking classroom. Check out pages 381-382 in the article for more detail if you are interestd. That said, I find this a really useful framework in that it sets a goal — a thinking classroom — and uses structures to move toward that goal, rather than treating each structure as an end by itself.

Inputs vs Outputs

I notice that these elements seem to be focused on teacher inputs. The way students are grouped, the way they do their work, the way questions are answered, the moments chosen for instruction. These are all teacher moves to encourage thinking. But there is little attention paid to the learning outputs — the quality of thinking and learning that is happening. Assessment falls in that category, but Peter frames it in his paper as:

Assessment in a thinking classroom needs to be mostly about the involvement of students in the learning process through efforts to communicate with them where they are and where they are going in their learning. It needs to honour the activities of a thinking classroom through a focus on the processes of learning more so than the products and it needs to include both group work and individual work (382).

I think I agree with that statement, but it doesn’t provide much specificity. When do I figure out if kids are learning? How does responsive teaching fit into a thinking classroom?

I’m excited to try out some elements of the thinking classroom this coming year, and hopefully flesh out what they look like and how they work in my classroom. But I don’t want to do so with an exclusive focus on the inputs. If I execute these aspects of a thinking classroom, I will create an environment where students become more likely to engage in thinking and reasoning in my class. But I don’t want to act as if, just because I’m using some effective teacher inputs, my students are certain to learn.

I would conjecture that, if the principles of a thinking classroom are useful to occasion thinking, these structures have to be complemented with a system of formative assessment focused on the outputs and the products of that thinking, so that I can make sure each student is actually learning, and learning what I think they’re learning. And if they’re not, I need systems to be able to responsive and provide new learning opportunities.

I’m starting to stack up more goals than are reasonable for this year, and I’m not sure where this one will fall. But here goes: work to promote the principles of a thinking classroom for my students, and match that with equal energy and attention to whether students are actually learning and figuring out how I can respond to what I learn about their learning.

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