At some point this year (2018), I’ll have a book for you to read from Stenhouse that proposes a framework for effective math classrooms. These are the three broad ingredients that create a successful math classroom as well as how a student experiences math. They are:

- Academic Safety – the social/emotional state of a student and her self-regard as a mathematician
- Quality Tasks – the thing that students are doing, working on, and/or creating
- Effective Facilitation – the short- and long-term moves that promote mathematical thinking and sensemaking

Every successful math classroom I’ve been in has each of these three hallmarks in spades. In fact no successful classroom I’ve been in *hasn’t* had each of these hallmarks working for it. They’re our *necessary conditions* for great classrooms.

They work independently and in concert and can be the lens through which we can better understand classroom issues. Let’s take a common issue of *unproductive or inequitable groupwork*. Effective strategies will tackle one, two or all three of these elements. Let’s use this framework to better understand the issue, before we jump into the solution.

*Is the issue one of Academic Safety?*

Students may not be engaged in groupwork if they self-identify as a “non-math person.” It’s possible they’re only living up to the social academic status they’ve been given. How do students see themselves as mathematicians? Do they see themselves as mathematicians? Do their peers see one another as mathematicians? If so, how so? Are they publicly acknowledging the mathematical smartness of their peers?

*Is the issue one of Quality Tasks?*

I’ve been in classrooms where the issue around groupwork began with the fact that students weren’t being assigned groupworthy tasks. If you’re going to require an assignment occur in a group setting, the task ought to require (or at least be enhanced by) groupwork. Tasks are often developed for individuals but assigned to groups.

*Is the issue one of Effective Facilitation?*

How was the groupwork time introduced? Did you just assign the task and say “go” or did you have a structure in place? Do students have specific and understandable roles or is it the onus of the student to figure out where they fit into the groupwork dynamic? What norms are present in your classroom (and no, not the norms that are on the wall, but the ones that are actually present)?

Once we start to answer some of these questions, we might be able to better identify potential solutions. Maybe the classroom needs defined group roles. Maybe a norm of “same problem, same time” needs to be enacted. Maybe tasks need to be developed to push students deeper into the math content. Or maybe it’ll generate additional questions or additional need for understanding the issue at hand.

And as I mentioned, it’s possible (probable) that issues will bleed between our three pedagogical elements. Certain tasks can reinforce messages about mathematical self-regard. Unstructured groupwork can reinforce issues of academic status. It’s messy work, this teaching. Hopefully this framework will help you better understand the complex dynamic of a classroom ecosystem.

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