Which Comes First in the Fall? Norms or Tasks?

(Reblogged from the Stenhouse summer blogstitute. If you haven’t checked it out yet, take a peek–lots of authors wrote posts!)

I periodically hear discussion about whether it’s better to start the new school year by establishing norms for math class, or to dive right into a rich mathematical task. I’m opinionated, and I’m not shy about my opinions, but in this case, I’m not joining one team or another. They’re both right.

The first few weeks of math class are crucial. You have a chance to unearth and influence students’ entrenched beliefs—beliefs about mathematics, learning, and themselves. You get to set the tone for the year, and show what you’ll value. Speed? Curiosity? Mastery? Risk-taking? Sense-making? Growth? Ranking? Collaboration? You get to teach students how mathematics will feel, look, and sound this year. How will we talk with one another? Listen to our peers? Revise our thinking? React when we don’t know?

In Becoming the Math Teacher You Wish You’d Had, I wrote about a mini-unit Deborah Nichols and I created together. We called it, “What Do Mathematicians Do?”, and we launched her primary class with it in the fall. We read select picture-book biographies of mathematicians, watched videos of mathematicians at work, and talked about what mathematics is, as an academic discipline. We kept an evolving anchor chart, and you can see how students’ later answers (red) showed considerably more nuance and understanding than students’ early answers (dark green).

Throughout, we focused on the verbs that came up. What are the actions that mathematicians take? How do they think? What do they actually do?

In the book, I argued that this mini-unit is a great way to start the year if and only if students’ experiences doing mathematics involve the same verbs. It makes no sense to develop a rich definition of mathematics if students aren’t going to experience that richness for themselves. If professional mathematicians notice, imagine, ask, connect, argue, prove, and play, then our young mathematicians should also notice, imagine, ask, connect, argue, prove, and play—all year long.

In June, I saw this fantastic tweet in my timeline.

Asked Ss: what’s a mathematician? Blue responses: before 3 act task. Red: after #mathmindset @gfletchy pic.twitter.com/lltkcclb4h

— Sarah Burzynski (@SarahBurzynski) June 8, 2017

It caught my eye because Sarah’s anchor charts reminded me of Debbie’s anchor chart, but Sarah had pulled these actions out of a task, rather than a study of the discipline. I love this approach and am eager to try it in concert with the mini-unit. The order doesn’t matter to me.

We could (1) start with a study of the discipline, (2) gather verbs, (3) dig into a great task, and (4) examine our list of mathematicians’ verbs to see what we did. Or, we could (1) start the year with a super task, (2) record what we did, (3) study the discipline of mathematics, and (4) compare the two, adding new verbs to our list as needed. In either case, I’d be eager for the discussion to follow, the discussion in which we could ask students, “When we did our first math investigation, how were we being mathematicians?”

Whether we choose to start the year by jumping into a rich task on the first day, or by engaging in a reflective study about what it means to do mathematics, or by undertaking group challenges and conversations to develop norms for discourse and debate, we must be thoughtful about our students’ annual re-introduction to the discipline of mathematics.

How do you want this year to be? How can you invite your students into a safe, challenging, authentic mathematical year? How will you start?