So you’ve decided to undertake inquiry-based learning. That’s great. I’m really glad you see the inherent value in having students swim through a challenging problem on their own a bit before the teacher jumps in with instruction. I’m also glad you’ve been creative at creating new mathematical tasks with cool entry videos, perplexing pictures, and solid scenarios. Looks like you’ve got your curriculum mapped out, all ready to go for the 2013-2014 school year. Really, you’ve done incredible work this summer as you’ve restructured your curriculum with the help of awesome, engaging tasks from the MathTwitterBlogosphere. It’s fantastic. You’ve come a long way. You’ve shown tremendous agency.

Now what? We’ve got all these nifty tasks tied to standards, but what do we actually, you know, do with them? Sadly, even though we’re all rowing the same direction with regards to inquiry based learning and complex mathematical task driven learning, your students are (probably) not at the place where you can just say “GO!” and they’ll spring in to action. Facilitation needs to happen. And while it’s great to have a protocol like the Know/Need-to-Know process (below) handy, if you’re doing 3-5 tasks per unit, any single protocol, no matter how effective, can get pretty boring after a couple rounds of it. While I do believe in giving students the power in common language, it needn’t be that common.

Here are a few ways facilitate the transition from the entry event (the artifact or problem scenario that launches the task) to the student work time.

1. The Know/Need-to-Know Process (NTK).

I’ve blogged a bit about the NTK process before. It’s certainly my go-to protocol. It works well when deconstructing longer (or wordy) problem scenarios. It’s got its problems though. If you’re not adept at facilitating the protocol or just leave it to the students to fill in some blanks, you’ll get some pretty crappy Need-to-Knows, heavy on logistics (when is it due?) or worthless Next-Steps (teach us how to do the math in this here problem). The point of the NTK process isn’t to establish how many words are in a written task, it’s to aggregate prior knowledge and begin brainstorming solution strategies.

2. #anyqs

The good old “Do you have any questions?” “protocol”. Certainly one of the more fun ones. I’d suggest having students jot down their questions before aggregating them as a class. Dan Meyer does a nice job of this by adding “+1’s” when there’s a repeat question. Ideally you’ll have an overwhelming majority of students asking the same question.

2 1/2. Related: Jeff  de Varona (@devaron3) does a nice bit about “what do you think I’m going to ask you?” after producing the problem scenario. I’ve never done that but it seems on point to me. Here’s an entirely stolen-and-published-without-permission of one of Jeff’s worksheets that has that little nugget in there.

3. Visible Thinking Routine: See, Think, Wonder (STW)

Also similar to #anyqs, but slightly more structured, STW was developed as a way of interpreting and discussing works of art, which, if you’ll allow me to opine, ought not to be so different from math problems. It also has the added bonus of adding a layer of evidence-based things the students notice about the picture or video that #anyqs sometimes lacks. Students observe an artifact and discuss what they see, what they think about what they see, and what it makes them wonder. This protocol also works well when having students peer-evaluate each other’s work.


4. Estimations

I think many of us know the power of having students put some estimations up before launching in to the problem. See, they know how to do it over here.

5. Have students develop a concept map before they begin working on a solution.


This is a nice way of having students recall previous lessons and mathematical knowledge. It also helps to bin those logistical need-to-knows that often muck of the NTK process (above).


So there are 5 (and a half) quick ways to move from that awesome, engaging entry event of yours into actual mathematical work. What are some additional protocols or structures you have in your classroom to elicit mathematical strategery?

5 thoughts on “Kicking things off: How do I start the facilitation of a problem?

  1. If one of your goals is to encourage mathematical conversations, it might help to have some ideas about what you might say that doesn’t give away the punch lines. Here’s a one-page summary of some good deflection, from Bob Kaplan, who leads math circles in Boston.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s