Some of the best days in my classroom this year were the first days of students grappling with a good (low threshold, high ceiling, high cognitive demand, content-illuminating) problem. Students were engaged, discussing, modeling, struggling, defending their thinking, etc.

Many of these problems require multiple days. By the end of the first day, students may have “gotten” parts of the problem, may have even generalized, but they weren’t (according to me) done. Many students though, despite high interest/engagement on the first day, demonstrated much less interest in returning to the same prompt.

The great thing about these good problems is how much you can do with them! So how do I teach/motivate students to sustain their interest over multiple days with the same prompt? Will discussing the value of sticking with the same problem (the why we do this) and a class norm of “you’re not done until you’ve used at least two methods and two (three?) representations” do the trick?

Thoughts?

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My thinking is going to 5 Practices for Orchestrating…as I understand them. In this model of the You, We, I, it seems most problems are wrapped up in a day…I think the idea is to let all students work it their way, then discuss the advantages and disadvantages of each, then wrap it up as something to know. The follow up, through homework (?), seems to be the weak point of discussion after the You, We, I, as to what do you want the take away for the students to be…I say you make them go home and solve the problem two different ways and come back and discuss it…

I am kind of anti-homework (maybe that’s problematic).

I am hoping that requiring multiple solution paths to many problems will help. Also, as I map out our Patterns unit, I seem to be using a format where students solve up to 5 problems/week as they see fit, and then choose one to go into depth with. Hopefully, allowing for choice will help students choose their most-compelling problem to spend more time on. And I don’t need them to spend more than a day on most problems, just some …

I’ve had the same issue at times with my own classes. What do you think about the idea of asking students at the end of the day, “what do we need to do tomorrow in order to continue our work on this problem?” Maybe having them set the path will lead to more buy in?

My other thought is that they might feel as though they are done with the task, which, regardless of whether we agree or not, will mean they won’t be chomping at the bit to keep thinking. To me, this means we need to find a way to disrupt their thinking or create a sense of disequilibrium. Maybe we could pose an extension to their work, probe an area that they haven’t thought about, find a contradiction in their previous result, or even create a new (but similar) problem that will re-engage them in the big mathematical ideas.

Not sure…but it’s a great question you pose!

All of those sound like good ideas. I try to do lots of disequilibrium by having students compare methods/confer when they disagree (generally works well, though that doesn’t always help create enough motivation for day 2).

I want to try asking students what we still need to do to fully answer the problem. Yup. The answer the more I read and think this summer seems to be, ask the students, get them to generate the question — so anti-thetical to my own math learning, but completely in line with my philosophy now.