Geoff Krall
In the past I consistently struggled with making the turn from the excitement toward problem-based learning (PrBL) to the actual design of complex, engaging problems. Typically I would spend the morning building the buy-in (the “why”), another part of the morning conducting some sort of problem simulation to showcase PrBL (the “how”). Then my instructions were along the lines of “OK gang, after lunch you’ll start designing your own tasks!” If you’re like me, you find it difficult to be creative on demand*. (I mean, if you’ve been keeping up with the infrequency of my blog posts in the past year you probably know that already).
Don’t get me wrong, I have little patience for math teachers who say “they’re not the creative type.” And I do think creativity is an under heralded attribute teachers need to have. It’s difficult to be creative at gunpoint.
I’ve started codifying what I believe is a more agreeable framework. Many of the successful implementation of inquiry-based, complex tasks has followed this progression (often over the course of multiple coaching sessions):
First: Find
Then: Adapt
Finally: Create
We start by finding (and often trying out) a task; then, at a later date, we try adapting a task (which we then implement); finally – and this is a tall ask – we try out creating a task more-or-less from scratch. This final step is probably more of a slow-walk from adapt than a full on design sprint.
Find
There are countless websites with open accessible tasks of ever-increasing quality and navigability. You know ’em, you love ’em. You can find a bunch on the “Math-like Blogs” list on the right side of this page. You can also find well organized tasks at IllustrativeMathematics, Shell Centre, Teacher.desmos.com, openmiddle.com and NCTM’s Illuminations.
An afternoon of PD spend simply clicking through your favorite, say, three of these resources is an afternoon well spent. That’s how the ol’ curriculum maps came to be.
Find something compelling and pretty soon you’ll find a ton of stuff you find compelling.
Adapt
Once you’ve found some good stuff, try to see if you can take something that’s pretty good and make it better. I’ve presented about that before: [NCTM] Adaptation.
This requires a bit more discussion and contemplation. You start to turn from “I like this task” to “What do you like about it?” Once we start adapting we are developing an implicit or explicit criteria for what makes a quality problem.
Maybe you adapt a problem by removing the sub-steps. That would suggest you like problems that allow for a lot of “open middleness.” Maybe your colleague adapts a problem to a hands on activity a la Fawn. That speaks to how much you value tactile experiences and students actually doing stuff.
Now – and only now – ought we turn to the ever challenging work of creation.
Create
Most of the time, creation of a task comes from either inspiration and/or sheer luck. I’ll see an advertisement or watching a movie and see something that’s kinda mathematical. Like I said, really tough to do on-demand, and also really tough to do in any kind of standards-aligned way.
But it’s also absolutely crucial! Not only does it work out your creative muscles, it generates tasks for the rest of us to find! It’s a give-a-penny / take-a-penny situation. Even if you’re not teaching, say, geometric constructions in your Algebra 2 class, maybe you get struck by a divine lightning bolt of inspiration that the rest of us can draw on. In that respect the Find –> Adapt –> Create framework could be seen as a cycle.
Find –> Adapt –> Create –> Other people find your creation
But yeah, it’s difficult to do on a good day, it’s much more difficult to achieve when I’m hovering over individuals harping on them: “got anything yet?”
And this isn’t just true for tasks. Consider other instructional tools.
| Find | Adapt | Create | |
| Rubrics | NTN Learning Outcome Rubrics (Math) | Pull from a few of the rubric indicators | Design your own, based on your grade level, school context and content area |
| Lesson Plan Template | Problem Planning Form | Modify based on your class time | Design a lesson plan template that works for an entire department |
| Math attitudes survey | Here’s one I developed | Steal a bit from it, but identify a few of the specific things you’re trying to deduce | On your next iteration, make it totally your own! |
I do believe that the best instructional experiences students have are by-and-large teacher-designed. Getting to that point is challenging so start with the stuff we have and slow-walk yourself into creation mode.
Y’know, unless inspiration strikes you like a lightning bolt while you’re sitting on the couch. In that case, disregard everything I said and go nuts, Creator.
* – Note: to contradict myself, this was not true of PBL Chopped! That was absolutely a fantastic experience of solely creation with incredible project ideas.
Read more from Geoff at Emergent Math.