Creating Curiosities in Mathematics

Something that’s always fascinated me about Dan Meyer’s approach to creating curious mathematical learners is the carefully scaffolded approach he puts into his “any questions” activities. There’s no strict formal guidelines for adhering to rote mathematical thought, and quite often the ability of students to ask non-mathematical questions about their math problems can be just as important as the mathematical ones. If continued student engagement is essential to effective teaching, then you need more than just a teacher dredging up prior knowledge about a topic. You need learners to own their curiosity throughout a lesson.

For example, I could craft a simple math problem about figuring out area and volume around a road construction project. The main road going through my town is currently being resurfaced, and it would be easy to engage students with a simple question about how much material would be needed to resurface the road. Simply get the dimensions of the roadway that’s been milled (length, number of lanes wide, and depth of milling), and then let the students figure out how much asphalt will be needed. That creates a nice little real world problem that can be solved in a few minutes.

Or, you could show them this:

What questions immediately come to mind when you watch that 45 second clip of the milling machine in action? Are they math related? Are they non-mathematical? Are you sure? Go ahead…watch it again if you need to.

I’ve watched this clip three times now (four if you count me actually watching it first hand), and here’s my top five questions:

1. How much material is being stripped away from the road surface?
2. How many truck loads will it take to haul away the entire stretch of road being resurfaced?
3. Does the guy running the milling machine ever get bored?
4. What happens when they come across a manhole cover?
5. Will the new surface be laid down as quickly as the old surface was to tear up?

What if you allowed your students to ask questions like this? To wrestle with “real world curiosities?” Would it make a difference? Could you turn a simple math problem that would take about five minutes to solve into something more? Perhaps a small student-driven project that would take a few days? What do we gain when we allow learner curiosity to co-mingle with our learning targets?

Thankfully, Dan Meyer provides a lot more scaffolding on his 101 Questions website beyond just this initial activity, but I’ve found that getting over this initial hurdle is often what teachers need to do most. Even if just once a day, or once a unit to start. Get students’ minds wrapped around their own questions, not just the ones you’ve selected from the text. Finding a balance between where we need learners to be, and how they get there, is that wonderful melding of art and science that makes my inner teacher smile.