Math Class Drops the Mic

A blog about teaching, with an emphasis on math.

Tuesday, December 8, 2015

Making Mastodons Real

For many years, in addition to teaching I ran an outdoor education program at a school in urban southern California. Most of my students lived far-removed from the natural world and outdoor education was literally a breath of fresh air for them. Usually we took students to Joshua Tree National Park, a land of giant granite boulders sculpted by the wind and glowing gold in the setting sun. One evening we drove into the park with a new group of middle schoolers, their faces pressed to the window in awe of the hulking stones looming like mastodons. One kid, who had studied the basics of geology in his science class, nevertheless innocently exclaimed, “Woah, who put these here?”, thinking that the fabricators of Disneyland had been hard at work in Joshua Tree. This climbing trip made those stones real for the students, bridging the gap between the abstraction of nature and the reality of rocks.

Climbing in Joshua Tree

How do we bridge the gap between the abstraction of mathematics and the reality of the world it quantifies? We can’t always take a field trip, but we can challenge students to do small experiments, measuring and calculating in the context of some real-world problem. In this way mathematics becomes a tool for understanding something about the world, not only an abstraction. Don’t get me wrong, the formal abstractions of mathematics are awe-inspiring. But my students in southern California needed some help connecting their understanding of geology in the classroom with the actual world in their midst. And students come to our math classes yearning for the numbers to become real in some way.

The best way to get a student interested in rock climbing is not to climb with them. It’s to go on a scramble, a hike through uneven terrain, involving some boulder hopping and creative wiggling. Eventually a kid will want to go higher, and I tell them, “Ok, let’s get a rope!” In the same way, I love seeing students creatively engage with problems at the limits of what they know until finally they are asking for a tool to solve a problem, or even developing one. Building anchors and tying into ropes for its own sake is pretty boring, but when you really want to climb something it’s brilliant.

Courage To Core represents my fifteen year effort to develop materials that give students a certain amount of autonomy to grapple with real world problems and build the tools to solve them. I’m so glad that Teachers Pay Teachers has given me the chance to share these materials with you. My most recent resource is linked below—I hope you and your students enjoy its narrative and experimental nature, and that together we can bridge the gap between the abstract and the granite.


  1. The way our school structure is organized makes it challenging for our learners to connect real life to the abstract and, for teachers to create such experiences. Thank you for understanding that many of our children have difficulties with the abstract and require inquiry and exploration in order to properly learn mathematical concepts.

    1. As I look around today I see more teachers and schools striving to bring more of the world into the classroom, and more of the classroom into the world, and give students a structure for creative engagement with that world. Exciting times! Thanks for your comments!

  2. The large class public system makes it so much easier to push concepts than teach the why. If you can sneak those real world application moments in, it makes such a difference in a student's understanding and motivation. It sounds like you're doing a good job of both.

    1. It is amazing to see how teachers are challenged these days with huge class sizes, limited time and space, and few prep periods. It's so hard to build space and structure for engagement and experimentation with the real-world and models of it. And yet, the tools for engagement are getting easier to find and use. Hopefully teachers can be given the time, the class sizes and the resources to allow for more real-world engagement. Thanks for your comment!