How cool were those first graphing calculators from Texas Instruments? I loved the immediate connection between equation and graph. I also spent my own money on MathType to spiff up my worksheets. Then I spent more of my own money for a personal copy of The Geometer’s Sketchpad so I could get up to speed using the school license we had just bought.

I spent the summer reading research papers and working on curriculum projects, all on a Dell Chromebook11 that I borrowed from the school’s tech department. What a joy to leave the laptop behind! I traded a couple of pounds for a daylong battery. I’m expecting to have twenty of these in the various geometry sections this year, but it will be a few more weeks before they’re unboxed, up and running. 

I had thought that the next great revolution in technology for the high school mathematics classroom was going to be a suite of killer math apps for kids’ phones. Instead, I’m finding that a few sophisticated—and free—programs are changing the way I teach. My two favorites are Desmos and GeoGebra, both intended to make mathematics visual.

Desmos is a graphing program whose ease of use lets students play around with mathematical ideas from algebra to calculus. Both the graphing and equation screens display together, so it’s easy to see how changes in one influence the other—we pull it up in class and build functions on the spot to explore how something works. (You need an Internet connection for this one.)

GeoGebra is a dynamic geometry program that also knows algebra and functions. It runs in a variety of operating systems or streams as an app, meaning that you and your students can use it on and off the network. This is a sophisticated program that lets kids start testing ideas right away—as they learn more, they can do more with it.

Sometimes the exactly right thing to do is to give students a handful of printed problems that they dig into with a pencil and solve. I have textbooks at hand and hard drives full of handouts. As do we all. What’s harder is to give students the toolsto explore something that they are just beginning to understand. Students explore construction faster and deeper in GeoGebra than they do with a compass and ruler. They latch onto the power of coefficients with Desmos more effectively than with the handheld graphing calculator. These programs are empowering, and they run on stuff kids already have—phones, tablets, and curiosity. I love teaching, but technology is giving students the power to learn along with me, instead of simply from me.

I’m excited again, and the school year has only just begun!

Greg Stephens, stephensg@hohschools.org, is a high school mathematics teacher, department chair, and instructional leader for the Hastings on Hudson School District in New York. He just rotated off the Mathematics Teacher Editorial Panel but is keeping busy in a doctoral program at Fordham University in New York City. At the moment, his thesis topic is the impact of digital literacy on the high school mathematics classroom, but the hardest thing of all is picking just one topic to focus on!