Every day it seems like K-12 students have more powerful tech tools at their disposal. But what are they to do with these tools? If the answer is not much more than watch lectures and take quizzes, we are missing the boat. When I’m asked for tech recommendations for middle and high school, there are two apps that I most want to get in students’ hands: Desmos and GeoGebra.
Desmos is what graphing calculators want to be. Free to anyone with a browser, built on HTML5, it graphs in color, adds sliders seamlessly, saves by URL, has free accounts and updates regularly, often answering teachers requests. What you may not know is that they’re working with teachers like Dan Meyer and Christopher Danielson to make exploratory activities using Desmos technology. Check out https://teacher.desmos.com/. Among the wonderful features is some truly amazing support for the teacher’s assessment of student understanding with real time monitoring of the students’ work. Desmos is also on iOS, with an updated app coming soon. Curious? Here’s a post on the Desmos blog by Lee Bissett about using it in a middle school, or there are several Fawn Nguyen posts on using Desmos in her classroom. There’s even a collaborative blog dedicated to challenging Desmos creations.
As great as Desmos is, my heart belongs to another program.
The research on the impact of dynamic geometry programs goes back decades now. A quick search of “MTMS dynamic software” and you can find a bevy of great articles, covering teaching ideas in geometry, algebra and data. But cost has been a barrier for schools. And even if schools had the software, students didn’t have access at home.
So when I heard about GeoGebra (around version 2, I think), I was quick to give it a try. Instant mathcrush. Every object you make has a geometric and an algebraic identity; it’s Descartes’ fantasy world. Students took to it quickly, and even started using it from home. GeoGebra is free and open source. Starting with version 4, they also began a great support/feature/service: GeoGebraTube. Modeled on YouTube, everyone can upload their GGB work here to save or share it. Students can submit work this way, or access activities selected by their teacher. The activities can be downloaded or opened up directly in the browser. GeoGebraTube is searchable – so you can usually find an activity on your topic made by someone else, from elementary school topics up through research mathematics. You can also make GeoGebra “books” – collections of activities in one place that you can share with a single link. (See Jennifer Silverman’s cool book on straightedge and compass.)
As students are engaged in a GeoGebra activity, they are exploring and making connections on their own. It’s one of the best tools I’ve ever used to get students to make conjectures of their own, discover reasons for an argument or proof, or build experience to generate intuition. Examples from my blog include Percent Game Remixing or Flip Flop (about reflections). The ability to incorporate pictures into your sketches makes for great modeling practice. (Here are several quadratic ideas for this.) Because the interface is often just click and drag, there’s no start up time for students learning how to use the program. Read how Jed Butler uses the applets to get at area formula understanding.
But the most exciting opportunity is for the students to start to learn the program. For example, Audrey McLaren and her students did astounding projectile projects. The program is powerful, and a tool that will grow with students throughout the rest of their career. I’m literally learning new things every day through use of the program; often through trying to dynamicize a classic theorem (like the Euclidean Algorithm for the GCD) or some intriguing art with mathematical properties (like Truchet squares).
As an opensource community, if you want to get into GeoGebra at any level you will find support. We’ve just started #ggbchat on Twitter this summer (every other Wednesday at 8 pm Eastern), and the GeoGebra forums are helpful to novices and masters. Or ask me – I love collaborating on GeoGebra. It’s not like I have a problem. I could stop anytime I wanted to…