At yesterday’s Cohort 21 Face to Face (F2F) session we learned about different models of how to look at tech integration. Probably the most well known of these is Puentedura’s SAMR model, which identifies a new technology’s utility as Substitution, Augmentation, Modification, or Redefinition. Typical examples given are things like word processors, which can substitute as typewriters, but augment the functionality through the ability to edit, format, spell check etc. It moves into modification and redefinition territory when it allows you to do things you couldn’t imagine doing with the old technology.

But there’s something about those examples that kind of bug me a little. The description of the technologies often starts with how it can be a substitute and builds from there, rather than starting with how it can modify or redefine the task. So let me introduce you to one of my favourite tools: Desmos.

Desmos is a calculator. Well, that’s kind of an understatement. Desmos is a simple, free, online graphing calculator that lets you expeiment and visualize complex math in real time. While you can use it to solve problems for you (quadratic formula anyone?), it’s real power is in visualizing functions. Got a question involving two equations and two unknowns? Through ’em in Desmos and *see what the answer means*. Want to see how changing a variable changes a graph? *Adjust it with a slider*. Want to see why two slightly different frequencies produce dissonant beats? Watch an animation (seriously. Open the link, and hit the “play” button beside the k variable). Students have a question about why something happens in math or physics? Have them build the equations and *play* with them. And I mean play. It’s *fun* (non-math and science people may just have to trust me on that…).

Although it is a math tool, it can be used to show *how* math can be used to create simple games and artwork as well as simply presenting math in a very simple and visual way.

Desmos is not just a calculator. You would actually have to try pretty hard to use it just as a calculator. So on the SAMR scale it falls immediately in the Modification/Redefinition end. And with it’s simplicity and flexibility, I’d say it qualifies as an invisible refrigerator.

Ed, what a great post! Thanks for the extra-prompt to click that link…it worked! I was entranced, and then clicked them all together – whoa!

I would love your feedback on what grade Math we could embed this in – or even use in the Prep school to introduce the idea of visualizing math equations.

Thanks,

garth.

I’m not sure what grade graphing is introduced, but I would use this at any grade where graphs are introduced. The slope-intercept form of a line is y = mx + b. Dropping in sliders for m and b would make their meaning immediately obvious.

I also love Desmos! I use it for the exact same things in grades 11-12, and find it particularly helpful for visualizing functions. Plus, I LOVE LOVE LOVE the sliders – so easy and so clear!

Great post!

Ruth

Thanks for sharing this on Saturday. It’s a simple, easy, and effective way to show how variables impact functions and equations. So many practical uses. I will be sharing this with our math department.

Cheers,

Tim

Hi Ed,

After the amazing discussion about Desmos yesterday, I had to look into it more. I checked with our Math department, and sure enough, they are all HUGE fans. One teacher has used it by taking a photo of a student about to shoot a basketball into a hoop, overlaying it on Desmos, and asking students to develop the equation for the parabola that would all the basket to be made. Pretty awesome!

Thanks for sharing with the group yesterday. Your application of the SAMR framework is right on!

Les

I like that idea of overlaying the parabola over a photo (or better, a series of consecutive frame grabs). I wonder if I can figure out how to use that for analysis of linear motion. Hmmm…

This is awesome Ed! Thanks for the post. I’ve shared this with the Physics teacher at LCS.

Yes, I’m a big fan of Desmos as well. Along with Wolfram Alpha, it has given me and my students very powerful tools to check our intuition, along with our calculating abilities!