A Graphing and Learning Journey

After a little archaeologic research, I can tell you that my earliest saved Desmos graph is from March 26, 2014.  That’s just over three years ago.

I remember thinking then what a game changer Desmos was. I was stoked about how this could potentially transform teaching.  The graphs!  They were dynamic! And you could graph even non-functions. And the graphs were pretty!  I was truly in love and I thought about how finally (FINALLY!) my students could visualize the beauty and wonder of math in a way they had never been able to before.

This was going to change things for my students. I was 100% sure of it.

And I wasn’t wrong. But that’s not what I’m here to tell you about. 

What I never imagined was the profound impact using Desmos would have on my own mathematical understanding.

Through making more and more involved and intricate graphs, I have discovered myself learning how to do things I never ever imagined I would be able to.  And how did I learn it? Through a little bit of research combined with a whole lot of thinking, graphing, and playing.

Bear with me here for a quick walk down memory lane:

2014: A year of using Desmos to do teacher-y things I would normally have just used a TI calculator to do.  (plus a little more than TI does…like an awesome movable tangent line! Go Desmos!)

2015: A year of getting a little more creative with my graphs. A fish? With chomping teeth? Wowza. That’s some pretty sweet stuff. And check out the shading on that beach umbrella. Is it any wonder Desmos is my latest favorite thing?

2016: The year everything changed.


This pentagon construction? This is the graph that changed everything. This graph taught me more about using and writing parametric equations than I ever learned from a mathematics course.

Pentagon Construction (2)

And since then, I have continued to learn about parametric equations, about writing and composing functions, and about using sliders & lists to get some beautiful graphs:

cross sections - proportional rectangles


Heart Chain Reflect over Circle

Light Art


Non-Function AsymptotesParametric Butterfly

If you had told me in March of 2014, when I had saved my first graph, that in 3 years’ time I would be writing the equations for graphs like these, I would never have believed you.  And yet, it happened.

Desmos is not only a powerful learning tool for our students, it is a powerful learning tool for us, the teachers.

If you’re a math teacher, I challenge you to begin getting inspired to create graphs. There is so much to learn, all of which can enrich your content knowledge and help you to become a better teacher for your students! If you’re not a math teacher, but just like graphing for fun, keep at it!!!!!!!

Where can you get inspired?

  • Start following people on Twitter who are doing interesting mathy graphy things.
  • Check out Dan Anderson’s site: http://dailydesmos.com/.
  • Try some graphing challenges from learn.desmos.com.
  • Or? Look for inspiration in your daily life. Are you watching raindrops hit puddles? Maybe consider making ever-expanding concentric circles! Are you watching a bicyclist pedaling down the road? Try graphing the path the pebble takes!

For me, the next challenge is to make a tornado (at the request of a student.)  Keep an eye out for it on Twitter!

Happy graphing, people! And happy learning.

*link to the title graph.

Light Art