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

Ellipse

Heart Chain Reflect over Circle

Light Art

Lissajous

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

Anonymity

Show Fake Names.JPG

You can now hide student names by clicking on the little dude with the hat in the corner!  Desmos will (temporarily) change the names of the students to the names of famous mathematicians.  Now you can show the class what they’re all working on while keeping the students’ identities hidden.  Love this new feature!

New Features!

I am really digging the new features Desmos has rolled out.  My favorite two features are:

  1. You can now hide a folder of content on a graphing screen.
  2. You can easily add a graph image to a screen with text and/or student input.

Here are some ideas for ways to use a hidden folder of content:

  • Have students practice writing equations of lines, parabolas, piecewise functions, or whatever you happen to be working on!  Make a folder, write a function, and graph it as a dashed line.  Then write some text instructing the students to write the equation of the function.  It is easy to write an activity like this, and as students work, all it takes is the briefest glance at the teacher screen to see which students need intervention.
  • When you have lots of complicated formulas, it can be distracting for students to see lots of folders with all of the “background work” hidden.  I used to just make a folder labeled something to the effect of “hidden stuff” or “triangle” or, in the case of the example I’ve linked, “umbrella”.  Now I just hide the folder.  So easy!

I doubt you need help figuring out an effective way to use a graph alongside a question, but if you want an example of how I’ve used this, check out my last blog post!  Just remember