Playing With Functions

For this assignment in my Creativity in Teaching and Learning class we were asked to develop a playful introduction to our topic area (functions). I came up with two introductions (because I couldn’t decide and both might be effective in different contexts).

The first introductions uses a technology that I’ve relied on several times throughout this course, What I’ve done is created a very basic smiley face in Desmos. The task for students is to create a “non-basic” smiley face using at least three different families of functions, at least ten functions, and at least one animation. They should strive to be as creative as possible. They should look to other pieces of art for inspiration. This is a good introduction to functions because students have a lot of flexibility to “play” with the mathematics. They’ll have to figure out how to shift functions vertically and horizontally as well as stretch and squeeze them. They’ll also have to figure out how to restrict domains so that the graphs are limited to just the face.  Having them do an animation will ensure that they will learn how to use sliders in an organic way (because they have to create an animation, not because I said “please create a slider). My hope is that this will help them see where sliders might be helpful in future problems. I also think, with reflection and future application, that this will provide a good foundation that I’ll be able to connect back to throughout the year.

Desmos Smiley

Animated smiley GIF

The second idea I have for a playful introduction to functions, specifically position versus time functions, came from this project where I had students walk out position versus time graphs and record it. This new idea however requires a bit more technology. What I’d like students to do is play around with a physics device that records distance versus time data of any object in it’s path (It’s an Xplorer GLX). My instructions to students at first would be pretty open. I want them to create interesting functions from walking, running, dancing, or by whatever means of movement they’d like to use. I would also bring in different objects for them to use (giant bouncy balls, toy race cars, basketballs, etc.) to help them make different functions and stretch their ideas for possibilities. This device also allows students to save graphs and project for the class. This would be a good introduction to distance versus time functions and I think the feeling functions activity is a great end of unit activity (for my unit on applications of derivatives). We would then have discussions about how we might use this data in a practical way.



Playing is an important tool for creative individuals. When we allow ourselves to play with concepts it lets us see concepts in new ways. It’s an exercise in divergent thinking. We might be inclined to look at the physics devices as simply measurement tools. But if we open our minds we might see that a measurement tool can actually be a playful access point to the concept it’s designed to measure. This is difficult for me to write but the two graphics below demonstrate how we might rethink the tools in our content areas to allow students to more playfully access certain concepts.

Playing with tools

Playing with toolsWhile completing this assignment I found that just approaching something in a playful way has a great deal of value. I was able to let my mind wonder, without constraint. In my content area I’ve found the more I “play” with mathematics the better mathematician I become. One of my biggest takeaways is that play has a real value to learning that I think I’ve often overlooked.

We learn through play. It’s one of the purest forms of learning.

I want to finish with a final observation regarding having students play with concepts. I’ve found that the more open ended the the project the more students struggle with how to approach it. They’re almost dumbfounded by the freedom. This is partly from school but also from living in a culture where we don’t value free play. Considering that in the coming decades we, as a society, will face some the biggest challenges in the history of humanity, I think it’s important that educators integrate tasks that will result in more creative problem solvers and divergent thinkers. We should start by showing students the value in constructive play.

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