Fifteen years ago I left a computer programming job to enter the teaching profession. My primary reason for doing so was that I loved math and wanted everyone to derive as much pleasure from it as I did. Math was a subject that everyone loved to hate, and I decided that I needed to do my part to try to fix that. At the time, I thought that my enthusiasm alone would win my students over—once they saw how passionate I was about my subject, they would naturally become curious and want desperately to see the beauty I saw in mathematics.

I hope you’re smiling at my naïveté right now, because I’m cringing at it.

I know better now about what to expect from my students, but my enthusiasm remains unbridled. One thing I will occasionally do on the First Day of School is show my classes the “Pure Imagination” song from the movie Willy Wonka and the Chocolate Factory. Besides being a great song, it also perfectly captures my own view of what mathematics is: A place where you are free to explore wherever you like and play with whatever you like, and, regardless of where you go, you are bound to be surprised and delighted by what you find:

There is no life I know

to compare with pure imagination

Living there, you’ll be free,

if you truly wish to be. . . .

Every school year, one of my goals is to give students a glimpse of this perspective. It is an enormous challenge, though, because most students are very resistant to the idea that math is anything more than a set of special-purpose algorithms to be memorized and executed. Despite what the song says, it’s not because they don’t “truly wish to be” free. It’s just that, when it comes to their experiences with math, they are veal calves.

The life of a veal calf is a sad one, to put it mildly. It is typically raised in a cage, unable to ever do much more than pace back and forth in a confined space. I’m told that if such a veal calf is ever released from its cage onto a large, grassy field, it simply continues to pace back and forth in a small area, unable to even comprehend that it has been freed.

Our students do truly wish to be free, but they need a lot of explicit instruction, modeling, encouragement, and practice before they can broaden their minds, experience that freedom, and find the joy in mathematics that I and millions of other human beings do. A tall order but, for me, one worth pursuing. I share Paul Lockhart’s sentiment as expressed in A Mathematician’s Lament (2002): “The only thing I am interested in using mathematics for is to have a good time and to help others do the same. And for the life of me I can’t imagine a more worthwhile goal.”

Matt Enlow, matt.enlow@danahall.org, preaches the gospel of mathematics at Dana Hall School in Wellesley, Massachusetts. He is a regular contributor of (mostly) original math problems to Brilliant.org and tweets (mostly) mathematical musings at @CmonMattTHINK.