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I wonder what it would look like if we taught mathematics the same way we teach art, music, and poetry?  What would our classrooms look like if students didn't see math as utilitarian until much later, but instead were encouraged to play around with numbers, shapes and patterns, and to solve puzzles with no purpose applicable to the real world outside of school?  Would math excite more students if taught through play, without tests and standards? 

Mathematician Paul Lockhart and I share the opinion that math is fundamentally a playful endeavor.  In 2002, Lockhart wrote a famous paper called A Mathematician's Lament. In it he talks about how school drives the joy out of mathematics.  “That's what math is,” writes Lockhart, “wondering, playing, amusing yourself with your imagination.”  He believes that we have completely removed imagination from math classes.  In Lockhart's opinion, this is the same thing as removing math from math classes, since math is a game of the imagination.  

If we taught math in this way – using play and imagination – would it be more universally popular and effective?  Would more students want to play around with numbers, shapes and patterns?  Would understanding an insight become more important than being "right” and "wrong”?  Understanding is a direct result of engagement, and engagement in math is trial and error, zooming in, then out, following several paths, backtracking, and walking away from and coming back to the same problem several times.  Giving space and support to students for this type of thinking and problem-solving in math class can help students enjoy their experiences more fully, and master the content at a deeper level. 

If everyone were exposed to mathematics in its natural state, with all the challenging fun and surprises that that entails, I believe we would see a dramatic change both in the attitude of students toward mathematics, and in our conception of what it means to be “good at math.” According to Lockhart, we are losing many potentially gifted mathematicians— creative, intelligent people who reject what they feel is a meaningless and sterile subject because they naturally dislike the tedious.

Einstein famously said, “I am enough of an artist to draw freely upon my imagination.  Imagination is more important than knowledge.  Knowledge is limited.  Imagination encircles the world.”  So let's circle back to what math can be – a way to develop creativity, curiosity and vision.  While I don't have the artistry or imagination of Einstein, I do have enough to perceive an entirely different math classroom, one where the skills that are most important are not the ones that are easiest to test, but rather the ones that draw upon creativity and build deep capability among our students.