- What happens when I draw a triangle within a rectangular box?
- Is infinity a number?
- How many ways can I symmetrically tile a surface?
- Why does adding up a list of consecutive odd numbers, starting with the number one, always make a square?

In A Mathematician’s Lament, How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart, mathematician and educator, bemoans the current state of mathematics education in the United States. In his lively and poetic essay-turned-book, he grieves for students who are deprived of math’s true beauty, for they are prevented from playing and asking and discovering an imaginative world filled with patterns and questions and possibilities. Instead, America’s very standardized math curricula chains students to formulas and tests and dispassionate teachers.

I first read Lockhart’s convincing essay in a free pdf form; he has since added to the essay and published it into book form. It is a piece of work that I wish every student, parent, and teacher would read. No. I wish everyone making decisions for this generation of students would thoughtfully consider the significance of Lockhart’s argument.

Today’s students need to ask the crazy questions. They need to collaborate and solve problems in a creative way. They need to see a world full of wonder and possibilities without shirking at the thought of digging deeper to come up with their own solutions.

Which is more interesting…using a formula that someone handed you without explanation (and made you memorize and practice over and over), or hearing the story of one of the most beautiful, fascinating problems and one of the most brilliant and powerful ideas in human history? We are killing people’s interest in circles, for god’s sake!

In order for a student to engage with mathematics, she needs to be invested and inspired. Instead of proving a theorem, why shouldn’t she be given the freedom to discover her own? Instead of being given the formula, why shouldn’t she be given the freedom to make up her own rules, her own questions, her own solutions. If only given a formula, where is the problem to be solved? It has already been asked and answered. Gone is the beauty of discovery.

These are exciting fields in exciting times. I wonder, though, if interest and ability would be greater if students grew up experiencing the joy of math through the guidance of an inspired and knowledgeable teacher?

Shouldn’t life be filled with plenty of fun and beauty?

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