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4th January

Paul Lockhart: A Mathematician’s Lament


This holiday season, a friend sent me A Mathematician’s Lament, by Paul Lockhart who has taught math at Brown and UC Santa Cruz, and for the last 14 years at St. Ann’s School in Brooklyn. After reading this book, I think I may be in love with Dr. Lockhart. Or at least I hope to meet him one day.

In place of discovery and exploration, we have rules and regulations. We never hear a student saying, “I wanted to see if it could make any sense to raise a number to a negative power, and I found that you get a really neat pattern if you choose it to mean the reciprocal.” Instead we have… the “negative exponent rule” as a fait accompli with no mention of the aesthetics behind this choice, or even that it is a choice.

When I read the following excerpt to my kids, they cracked up - and totally agreed:

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number,” while 5/2 is an “improper fraction.” They’re equal, for crying out loud. They are the exact same numbers, and have the exact same properties. Who uses such words outside of fourth grade?

Then he gets to the heart of the matter, the real challenge for us, as educators:

Of course it is far easier to test someone’s knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaning…. In practice, the curriculum is not even so much a sequence of topics, or ideas, as it is a sequence of notations.

Finally, here is the essence of what he believes — and what we believe at HVA — about the teaching and learning of mathematics:

Mathematics is about problems, and problems must be made the focus of a student’s mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process — having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other’s work. Specific techniques and methods will arise naturally out of this process, as they did historically: not isolated from, but organically connected to, and an outgrowth of, their problem-background. 

Lockhart writes about unity and harmony and the beauty of math. He is passionate and some would say radical. I would say right on.