Paper of the Day: “A Mathematician’s Lament”
by Paul Lockhart
Today’s Paper of the Day continues this week’s theme of “education”; this time, with a research mathematician turned educator’s thoughts on why K-12 math education ends up leaving so many graduates with negative feelings toward math.
I like this paper a lot, because it resonates so strongly with my own experience of middle- and high-school math. I had several great teachers, but somehow it all seemed like an exercise in memorization, at best, or obscurantist puzzle-solving, at worst: a sequence of parlor tricks; when you see this pattern, do this transformation (it’s called “integration by parts”, but you will not be required or encouraged to know where it came from or why it got the name).
Lockhart reserves his greatest ire for high-school geometry and its introduction of “formal proof”:
The student-victim is first stunned and paralyzed by an onslaught of pointless definitions, propositions, and notations, and is then slowly and painstakingly weaned away from any natural curiosity or intuition about shapes and their patterns by a systematic indoctrination into the stilted language and artificial format of so-called “formal geometric proof.”
I can attest that my friends and I felt the same about the strange (in hindsight) two-column and acronym-heavy format in which “proofs” were presented, if not quite so eloquently (we’d often give up halfway through a homework exercise and cite the “BOB”, as in “back of book”, theorem).
I’ve eventually made peace with math, if not perhaps with real numbers and calculus (which calculus? They never tell you there are others; they actually mean the differential and integral calculus for real analysis.) For me, years of programming eventually led to studying the foundations of computer science: discrete math, abstract algebra, formal logic, and various calculi all have rich roles to play. A proof can be a sensible argument by induction, which is a fancy word for covering all the possibilities; nary a two-column table full of acronyms in sight.
It’s turned out OK, and I’m slowly learning how to read, understand, and do “math” again. But I wish that it hadn’t taken me so darn long to recover from my math trauma.