Understanding math: a dialogue – and a question for you

From the utterly brilliant (free here! here, too!) essay A Mathematician’s Lament, by Paul Lockhart.  This document has apparently been circulating in the education underground for quite some time and is a wonderful read for anyone who feels that math education (including their own) is “missing something.”  Lockhart says what’s missing is… well, math.

Imagine how dumb it would be to “teach” art or music to students through theory, terminology and workbooks (they must instead listen to art/music, DO art/music, etc!).  Yet, says Lockhart, this is exactly how we “teach” math (actually, the quotes could go on the word “math” as well, because he reckons we’re not teaching math but “math”… okay, never mind). 

Why do we do it that way?  Because that’s how we learned it ourselves.  Math teachers are not often math lovers or even math doers at all.  Just as a teacher who’s never been to a gallery or lifted a brush should probably not be teaching art, a teacher who has never had the experience of doing math should not be – CANNOT be – trying to teach it to others.

I won’t attempt to rewrite the essay, but I did want to share part of one of several dialogues found throughout the essay.  Entertainingly, Lockhart uses two characters borrowed from Galileo – Simplicio and Salviati – to voice the opposing viewpoints.  Emphasis in bold is mine – I love this line so, so much.  After you’ve read it, I have a question for you – whether you’re homeschooling or not.

SIMPLICIO: All right, I understand that there is an art to mathematics and that we are not doing a good job of exposing people to it. But isn’t this a rather esoteric, highbrow sort of thing to expect from our school system? We’re not trying to create philosophers here, we just want people to have a reasonable command of basic arithmetic so they can function in society.

SALVIATI: But that’s not true! School mathematics concerns itself with many things that have nothing to do with the ability to get along in society— algebra and trigonometry, for instance. These studies are utterly irrelevant to daily life. I’m simply suggesting that if we are going to include such things as part of most students’ basic education, that we do it in an organic and natural way. Also, as I said before, just because a subject happens to have some mundane practical use does not mean that we have to make that use the focus of our teaching and learning.  It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not why we teach children to read. We teach them to read for the higher purpose of allowing them access to beautiful and meaningful ideas. Not only would it be cruel to teach reading in such a way— to force third graders to fill out purchase orders and tax forms— it wouldn’t work! We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math.

SIMPLICIO: But don’t we need third graders to be able to do arithmetic?

SALVIATI: Why? You want to train them to calculate 427 plus 389? It’s just not a question that very many eight-year-olds are asking.

There’s more, but I’ll leave it there (tantalizingly, I hope).  Here are those download links again: here! and here!

I’m fascinated by what he calls the “Ladder Myth” of math curriculum, whereby we arrange all of mathematics into a rigid “sequence of “subjects” each being in some way more advanced, or “higher” than the previous. The effect is to make school mathematics into a race— some students are “ahead” of others, and parents worry that their child is “falling behind.” And where exactly does this race lead? What is waiting at the finish line? It’s a sad race to nowhere. In the end you’ve been cheated out of a mathematical education, and you don’t even know it.”

Why have I never heard of this guy before?  To finish off, here’s a terrific video from the man himself, especially the first minute…

So here’s my question, whether you homeschool or not: 

How can we ensure that our kids come away loving math even if we and/or their teachers didn’t or don’t???