Monday, May 11, 2009

How to teach math

> On Sat, 09 May 2009 15:30:52 -0400, Kenneth Tilton wrote:
Well, i was not really trolling, I was forking the thread to make fun of  the New Math that tried to get the numeral/number distinction across to five year olds.

Someone responded:

You find it better to start with medieval concepts working gradually on to the mathematics of XIX century, while explaining each next year what was wrong with the things they learnt a year ago?

I said all that? Ma's gonna be right proud. But... 

Funny you should ask. Yes, I suspect the path society took to get to what it knows now about math is the path an individual neuronal mass should follow. ie, kids should encounter zero and roman numerals and place value and algebraic variables in the same order society developed those ideas.  The history of math is your math curriculum guide.

The New Math erred by selecting the logical organization of mathematical concepts as its curricular pole star. Next came Constructivism, which wanted kids to reinvent math. From scratch. Cool idea, but too slow.

Instead, let the history of mathematics dictate the order in which things are directly taught. Maybe go further and teach math as history with less emphasis on computation. Math often advanced when needed to solve real problems. Maybe we can shut up the little devils asking why they need to learn this stuff.

As for explaining all along the way what was wrong with the ideas taught the day before, hey, ever read a book on programming? They typically develop a chunk of code iteratively, presenting ever more improved variations on a primitive original. Come to think of it, ever develop some software? Same thing.

Here's the deal: most folks do not even know zero had to be invented. One understands zero better if one has done without it and then the teacher invents it for you. Something like that.