On Tue, 27 Nov 2001, Horn, John wrote: > Wow. That was a great explanation. Can I borrow you when my kids start > asking me for help with their math homework? ;-) > > My trouble with explaining things like this is that I do too many things > automatically while solving an equation. I think I'm explaining every step > but I end up skipping 2 or 3 steps because I don't even realize that I'm > doing them. Not until I get a blank look from the person I'm helping!
Thank you! Skipping steps is part of what makes these things difficult, but an even bigger part, I think, is that most teachers don't explain the context in which decisions are made. Some people grasp the context automatically and have little trouble, but I didn't, and my very desire to do things correctly and logically caused problems because I was reasoning based on a false set of assumptions about how algebra was supposed to work overall. I couldn't even figure out how to ask for help because the question I needed to ask was the obviously stupid and humiliating, "Why are we doing algebra at all?" To which the obvious (and, as it turns out, incredibly insulting and stupid) answer is, "So you can get a job when you grow up." I think most teachers handle math by giving a set of definitions and rules and then showing how to solve problems. But with algebra there's a bigger conceptual picture to be grasped, and without that big picture many of the problem-solving steps make no sense. The big picture involves some strategic and tactical reasoning that have nothing (obvious) to do with the rudiments of math as most of us are taught it. Learning to do algebra is not like learning to emulate a computer running a script, but that's how many people teach, and I think it screws a lot of students up. Another way to look at it: algebra is typically taught as a means to an end, a method for solving equations. But it's not (what's an equation? why is an equation?). It's a system of thinking about mathematical means and ends, and unless you're introduced to the big picture, all you're left with is struggling to learn by rote a subject that isn't "rote" at all. Marvin Long Austin, Texas
