I can’t actually recall where I’ve seen someone else say that e.g. “An algebraic proof is a series of steps that you can tell are locally licensed because they maintain balanced weights”
The metaphor of a scale is at least a common teaching tool for algebra: see 1, 2, 3.
I was taught algebra with a scale in the sixth grade. We had little weights that said “X” on them and learned that you could add or take away “x” from both sides.
Yeah, we were taught in basically the exact same way—moving around different colored weights on plastic print-outs of balances. I’ll also note that this was a public (non-magnet) school—a reasonably good public school in the suburbs, to be sure, but not what I would think of as an especially advanced primary education.
I join lots of other commenters as being genuinely surprised that the content of this post is understood so little, even by mathematicians, as it all seemed pretty common sense to me. Indeed, my instinctive response to the first meditation was almost exactly what Eliezer went on to say, but I kept trying to think of something else for a while because it seemed too obvious.
But I don’t recall ever getting that in my classes. Also, the illustration of “first step going from true equation to false equation” I think is also important to have in there somewhere.
The metaphor of a scale is at least a common teaching tool for algebra: see 1, 2, 3.
I was taught algebra with a scale in the sixth grade. We had little weights that said “X” on them and learned that you could add or take away “x” from both sides.
Yeah, we were taught in basically the exact same way—moving around different colored weights on plastic print-outs of balances. I’ll also note that this was a public (non-magnet) school—a reasonably good public school in the suburbs, to be sure, but not what I would think of as an especially advanced primary education.
I join lots of other commenters as being genuinely surprised that the content of this post is understood so little, even by mathematicians, as it all seemed pretty common sense to me. Indeed, my instinctive response to the first meditation was almost exactly what Eliezer went on to say, but I kept trying to think of something else for a while because it seemed too obvious.
GOOD. Especially this one: http://www.howtolearn.com/2011/02/demystifying-algebra
But I don’t recall ever getting that in my classes. Also, the illustration of “first step going from true equation to false equation” I think is also important to have in there somewhere.
I love this idea, so I’ve taken it to the next level: http://sphotos-a.xx.fbcdn.net/hphotos-ash4/405144_10151268024944598_356596037_n.jpg
Hanger, paper clips, dental floss, tupperware, pencil, ruler, and lamp. If we’re trying to be concrete about this, no need to do it only part way.