[WildTurkey]

I agree, having an incorrect oversimplified visualization is a real pain. It sticks. Sort of like those musical earworms.

I bet you really flipped when they introduced fractions, and then low and behold, IRRATIONAL numbers and then, WOW, complex numbers! Why didn't they just start off with complex numbers instead of teaching that INCORRECT, OVERSIMPLIFIED visualization of integers. It sticks, right?

[discostu]

There you go again, using an example that doesn't apply and is actually quite asinine. Fractions aren't over simplification. Fractions continue to work no matter how far you go in math, fractions are fractions are fractions, and nothing about irrational or complex numbers makes fractions a lie.

Simplification by omission - OK and generally necessary
Simplification by substitution - BS by a different name

[e p1uribus unum]

As a matter of fact...

In third grade I was seriously excited when I figured out a way to take more away from less (that's how I thought of it)

The teacher absolutely and authoritatively told me it was not possible and to behave and do the problems.

It did stick and was hard to unlearn.

Its another matter to expand learning. Fractions were major fun..the did not falsify whole numbers, they added.

Look, I'm seriously bad at some things. Music for one; however much I enjoy it, I really don't understand it. I don't try to teach it. I could only do harm.