"Is Algebra Necessary?"

Vorde

I think there is a bit of a catch-22 here, considering we are on a physics forum.....

But I agree with your point.

Ivan Seeking

We should be teaching Intelligent Design and not Algebra. Seems pretty clear to me.

Vorde

This man is a genius.

Integral

IMHO, a large part of the problem is that many elementray school teachers are math phobes themselves. Since they are the ones that set the tone early, we are fighting a uphill battle.

Rather then no child left behind we should be finding the talented and pushing them ...HARD!

SW VandeCarr

I think kids develop a mental block right at the start. They understand that a+a=2a. But then you have to tell them about a+b.

miglo

saw this article today, i was going to post it on PF but i forgot, glad to see it popped up though

i think a lot of kids who are failing at algebra just don't care about the subject, and because of that they would rather just fail than have to put in the time to get a decent grade

but then again there are some bad teachers out there, and i would know since i had an algebra teacher who spent more time playing world of warcraft during class rather than teaching

arildno

Correct. The no child left behind policy is silly and unrealistic, simply because there aren't enough good teachers who'd bother with teaching 6 and 7-year olds who are too dumb to begin with.
We WILL have enough good teachers to teach the bright ones, though.

arildno

Most would understand it a lot better if we simply wrote: a+a=2*a, just like 3+3=2*3, and so on.
It is extremely unpedagogic to use algebraic short hand 2a, but I don't know if we ever manage to get even this idiotically simple thing across to the school system.

SW VandeCarr

I don't agree. Your suggestion happens to work in this particular example, but in general: a+3a+3a=7a. It's understood that 2a means 2*a and 1*a is equivalent to a. You missed the point of my example. My post was to show the difference between arithmetic and algebra. Arithmetic addition is reducible. That is, a string of numbers can be reduced to one number. However there are additive expressions in algebra that are irreducible (as formulas).

arildno

3+2*3+3*3=6*3

In short:
Prior to even teaching algebra, kids should learn to do arithmetic in "new" ways, for example:

"Calculate 3*2+4*2-2*2 in two different ways"

arildno

In the bad, standard way of teaching algebra, you mix together three new "things" from the start, making the required leap of understanding that much bigger:

1. Introduction of letters-as-numbers
2. Suppression of multiplication signs
3. Adding together in a wholly new manner.

2. isn't necessary at all, and just muddles the whole thing, while 3. could be profitably taught at pre-algebra level.

SW VandeCarr

OK. But you have to remember that multiplication is simply a shorthand for repeated addition.

arildno

"My post was to show the difference between arithmetic and algebra. Arithmetic addition is reducible. That is, a string of numbers can be reduced to one number"
The weight of this being??
The need to suppress the multiplication sign??
The need to wait utilizing the distribution law in computation until you get to algebra level?

essentially, I don't see your point at all.

arildno

And why should therefore the multiplication sign be suppressed from the start in learning algebra??

Vorde

I have no academic or scientific experience with this subject, only what I have learned from middle school tutoring and actually being in an Algebra I class, so take my statements with due skepticism.

But of the many things I have seen causing trouble and halting understanding in math, the shorthand for multiplication is not one of them.

I think VandeCarr's point was that if you are going to respond so negatively to the suppression of the multiplication sign, why aren't you responding equally so to the suppression of repeated addition as multiplication. Sure you can define multiplication as an operation of its own, but I promise all young math students know multiplication only as repeated addition.

arildno

"why aren't you responding equally so to the suppression of repeated addition as multiplication."
That is supposed to be thoroughly learnt when multiplication is introduced to begin with, and is therefore to regarded as "mastered" when you get to algebra.

SW VandeCarr

I agree. There is a conceptual difference between arithmetic and algebra. An expression like a+b is irreducible because it involves different categories. 'b' things and 'a' things cannot be added unless one reformulates the problem and this involves categories or sets. These formal concepts are usually reserved for higher math, so the kids have deal with this issue in their own way.