procees vs results

Ok, fayanoraand friends have been ranting about education. Especially about math.

One of their gripes was getting marked down for getting the right answer, but not using the method the teacher was teaching.

Well, sorry, but the hole *point* is that you are being taught the *process*, not the answer.

As an example, yes, you were able to use a hammer and nails to fasten those two pieces of wood togeher. But you were supposed to be learning how to use a screwdriver ansd screws.

Now, I'll freely admit that a lot of teacher go overboard on this, and a numbr of those don't actually understand about the "process vs results" bity. Or at least don't understand it as well as they should.

But it is a valid point.

A lot of the stuff they are trying to teach you is stuff that later lessons will buuild on. And if you use a different method, you won't have the method they were trying to teach you to buiuld upon.

So yes, *how* you got the answer is often more important than getting the right answer.

At the same time, there are *simple* things that most math classes fail to teach students. Things that would actually help them to understand faster.

The biggest example is inverse operations. That is, stuff like subtraction being the inverse operation for addition.

So if 2+3 = 5, then 5-2=3 and 5-3=2

Ditto for multiplaction and division.

And even more important, but rarely explained is the relationship between addition and multiplication much less between division and subtraction.

Multiplication *is repeted addition. 5*3 is 5 3s added togeher or 3 5s added togerher.

And more importantly (at least for getting some students to understand) is that 15 divided by 3 is "how many times can you subtact 3 from 15?"

I tutored some folks in math years back and the Aha! moments when I explained that sort of thing were a wonder top behold.

Another thiong, that they tried to do with the New Math in the mid 60s, was teaching you *why*. Especially the why of the method. Alas, while I got hit with that at just the right time, not everbody did.

And it's one of the things that seems to have gotten lots. They seem to have kept the exercises, and some of the methods, but lost most of the explanations.

BTW. Fay, 3+5 *does* equal 8 "because I say so". That particular level of math *is* purely arbitrary.

Yes, in the real world, it's pretty easy to show that 3 apples plus 5 apples gives you 8 apples. But you can have valid mathematical systems where that isn't true. They just don't apply to discrete, real world objects.