Perhaps I was being a bit extreme and I like the gist of your
idea here.
The problem I see with the way things have been done, is they're
tying too many things together into one place, including
self-esteem. Removing an "I *can* do this" attitude and trying
to replace it with new building blocks is a dangerous process
that needs to be handled carefully. I've seen people in the
military that they broke down and remolded in the fashion... but
they were over 18 years old.. and even some of _them_ cracked
and couldn't be put back together again. Thankfully, it
_generally_ works, but I don't worry about the "general" but the
outliers. Our greatest resources for future innovations whose
creativity is cut off to exchange it with conformity.
I don't see the need for the exchange. Separate the steps.
That's why I like your "simplify the proof" idea. Here's how I
would do it:
Instead of having to "show your work" (make it optional) for
their OWN math problems, they should look at MANY MANY examples
of _other people's work_ and offer possible ways that it can be
simplified.
Who knows? Perhaps by showing a LOT OF different math styles, a
kid might find *their* logical process shown up there and
_decide_ to choose a different way, or continue with the ways
they're comfortable with.
For example: I do math in my head. But I have my own ways to do
it. It's not what they taught in school. I have an intuitive
math sense. If I was to break it down into steps that work - and
they work *very very quickly* in my head - it wouldn't look
ANYTHING like the type of methodologies I ever saw in school, or
even in some of the newer Common Core methods (going by 5s and
10s).
Even the institutionalized methodology for doing math, was once
simply one person's short-cut for math. The beauty of math is
that it's SO FLEXIBLE; you can get there by MANY MANY roads.
The "efficient formula" seems nice, and may work for some people
and I _suppose_ it *could* be the "preferred way". I just don't
like it being the EXCLUSIVE way.
I suppose, in that sense, Common Core is doing some of it
better. Maybe I've just outlined the idealized Common Core;
initially I _thought_ that's what they were going to do, but
they weren't, and they're not; they're just substituting one
dogma for another dogma.
Anyway, I like the idea of showing various ways to accomplish
the same thing, so long as it doesn't force a single method to
dominate in their OWN WORK that's tied to grades.
In Common Core literature, they say, "Expect the grades to go
down for a few years. Since Grades are simply a measuring tool
and not saying if you're a good or bad student, therefore grades
don't matter".
Nice if it was true, but it's wrong. Grades DO matter.
Kids/parents/aunts/uncles keep score. Can't take the sports out
of academics; and making it hard for EVERYBODY by removing all
the working shortcuts doesn't help things.
Ok.. looks like I started my common core rant tongue emoticon I
should shush.
