Concern over my learning style

[jonsul]

[my bad, I didn't read the update to use this the mail-list when I
first posted this in the forum. You can close the thread I made there
I guess]

I think that I've most struggled with math because of the way I learn.
If I can use it and play around with it I can learn it for life. I'm
not very good at just memorizing stuff and using it later. Which is
why I find programming so easy for me, you give me the problem and I
can do some research and then build it myself with every tool known at
my disposal. I think that is what sets it apart from arithmetic is
that there's little fog of war, no curtain blocking half of the
building blocks I could use to reach an answer. Most of my experience
in learning math has been being told to just memorize it and don't
worry about it till later. That doesn't work for me, I need to know
why I'm learning this and how it's working the way it is.

With learning math it seems teachers are intentionally holding back a
lot of it to teach us in baby steps. In some programming courses I've
taken they've been like this too, but with programming I have a wide
amount of resources open to me that removes the curtain. Because of
this 80% of what I know about programming I've taught myself. I can't
find resources like this easily for math.

My concern is that math may not work like that. Will I always just
have to memorize equations and not know why they're working? Will I
ever have everything open to me? Is this something I can hope to
accomplish?

Thanks

[Alan Cooper]

Don't worry, what you describe as your style is the right one for math.
For each concept or rule: Play with it, test it with examples, and try
to find an explanation for why it is true. Then you won't have to
memorize it because you can't ever forget something that you have
actually understood.
Whoever told you "just memorize it and don't worry about it till later"
isn't any kind of "mathematician" that I'd want to be associated with.
cheers,
Alan

[Joe Corneli]

> With learning math it seems teachers are intentionally holding back a
> lot of it to teach us in baby steps.

In my view, "intentionally holding things back" is bad,
but baby steps can still be good, sometimes. It should
be your choice -- sometimes you might use baby steps,
sometimes you might use giant leaps. If you have a goal
in mind, you'll likely wind up going in the right direction
after a while :).

> My concern is that math may not work like that. Will I always just
> have to memorize equations and not know why they're working? Will I
> ever have everything open to me? Is this something I can hope to
> accomplish?

I hope it's something over time many people working together can
accomplish. It's just not the way things are set up "by default". But
I think you *can* simulate it in small-scale forms. E.g. pick a
relatively challenging textbook (e.g. the "Concrete Mathematics"
text might be one that would interest you, and besides, you'd have
someone to talk about it with here...) and the get as many supporting
texts and materials as you can find. You almost always have to make
*your own* map of the subject as you go. Doing exercises helps
with that... you should have some hard ones accessible, and
some easier ones around to help you work your way up to the
hard ones.

Another important thing is to be able to ask questions when you're stuck.
This group should help w/ that...

BTW, I noticed that a copy of Concrete Mathematics is online...
http://www.xpmath.com/ebooks/files/concrete.pdf