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Forgetting and Remembering, Re-inventing and Explaining

Date: 02/19/2011 at 12:54:50
From: Elaine
Subject: Help Remembering Math

Dear Person,

This is the first time I ever got on this website. I need a bit of help.

I can quickly learn math things I don't understand, but I always forget a
few days later. Do you have any way that can help me remember what I've
learned?

For example, one day I learned about ratios and now I forgot how to do
them until I Googled it. Can you help?

Also, just 'cause I'm only 10 doesn't mean you have to talk all kid-like
to me. I am highly advanced in my classses and am in APEX. I do a grade up
than the grade level I am in's work. So, feel free to talk to me as if I
were 14 or something.

                     Elaine



Date: 02/21/2011 at 14:35:42
From: Doctor Ian
Subject: Re: Help Remembering Math

Hi Elaine,

> This is the first time I ever got on this website. I need a bit of help. 
> I can quickly learn math things I don't understand, but I always forget a
> few days later. Do you have any way that can help me remember what I've
> learned?

So one might say that you haven't really 'learned' them, right? This is
normal for things you don't keep doing on a regular basis.

A couple of months ago, I was making bread every day, so I knew the recipe
for that -- how much of each ingredient to use, how hot to make the oven,
and so on.

But now that I haven't done it in a while, I'd have to look it all up
again! So did I really 'learn' it? 'Yes' in the sense that I was able to do
it. But 'no' in the sense of permanently committing it to memory.

On the other hand, there are things I haven't done for a long time that
I'd still be able to do right now if I had to. Hitting a golf ball, for
example.

What's the difference? I've hit a lot of golf balls, over a long period of
time; but making bread, I've only done a few times, all over a short
period. In a word: I've practiced golf a lot, but I haven't practiced
making bread very much.

The same thing applies to the math you're learning. If you don't keep
practicing, it will fade. But that has nothing to do with the fact that
it's math. The same is true of just about anything.

> For example, one day I learned about ratios and now I forgot how to do
> them until I Googled it. Can you help?

One other difference between really _learning_ something and being able to
do it with help is that when you really know something, you're able to
explain it to someone else who doesn't know it.

In the case of something like ratios, it's one thing to be able to set up
and solve a problem, by following some steps that someone else showed you.
It's quite another thing to be able to explain to someone else, not just
WHAT the steps are, but WHY those steps work.

Another way to think about this is: if you can re-invent something that
you've forgotten, then you really knew it. Otherwise, you didn't.

So how do you make use of this information? First, practice the things you
learn -- and in small sessions over a long time, not just a lot in a few
long sessions. It would be better to use a skill twice a day for a week
than to use it 14 times on a single day, even though that works out to the
same number of uses.

The second thing is, when you've learned something, try to teach it to
someone who doesn't already know it. Younger brothers and sisters are
perfect for this kind of thing. Other students in your class are also
good.

The important thing about this kind of teaching, though, isn't so much
what you say at first: "Do this, then do this, then do this, and you get
the answer." The important part is when the other person doesn't
understand, and starts to ask questions. It's when you try to answer the
questions that you realize that maybe you don't understand what you're
teaching as well as you thought you did! And that's when a lot of real
learning takes place: when you have to answer your OWN questions in order
to answer the OTHER person's.

That, by the way, is one of the reasons volunteers like to answer
questions for Ask Dr. Math. It constantly reminds us of how much we don't
actually know about things we thought we 'knew.' :^D

Does this help? Write back if you'd like to talk more about this, or
anything else.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 02/21/2011 at 16:14:21
From: Elaine
Subject: Thank you (Help Remembering Math)

Thanks! That helped a lot!
Associated Topics:
Middle School About Math

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