Re: Sixth grade science teaching

In article <1127746688.253674.262870@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
widsith <widsith@xxxxxxxxx> wrote:
>
>Paul J Gans wrote:
>> Grace Haliburton <kaosgrace@xxxxxxxxx> wrote:

[snip]

>Neither Grace, nor I, am arguing that memorization is not necessary,
>but that memorization _alone_, is not the best learning method, and is
>_fragile_.

Nor are Paul are I suggesting that mathematics _ends_ with getting
the tables in to memory. More in a moment.

>If you are taught things as standalone facts, without
>context, without relationship to eachother, once you forget, which you
>will when you dont use it, its lost. If you are taught the item with
>its context, then that context forms a web between the independent
>facts and allows for far greater resilliency, even if a few of the data
>points are lost.

Context, principles (associative, distributive, commutative laws get
you pretty far in re-developing the tables from a fragment), greater
context, alternate ways of viewing the process (arrays of skittles,
cuisinaire rods, areas of boxes, repeated addition, grouping of dots, ...)
etc. are good additions and ways to provide multiple frameworks upon
which to hang the facts. The multiple frameworks also make it more
likely that the facts are remembered for longer and more meaninfully.

The upshot, though, is that that, from where Paul and I are looking,
these are all just ways of getting the things stuck into memory. It is
important to get them stuck in to memory, we figure. The reason is
as exemplified by Grace's calculus example. When you're learning
the concepts of multiplication, getting 6x7 by adding 7 six times is
ok. It's a correct principle and leads, albeit slowly, to a correct
answer. But when you're out of multiplication class and in to, say,
calculus, it becomes an obstacle to learning the calculus if you're
taking that kind of time to get the coefficient in the derivative of
7x^6. By then, multiplication is assumed. It's an obstacle to further
learning to not have it in hand.

The speed is a related question. _some_ speed is a good idea. My
second grade (no special school or anything, blue collar area and the
town's school) had us learn the 9x9 addition and multiplication tables
to get through 10 problems in 10 seconds. This was no challenge to most of the
class, was made a game, was to progress at the student's own rate, etc.
But it did mean that when algebra started several years later, we weren't
still wrestling with the arithmetic aspect of doing algebra. We could
focus on that mysterious (for most of the class) matter of having
abstract symbols and to be carrying out inverse operations. Difficult
enough on its own. But there was no purpose or inducement to getting
speed beyond that point. A modest degree of speed is useful. A whole
lot of speed, as in your year of 50 problem races, is just silly.

Now the alert reader will have noticed that my own daughter did not
learn something that I consider reasonably important to learn. That's,
in part, because of a different and higher ranking principle of education
I hold. That is: About the worst thing you can to in encountering
a resistent student (say her with respect to math/science memorization
-- lines in plays she was in were little problem) is to try to force the
issue by frontal assault. (My oblique attempts didn't work either.)
Unfortunately she also encountered some (that aforementioned 3rd grade
teacher, iirc) who did try to force the issue, and the result is as
played out. Reinforces my belief, but didn't help her.

--
Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences

.

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