In article ,
Donna Metler wrote:

"Herman Rubin" wrote in message
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In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:

.................

No, it's not. The notion of a variable that
can represent a wide variety of things is a pretty serious
abstraction. At that age, language is much more concrete,
usually representing a 1-1 correspondence between the
word and that which it represents.

They do know about pronouns, and the ambiguity in
their use. They also know of ambiguity in common
nouns, and there are quite of few of them such as
boy, girl, table, chair, raindrop, dog, cat, rabbit,
and enough more for them to realize that this is
not the case. They can handle a story in which
rabbits are named Flopsy, Mopsy, Cottontail, and
Peter. How hard is it to get across the idea that
they can have any other set of names.

It is exactly this which can make it difficult. Very young children
overgeneralize. If something's furry, they may call it "doggie" or if they
see a woman, they may call her "mommy".

Later, they add specifics. That doggie is actually a cat, and his name is
Tom. That mommy is Stephen's mommy, and her name is Mrs. Jones. And
everything is in relation to the child.

To a very young child, EVERYTHING is a variable. As they grow up, they start
getting the idea that some things are fixed, can be trusted, can be depended
on and which can't. Because that dog is NOT a cat, and he's not a horse
either, even though all three are items in the set of "furry animals".
Stephen's mommy is not the same as Jamie's mommy or Kevin's Daddy. They're
not interchangable parts. And, no, the world doesn't stop when you're not
there, and no, it doesn't revolve around you.

Until a child is through this stage, which continues into early elementary
school, I don't think the concept of "they can have any name you give them"
is going to have the right effect-because young children already believe
this, and are slowly but surely learning that this ISN'T the case for most
of the things they encounter in day to day life.

Are you sure? This has NOT been tried, and I did not
even try it at all with my first child, and only did
it with my second child later. The difference in their
abilities was great, and they both would have benefited
from programs which went at their mental levels.

The first one got it without my teaching, from the books I
have mentioned before which use difficult vocabulary, when
in kindergarten. The second got in in connection with
learning the order of the alphabet; variables for the
various problems were used in alphabetic order, with no
regard to what was being discussed.

As I have said, the material being used for teaching was
not intended for the age at which they were taught, and
there were other drawbacks with them.

Children can learn abstract ideas if they are taught.
How hard it is to teach them is not at all clear, but
the idea that the process of abstraction, which is
quite difficult, is needed to understand abstract ideas,
is just plain false.

Another point; it is not necessary to be able to prove
theorems, or to carry out calculations, to understand
the underlying principles or the results.





--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
Phone: (765)494-6054 FAX: (765)494-0558