Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Chookie wrote:
In article ,
(Herman Rubin) wrote:
Abstract ideas are NOT merely abstractions of more concrete
ones, but exist by themselves. Done that way, children
can understand them.
Only if they are developmentally ready. Claiming
that they exist independently does not suddenly make them
less abstract and more accessible.
It makes them MORE abstract, and hence more accessible.
The abstract idea, when understood, is simpler than
what it is an abstraction of, if presented that way.
I thought I'd mentioned this earlier, but apparently it is a distinctive of
gifted people that they work more easily from the abstract to the concrete,
from theory to practice. Average learners go the opposite way.
But even gifted kids have to scale the developmental
curve, and will not be ready for higher level abstractions
until they're ready for it. That might be a bit sooner than
for others, but it's not instantaneous.
Also, there's a difference between abstract concepts
and general/theory vs. specific/practice.
What is a "higher level abstraction"? Generally, the
more abstract, the easier, IF one does not make a big
issue about what it means.
A higher level of abstraction means more removed
from the concrete. And young children do not think the
same way adults or older children do, particularly in
terms of how they are able to reason about abstractions.
So, while it may be the case that your assertions hold
true for those who are developmentally able to deal
with abstractions, I seriously doubt it holds true for
those who are not yet at that point.
Even a weak learner can go from theory to practice.
I'm not sure that assertion holds up. Some
studies at least suggest that weaker learners do better
the other way 'round. Personally, I don't have an
opinion there--haven't looked at the issue enough.
*I* prefer to go from theory to practice when learning
known material, but don't know that's representative.
If
one understands something, and I do not mean knows the
words or even knows how to prove the theorems, it is
easy to apply.
Well, sure. I don't believe anyone has disputed
that. (Though I have suggested that believing one
understands something is not always the same as understanding
something, and thus it is necessary to test one's
understanding through application.)
Best wishes,
Ericka