[Phys-l] Abstract vs concrete

["John Clement" <clement@hal-pc.org>]

The terms abstract and concrete have multiple meanings.  When one talks
about concrete vs abstract thinkers, the Piagetian terms are actually
concrete operations vs formal operational.  And in a certain sense these
terms are just labels determined by scores on a Piagetian test.  The formal
operational students can use statistical, proportional, and other fairly
well defined types of reasoning.  The concrete operational student should be
able to understand conservation of volume and of mass, but will not be able
to think proportionally.  In between would be transitional students who can
sometimes operate at higher levels depending on the context.

All of this requires some type of abstract thinking, even at the lower
level.  But there are discernable differences between the fully formal
operational students and the ones who are below transitional, and most
classes are a mixture of students at a variety of levels.  The good news is
that it is possible to push up students on Piagetian tests and when it is
well done, they also show gains on standardized tests.

So by all means we should be teaching abstract concepts, but in such a way
that students can make the connections.  In addition we should be teaching
in such a way that students increase their ability to think.  In other words
we should be engaging in cognitive enhancement strategies.  Anyone who is
interested in this subject should read both Shayer & Adey's works, and
Reuven Feuerstein's books.  They are available in the better libraries and
some can be purchased on Amazon.  Also I would suggest Anton Lawson's
papers.  Eugenia Etkina has read Lawson and is not infusing some of his work
into her teaching, so there is hope that PER will move on to the more vital
task of improving student thinking.

Maybe then we can stop pretending to teach so students can pretend to learn.

John M. Clement
Houston, TX

> > Remind me again as to why we are bothering to teach abstract
> > concepts to
> > concrete thinkers in the first place. Isn't it like reading poetry
> > to your
> > cat?
> >
> > Oops, now I remember. That's what we fake doing so we can make a
> > living!