Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: electric charge




Most people (not including young children) can visualize or be
taught to visualize the conservative flow of a substance such
as water. From there it is a relatively small step to visualize
the conservative flow of charge and/or energy and/or whatever.


While this is technically true the reality is far from the truth. In the
early years before school children discover the conservation of things so
that 6 objects in a line are equivalent to 6 grouped together. According to
Piaget's researches students in the early grades should also discover other
conservation laws such as the idea that a ball of clay weights the same when
flattened or that a liquid has the same volume irrespective of the container
shape. They should be able to respond that water rises to the same height
when marbles of the same size but different weight sink in identical
cylinders of water. Unfortunately a number of individuals do not actually
understand this.

The idea of conservation is a very difficult subject for many students and
many do not actually learn it at all. The relatively small step is actually
an enormous leap especially when they lack some of the previously mentioned
ideas. If the individual has achieved a level of thinking such that they
test as formal thinkers, the step is quite manageable. On the other hand
individuals who test as concrete thinkers seem to have extreme difficulty
with what we term simple conservation ideas. Even for formal thinkers some
of these ideas may still be difficult, because they actually require
"Theoretical" levels of thinking, which Anton Lawson has proposed as a stage
beyond formal.

One of the basic difficulties stems from the idea of change in a quantity.
You can get students to parrot back that when A loses the conserved quantity
B must gain. But when you put that idea in a slightly unfamiliar context
such as a graph of the conserved quantity vs time they have difficulty.
When asked to draw the graph for B given the graph for A and the starting
point for B, they will often draw what looks nice such as a symmetrical
graph. They do not apply the idea that B has to go up the same amount that
A decreases. My formal thinkers just look at it and immediately see the
answer. Similarly they will say that when B has a decrease in negative
charge when it touches A that A loses electrons, or other "funny" answers.
This happens even though they all know that electrons are negative and they
have studied the idea of charge transfer being responsible for electrostatic
effects.

Unfortunately fully formal thinkers (Theoretical thinkers?) usually do not
realize that what seems easy to them is difficult to others who lack these
methods of thinking. However it is possible to have students develop these
ways of thinking, but it requires substantial effort and an extended time.
Arons points out that up to 85% of adults seem to capable of becoming formal
thinkers, but sadly only 30% achieve it in our society. As a result I would
put most to be at most 30%.

John M. Clement
Houston, TX