Re: [Phys-l] Student engagement--GAIN

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

Ok then the intent is clear.  But the reasoning behind the intent can not be
discovered by logic or historical references.  The basic problem is that the
students are in general just equation hunting.  But when that habit is
broken we have found that the students become better problem solvers.
Actually they have been taught to be equation hunters by well meaning
teachers.

Again this is a case where logic can not tell you the optimum teaching path.
Only research and comparing different ways of teaching can give the
necessary insight into doing it better.  It never ceases to amaze me that
trained scientists can understand that research can reveal counterintuitive
physical principles, but not understand that it can also reveal
counterintuitive social and educational principles.

For example one would assume that it is better to communicate ideas and tell
students how to solve problems.  This is most logical.  But the research
shows that when you do that the students temporarily gain the ability to
solve only the problems you have presented, and can not transfer.  But if
you get them to struggle in groups first, then present an algorithm,
transfer does happen.  Both Michelle Perry and Schwartz have done work in
this area in math.

Math teachers are probably even more resistant to research because they wish
to think that all things are logical so teaching is an exercise in logic.
Similarly engineers tend to take the same point of view in a very black and
white fashion.

So the idea that students first need to use geometrical methods has been
presented.  In reality, physicists use geometrical methods, but sometimes
only mentally to map out a solution before using algebra to get the
solution.  That is the actual goal of the exercise, to begin to get students
to look at equations after mapping out a solution.  The graphical method can
be the way of solving, or just a way of visualizing how to solve.

I can remember that teachers would say "make a drawing first".  Well
students have the paradigm that they don't need to do that.  And many manage
to get by.  But if you give them problems where the drawing is absolutely
vital to solution, then they begin to see that it is a good way of starting.
But without that understanding, they will try to solve hard problems by just
writing down standard equations, or they will give up because they have no
way of starting on a problem.  Humans usually have to be confronted with
situations where only a new method will work before they change paradigms.
The genius does not need this, but the rest of us do.

I gave my students and Ah-ha moment.  I gave them the problem of finding the
force on a 1kg mass located on Mars, but exerted by the Earth when they are
closest.  I also gave a table of planetary and orbital radii along with the
various masses.  Some students utterly gagged on this because they had no
mental picture.  So I told them to draw the situation, and also the path the
planets took.  After that it became easy, but one student commented in an
Ah-ha fashion that the drawing really helps.  He may have had a paradigm
changing moment.

The real goal of education should be to have students transfer what they
know to slightly or greatly different situations, not just giving them the
ability to do set problems.  The experiments show that the traditional
method fail here.

John M. Clement
Houston, TX


> John Clement wrote:
> > Of course your puzzle is not the same because they start at the same
> time.
> > But my reply is do you know why the puzzle was presented in the
> activity?
> > It has a pedagogical goal.
> *** One can easily suppose that subverting the usual student means to
> formulating an algebraic solution was intended in all good faith, in
> order to facilitate inspection of geometric or graphical means.