Re: [Phys-L] [SPAM] Re: form of Newtons 2nd law

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

Ok, either way of stating the equation is certainly valid but...

What you do to get students to make sense is another completely different
issue.  When you "present" something that doesn't make sense they just
memorize.  But if you present something which makes connections to previous
ideas, they can connect concepts.  Then the concepts can be developed and
changed to be more consistent with how physicists think.  But if you insist
on a formulation which is alien you have killed the learning.

True one can not say mathematically that either F or A is a cause, but 99%
of people who are not professional physicists will say that force causes
something.  So you build on that paradigm, and co-opt it with time.

This problem shows up in NTN3 where students are simply told the law, and
the vast majority do not believe it.  So when you show it using the
published ILDs or any other good PER curriculum they begin to believe it
which means they will answer NTN3 law questions correctly in evaluations.

> From the point of view of having students do an experiment to find NTN2 you
have them pick the force or mass and measure the acceleration.  So it
naturally comes out that acceleration depends on force and mass.  The
acceleration is proportional to the force and inversely proportional to the
mass, and you bring out that idea.  This helps students to understand
proportional and compensation reasoning.  So in PER the natural form is
a=f/m.  It also helps them understand 2 variable reasoning.  Please get with
it and study the literature on how people learn or don't learn.  Physics
understanding does not confer an ability to teach well or to understand how
students think and learn.  The presented sequence is exactly what Modeling
and many other PER curricula do.

If you don't connect ideas and address the previous paradigm, it remains in
memory.  Because it has had lots of reinforcement it is much more powerful
than the recent veneer of learning that you have provided.  So as soon as
you ask questions which are different from the ones you asked in class the
student will respond with the previous paradigm.  One way of rooting it out
is to use a predict, confront, resolve cycle within a short time.
Essentially students have to have the existing idea in short term memory so
when you confront it, it is stored back changed during the reconsolidation
cycle.  Another way it to use anchor and bridging analogies where you pick a
case where they agree on the answer and then bend the ideas in a series of
steps towards the correct answer.  There are other ways which do things like
have the students debate alternative historical ideas.  This was found to be
very effective.

In the case of NTN2 the issue of causality is miniscule compared to the
issue that student think force causes velocity.  Just presenting the
equation in standard form does NOTHING to change this.  So keep the idea
that force causes something and bend it to causing acceleration or change in
velocity.  Then with maturity students may understand that mathematically
speaking there is no causality.  And remember that the common definition of
causality is different from the mathematical definition.  For a student to
understand the math definition probably requires them to be at the
theoretical level of reasoning, which is very rare.  You can't have them
jump from using concrete ideas to using purely formal ideas.  They have to
get there in a series of steps.

BTW if you read Lawson's book you gain an interesting perspective on
thinking.  And when you look at the research you find that propositional
logic thinking is rare in students.  Understanding causality mathematically
probably requires the ability to use propositional logic, rather than just
being able to know about it.  Math usually teaches just the latter.

John M. Clement
Houston, TX
 
> > I like the a = F/m form since an acceleration results from 
> a net force.
> > It's just easier to write F = ma (no fraction>) as N2L. 
> Similarly, I write
> > (derive) Ohm's law as I = V/R -- a current results from a potential
> > difference. Again, it's easier to write V = IR.
>
> I wouldn't have said that.