Re: [Phys-l] the importance of F causing ma (and not vice versa)

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

While this "should be" may be desirable, currently it not happening.  The
statistics are extremely dismal.  Only a fraction of students leaving HS
test at the formal operational level.  This has been true for at least the
last 50 years, and it is not improving.  Introduction of this idea is
probably not possible before grade 6 because the brain development has not
yet happened.  A good reading of Piaget's experiments and results is very
revealing here.

> The idea that equality is reflexive, symmetric, and transitive "should" be
> introduced in 7th grade (possibly sooner), and "should" be pretty well
> consolidated before students reach HS physics ... let alone college
> physics.

Equality is actually a very abstract idea and seems to be much more
difficult than causation.  It is actually probably a rung on the way to
higher thinking.  Now the mathematical definition of causation is more
difficult.

The real problem here is that theoretical thinkers do not understand the
problems at the lower thinking levels.  They consider their way of thinking
to be easier.  But when students are usually exposed to the higher thinking,
it is usually done in a direct instruction format which does not raise their
thinking.  Indeed it may even suppress the development of higher level
thinking in many students.  Remember students must go from the concrete to
the abstract to properly connect the ideas.  The concept the force causes
acceleration is much more concrete than the abstract F=ma.  And remember
that the brain does not automatically make connections in both directions.

> Equality is a much simpler notion than causation.  Why use something
> complicated as a rung on the climb to something simpler?  That violates the
> most basic pedagogical principles.

Now can anyone cite any studies which show that a=F/m is inferior to F=ma?
I have proposed indirect evidence and anecdotal evidence for the first
formulation.  Remember pedagogy is an experimental science, not a
theoretical construct,   yet.

John M. Clement
Houston, TX