Re: kinematics, traditional or not

[John Clement <clement@HAL-PC.ORG>]

> Robert Cohen wrote:
>
> > *You* know why defining v and a are useful.  *I* know why
> defining them is
> > useful.  Everyone on this list knows why defining them is useful.
> >
> > My point is that the *students* don't.
>
> I find this puzzling and very much outside my experience with students.
> Acceleration is a very concrete entity that students can
> visualize and have a
> feeling that they are "getting Physics" early on in the course.
> If as much class
> time is used to develop the concept of acceleration (e.g. - a
> ball thrown upward
> loses 10 m/s in speed every second) and to spend time doing
> conceptual type
> problems (throw a ball upward at 40 m/s - what is it's speed
> after 3 seconds)
> instead of doing clever but boring calculus derivations of the kinematic
> equations, the students will then be receptive to the more abstract and
> beautiful ideas contained in Newton's Laws. The calculus is in
> all the textbooks
> - there are better ways for us to use class time.

Actually acceleration is a very abstract idea, and is probably in the class
of theoretical ideas.  If you look at the work of Anton Lawson, he finds
that there are 3 ways to classify concepts, Descriptive, Intermediate, with
the hardest being theoretical.  According to his scheme most physics
quantities fall in this latter class.  He also finds that there is possibly
a level of thinking above formal operational at which the theoretical class
of ideas becomes easier to grasp.  He has some fairly persuasive evidence
for this.  A good reference to this is "What Kinds of Scientific Concepts
Exist?  Concept Construction and Intellectual Development in College
Biology", JRST Vol 37 #9, pp 996-1018 (2000).  I highly recommend looking at
it.  He says: "The meaning of theoretical concepts comes not from direct
sensory input but from the theories from which ideas originate.  Other
theoretical concepts about objects too small to see include things such as
photons electrons, quarks and any type of process that presumably involves
knowing what takes place in terms of interacting atoms and molecules...  "
He classifies the following as theoretical: molecule,  combustion,
convergent evolution, osmosis, gene, photosynthesis.

I totally agree that the proper activities can make students more receptive
to the ideas, and this lines up with various researchers results.  The
derivations are very unhelpful especially when viewed from the perspective
of the MPEX.  Students treat the derivations as just an assurance that it is
OK to use the derived equations.

John M. Clement
Houston, TX