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Re: a fan of 'momentum first'



At 15:08 -0800 4/9/02, kowalskil wrote:

The so-called "traditional" sequence starts with
static equilibrium, then F=m*a, then p, then E.
Where does the static equilibrium fit in the
"momentum first" sequence?

At about the same place relative to F=ma that is does in the
traditional sequence. We introduce the idea of force as something
that *can* change momentum, which leads to the idea of net force,
which leads to the first law which leads to the idea of static
(linear) equilibrium. Then we use the idea of impulse to develop F=ma
(which is derivable from cons. of p, just as cons. of p is derivable
from F=ma). It all fits together quite nicely.

Of course the idea of static equilibrium is not complete because the
concept of torque doesn't get introduced until later. But that is
true with the traditional approach as well. However, in our approach
we start with some necessary preliminaries, such as uniform motion,
and relative motion and some others. Among the "others" we introduce
center of mass in the context of balancing (actually center of
gravity, but as we all know, as long as the grav. field is uniform c.
of m. and c. of g. are coincident). Then when torques are introduced,
we can go back to the idea of balancing that was introduced at the
time of c. of m. and we find that the idea of torque is not so novel
that the students have to struggle to get it--there has been at least
part of the necessary gestation period before a new idea seems
"natural."

Relative motion and center of mass are important (but not totally new
ideas to students who have had any contact with the outside world),
because they are needed for our powerful approach to the physics of
collisions, which enables the students to do all sorts of
one-dimensional collisions by the time they are finished. And doing
collisions early allows us to kind of sweep the issue of how
velocities change under the rug until they are more intellectually
ready to tackle the concept of acceleration, which is an idea about
which their preconceptions are mostly wrong. So having a rich context
in which to introduce this idea is important, since we have to spend
about as much time disabusing them of their preconceptions as we do
enabling them to learn the correct approach to acceleration.

(When I say "we," I mean the course that Chuck Britton and I--and
some others--have been working on for several years.)

One of the features of the p-first sequence that we like very much is
that it lends itself to something of a spiral approach. That is, we
are able to introduce some concepts early, let them ruminate for a
while, and then reintroduce them and apply them a little later, when
the context for that idea is richer. We have found that, not only
does the approach allow us to delve a bit deeper into some topics,
but the logical development keeps almost all the concepts we consider
important in a context that makes it easier for the students to
absorb. The course really does build on itself--there are no units
that are entirely self-contained, so once the student completes that
unit and has been tested, they are still not free to just forget that
stuff and move on to the next new topic, because the next new topic
is an expanded extension of the last topic.

I wish I could say that we had done some systematic evaluations of
this approach, but we haven't. So, like John D. we can't say
definitively that the method is superior, but, for me, I find it a
joy to teach this way. Every class depends on the previous ones and
nothing comes out of nowhere. I hope that joy gets transmitted to the
students.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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