Re: F=ma

["Dewey Dykstra, Jr." <dykstrad@EMAIL.BOISESTATE.EDU>]

> I am worrying that the presentation of equations which
> will initially be parsed as sentences by our students
> may affect their ability to grasp concepts. Should we
> pay some attention to this (I believe utterly neglected)
> question? Any PER folks out there who might know of some
> relevant work? Dewey?
>
> Leigh

Leigh and members of the list,

I do not think that there is specific research on which way to present an
equation, at least none with which I am familiar.  Most likely the
conceptual issues as to the nature of force and acceleration would be found
to overwhelm any variations due to the form of presentation of the
equation, would be my guess.  Of course, those hurdles once overcome, then
an alternative to F = ma might make more sense.  In short I think that
equations are far too dense conceptually for students to grasp concepts
from them.  In their place and at an appropriate time in a learning
experience, equations can express and allow students to examine the detail
of relationships between concepts.

It is not research, but Paul Hewitt has long advocated a form similar to
that which Leigh has suggested:  F/m = a.  In some sense it sets an
experience or observation on one side (RHS) and the "factors" which are
used to explain it on the other.  In my conceptual physics class, I usually
trot this version out after it appears that as many of the students as
possible have built the conceptions for "a", "F", and "m", which fit the
conceptual scheme in which this equation is embedded.  They come to class
with conceptions already of "a", "F", and "m", but not ones which fit the
conceptual scheme of the equation.  Each one of them has to be addressed,
which is not easy because of the inter-relationships that we perceive as
existing between them.*  I do not have them do calculations with it so much
as invite them to note how fiddling with the sizes of "F" and "m" gives
something that varies in the same way as "a" does.

With time one could get further into the math...The appearance of the
ability to express verbally how the acceleration changes with changes in
"F" and "m" represents to me the presence of the necessary first step
before going on to doing calculations, but in a one-semsester course, I'd
rather go on to other phenomena.

A very interesting series of books has recently come to my attention on the
development of several important concepts in physics.  They are by Max
Jammer, who many of you may know through his other books on QM.  One is
titled:  Concepts of Force.  It was originally published in 1957 and has
been recently taken up by Dover in reproduction (1999).  You can find it on
Amazon.com.  The others are on mass and space.  All three are around $8 ea.
All "must haves" on any physics teacher's bookshelf.  It also looks like
there is at least one update on some of his early books.  The very first
chapter in his "Concepts of Force" book is a *very interesting* view of the
development and nature of scientific concepts.  One might notice Jammer's
use of one of the same quotes I use in my signature file.

My students when they get down to the issue of do you *really* need to have
at least a little force in the direction of motion to maintain it (say in
constant velocity), they decide the way to settle the argument is to
actually measure all the forces.  Certainly a good plan of action.  If
we're trying to explain nature let "Nature" settle the argument.  As we all
know this is much easier said than done, but can it be done?  There two
problems:  (1) It is almost impossible (if not actually) to measure *all*
the forces without assuming the answer to the question of whether or not
the sum of the forces is, first.  (2) We don't actually measure force.  We
measure observable effects, experiences for which force is the explanation.
Apparently "Nature" can't or won't tell us "the answer," so we have to
decide based on other criteria.  Perhaps if we thought of force not as a
causal agent, but an explanatory entity...

Dewey
PS:  Leigh, thanks for thinking to ask.  I hope that other "PER" types wade
into this thread.

*Dykstra, Boyle, Monarch.  Science Education 76(6): 615 - 652 (1992)



(Please note the e-mail address change, valid as of 8/7/99.)
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Dewey I. Dykstra, Jr.                 Phone: (208)426-3105
Professor of Physics                  Dept:  (208)426-3775
Department of Physics/MCF421/418      Fax: (208)426-4330
Boise State University            dykstrad@email.boisestate.edu
1910 University Drive                 Boise Highlanders
Boise, ID 83725-1570                  novice piper: GHB, Uilleann

"Physical concepts are the free creations of the human mind and
are not, however it may seem, uniquely determined by the external
world."--A. Einstein in The Evolution of Physics with L. Infeld,
1938.
"Every [person's] world picture is and always remains a construct
of [her or his] mind and cannot be proved to have any other existence."
--E. Schrodinger in Mind and Matter, 1958.
"Don't mistake your watermelon for the universe."  --K. Amdahl in
There Are No Electrons, 1991.
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