Re: little gee and its sign

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

> I just can't believe that a physics instructor would tell his/her class
> that g is acceleration!!!!!

I would agree with the substance of this, but not necessarily the tone.  I
can remember in HS wondering why one used the equation F=m g for a body at
rest with g=9.8m/s^2, when the body is not accelerating.  Using g=9.8 N/kg
is far preferable pedagogically.  It reduces the confusion that students
experience, and makes it a manageable idea.  In addition it emphasizes the
connection to Newton's gravitational law.  In an advanced class one might
wish to modify the value of g to include other effects, such as the Earth's
rotation, and give it a different interpretaton, but not for an introductory
class.  Yes N/kg = m/s^2, but intro. students do not think of that, and they
already have so many other new concepts to accomodate that this extra one
could be the last straw.

According to Piaget, people increase their thinking skill by being
confronted by a surprising event, that they are forced to accomodate.  If
the event is too surprising then the confusion remains and they can not
accomodate it by changing their thinking.  Too many surprising concepts at
once may actually overload the students.  A surprising event must usually be
an event that they experience, and not just something they are told, for it
to produce the necessary disequilibrium.  Students usually treat lecture
facts as things to memorize, and not things to believe or accomodate their
thinking to.


As far as the sign of g goes, this is really a problem of having the
students accomodate the idea that the sign has meaning, and that it must be
picked sensibly.  They need to have a variety of experiences where they see
that the sign matters.  This has to include being asked Socratically why
they pick certain signs.  This is actually an extended process, and is
seldom conveyed well by just giving them rules.  With my students I am
continually asking then whether the number they calculated is negative or
positive, and how do they know that.  When the velocity vector points to the
left is the value - or +, and what about to the right. Then of course there
is the second grade misconception.  They have been so trained to subtract
small numbers from large, that they do this when calculating change-in.  So
I push them to consider what it means, and how one can formulate a rule to
calculate it in a meaningful way.  I also point out the second grade
misconception, as being a rule they are using, which may not be appropriate.

Even coming up with contradictions in their thinking is not always
productive.  They often do not see the contradictions as having any
relationship to how they are thinking.  This also makes proof by
contradiction meaningless to many students.  A recent example of this was a
student who was calculating displacement from the front bumper of one
drawing to the back bumper of the next in a strobe (motion) diagram.  I
asked her to do this for several strobes, and pointed out that this made the
car skip instantly over certain regions of space.  She still insisted her
procedure was correct.  Finally after I got her to see the problem, she
realized she had to pick the same point on the car each time.  Giving her a
rule would have short circuited the process, and left her problem intact.

John M. Clement
Houston, TX