Re: [Phys-L] proportional reasoning, scaling laws, et cetera

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

Actually it is a both world. Students have to use both representations, and
Modelers find tha getting them to use the graphical representation first
helps them with using algebra.  By first, students have to initially use the
graphical representations without algebra.  Actually they also have to use a
description and a picture.  These make up the 4 representations that have to
be used for full understanding.  Students have difficulty with translating
between some of these, but once that difficulty is lessned, they understand
the physics much better.

The UMPERG group uses an activity to break students of initially looking for
equations. It is at:
http://www.srri.umass.edu/mop/MOPSamples
Number 16 part B is a killer.  Students can easily do Part A and C, but even
most calculus based students have difficulty with B, and forget it for
algebra based classes.  So you throw it at the students after they have a
basic equation for constant motion, and you monitor the groups.  When a
group has spent a bit of time on part B, you eventually tell them to to go
on and finish the rest, before coming back to Part B.  Or you tell them to
skip part B.  As a challenge you can aks advanced students to work on part B
later at home.  Typically only 5% of advanced students can do part B.  I
have even seen PhD physicists challenged by getting signs wrong, which of
course kills the answer.  This activity can also bring in the idea that the
precise location and time are not really mathematically exact because it
will depend on the observer, so an approximate answer is just as valid as an
algebraically precise answer.

Number 46 is great ranking task!

Of course to get students to use graphs, you define quantities graphically.
So you define V as the slope of an X-t graph.  You start with the graphs,
NOT the equations.  You can also appeal to the idea that the area is adding
up the contributions for each second, and that the "meaning" of 3.5m/s is
that something travels 3.5m each second.  You do not let them use the word
"per" because that is just a standing for the /, and does not convey any
meaning to students.  You can tell them that it means each, but that just
goes away and is not absorbed.  So saying it means you travel "3.5 m per
second", is just reading the expression out loud.  Students have to be told
that you can write the number, read it out loud, or give the meaning.  Why
doesn't math get them to give the meaning, and use that meaning when
figuring things out???

John M. Clement
Houston, TX


> I agree that slopes and areas are visually more appealing and 
> quite often easier to use, but how do you get students to 
> REMEMBER or BELIEVE that the distance covered IS the area 
> under the curve?  How do you get them to REMEMBER that it is 
> the velocity vs time graph, not the position vs time graph or 
> acceleration vs time graph.
>
> Some students respond to graphics and geometry, some students 
> respond to symbols and algebra. It is NOT and either/or 
> world, and I believe that if we bring them in together (much 
> like a treble hook on a fishing lure) at least one of them will catch.
>
> > And students who are way away from Calculus can get the 
> same results by
> > finding the areas under the velocity vs time graphs.
> >
> > Slopes and areas are WAY easier for some to grasp than 
> strict algebra based
> > derivations.
> >
> > .
> _______________________________________________