Re: graph interpretation, was "Proper" scientific notation

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Wed, 11 Mar 1998, John Gastineau wrote:

> At 10:32 PM 3/10/98 -0500, Donald E. Simanek wrote:
>
> > I do think (from my experience) that the student's experience in
> > constructing the graph greatly increases the likelihood that the student
> > will intelligently interpret such graphs.
>
> This is the logical connection that my experience does not back up. The
> two are certainly correlated, in that better students can do both, and
> lesser students can do neither. However, I do not understand how
> increasing a student's skill of graph construction increases graph
> interpretation. To me, it's like claiming that learning how to change
> the oil is a great way to become a good driver. The two are probably
> correlated, but there is no essential connection. That's the point I'm
> trying to make about graphing. Let's not be misled by the correlation
> into thinking that we'll make better drivers by teaching everyone to
> change the oil.

I don't see any correlation between skill in oil changing and driving
skills. I don't see the relevance of the analogy to graphing, either.

We were talking about *logarithmic graphs*. One makes a graph for a
purpose (usually to determine parameters of an equation or to make an
extrapolation). I agree with you that the mere act of *drawing* a graph
doesn't teach much, and has little effect on interpretation. When I ask
students to construct a graph, it's not merely to exercise their drawing
skills.

However, a common problem my students have when plotting on log paper is
how to label the cycles and to locate the points on the scale, particularly
the decimal parts. Once they understand the principle behind this well
enough to do it properly, *then* they will understand it well enough to
interpolate between divisions of a graph they are trying to interpret.

But I agree with you on another point you are implying. Too often skills
and 'understanding' don't seem to transfer. We see the connections, but
students don't. Too many students treat physics as a lot of little
unrelated pigeonholes, each having nothing to do with the others. I think
the common "encyclopaedic" textbooks are partly to blame, as is the
tendency of texts to give homely "faux explanations" and analogies for
each phenomena, without trying to intergrate them into larger pictures.

One reason student "understanding" often doesn't transfer is that it was
shaky, incomplete, or even wrong understanding. 

One way to find out whether students have the broader view is to ask
questions like this:

In *classical* mechanics and electricity and magnetism, we find that:
	1. Forces which act at a distance have an inverse-square
dependence on distance.
	2. Energy is a conserved quantity.
	3. The area of a sphere of radius R is proportional to R^2, its
volume to R^3. 
	4. Space is considered to be Euclidean.

Can these have any connection? Discuss, quantitatively. 

Remember, I said *classical*. I don't want a discussion of relativity or
quantum mechanics here.

> As Jerome E. wrote, 
> > The difficulty is with these log graphs that students can usually only
> > do it by rote. Very few have the slightest clue of what things like the
> > slope mean.

And why do they do it by rote? Because some teachers *let* them, do not
insist on deeper understanding, and don't test for it. Also, some teachers
assume it's *trivial* and don't go over it in class. If students have
never *had to* find a slope, with units, and interpret it intelligently,
they will never go beyond rote methods. 

I have had students fuss about such things as "How do we know which
variable to put on the x axis and which on the y axis?" as if this were an
issue of tremendous importance to them. Scratch that. I mean they feared
that it was an issue of importance to *the teacher*. Anyway, it's clear
indication that they are still in the "rote" stage of intellectual
development, a stage Piaget forgot to address.

The teachers I had, for all their faults, never let us *get by* with rote
methods or incomplete understanding of the details of such things.

> Maybe our students have been different over the years, but I doubt it.
> Another issue to keep in mind is that what worked for US, in OUR own
> learning, won't necessarily work for our students. In terms of learning
> styles, we physics instructors who have made it through all the filters
> are the exception, not the majority. 

You are right on target here. Those who get degrees in physics are those
who have the ability to learn from books and enough self-motivation to
learn in spite of casual, careless and indifferent instruction. They are
the ones who can deal with and conquer complex procedures, ambiguous
descriptions, careless language, and poorly defined situations. They are
the ones who will worry about details and consequences and interrelations
*even when not specifically required to do so*. They are the ones who will
stubbornly persevere even in the face of failure and even without
emotional support from teachers. Few students have all those abilities, or
that kind of perverse motivation. Those who succeed in fields such as
physics or math and have made it through the trials and tribulations of a
fiendish obstacle course *are* the exception, not the majority.

Perhaps it follows that only a very few students can master physics. 
Whoops!  That's not a politically correct speculation these days. 

But what about those who supposedly *need* science in their profesions. 
Like doctors. What should we expect of them? What should they learn of
physics? I urge everyone to read Peter K. Schoch's letter in the March
1998 Physics today, exposing the almost total lack of understanding of
physics exhibited in a textbook for medical students. If doctors really
*needed* physics, they surely aren't getting it from such books (and most
are that bad, in my experience). I heard a talk by a physicist who sat in
on courses doctors take at a large university, and was appalled by the
almost total misunderstanding of physics of the texts and the professors.
I've experienced talks by faculty of medical schools showing the same
thing. I'm convinced that if your life depended on your doctor's correct
knowledge of physics, you might as well say your prayers--it would do as
much good. Fortunately in most cases your doctor doesn't *need* to know
physics, except for a very few specialists in certain fields. Perhaps
doctors would be *better* if they knew physics well, but that's hard to
test. 

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Professor of Physics                                FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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