Re: contribution of mathematics...

[kyle forinash <forinas@indiana.edu>]

I think Bob (below) is on the right track; arguing between purely
conceptual and purely problem solving approaches to teaching physics is
attacking a straw man.

Surely the thing that ultimately makes physics better than pyramidology (or
any other purely verbal description of the world) is the fact that we can
quantify things. In my experience it is very important to give students
(science and non-science) some idea that the concepts we use are proven to
be valid by experimentation which means connecting the real world to
numbers. Otherwise students approach the whole process the same way they
approach learning latin verbs. We are not guessing at the concepts here (or
making them up from nothing), they are not arbitrary; we are justified in
saying that we KNOW to such and such percent accruacy that theory X is true.

It seems to me the brilliance in the approaches of McDermott and Chabay and
Sherwood (who, if I'm not mistaken, do have support for their teaching
methods from research) is that they start with the physical world and help
the student build a quantifiable model up from scratch so that the student
has a very clear idea of how our current concept of, say, temperature is
built on the solid ground of physical measurement.

It seems to me the choice of which and how much mathematics to use
(algebra, calculus, or, a la Galileo, geometry) is a very small step if you
admit that you need some kind of quantification step to get started. Once
you convey the idea that  making quantifiable measurments determines which
concepts are the correct ones it would seem approprate, as Bob Morse
suggests, to use the level of mathematics best suited to the audience.

So I've got two questions for the PER people:
1) Can someone knowledgeable with the research literature clarify for us
whether the research actually shows students do better (quantified in any
way) given NO idea about the conection of concepts to quantifiable
experiments?

2) Is there any indication that we can teach anything meaningful about
physics without ANY hands-on laboratory experience where quantities are
quantified (measured and put on a graph for example)?

kyle

At 8:34 PM -0600 4/26/98, Bob Morse wrote:
> Gentle folk:  vis-a-vis the present discussion, I went back and pulled
> out five textbooks on introductory physics from the previous century
> (1837- 1895)  which were aimed at introductory physics (or natural
> philosophy) students. I was fascinated to find that only one had any
> algebraic equations at all!  All of them did have some mathematical
> relationships, but characteristically they described the relationships in
> terms of ratio or proportion, and gave the descriptions verbally.
> Several of them had quantitative problems based on the verbal
> relationships, and example problems.  Basically, these texts gave a
> qualitative description of phenomena, followed by a verbal description of
> the quantitative relationships, and then arithmetical problems involving
> the relationships.   The selection of texts is an accidental, not a
> random, sample but in light of the present discussion I find it
> interesting. Of the five books only one explicitly stated 'RULES' for
> computation, and even the rules were given in words, but with
> arithmetical examples immediately following.
>
> My point is that we need not describe relationships in algebraic terms,
> i.e. as formulae, in order to describe them in quantitative terms, and
> that there is a middle ground, a quasi-quantitative way of describing
> relationships that allows a certain rigor, but may be approachable to
> more students, than the abstruse (to some) short hand of algebra.
>
> Bob Morse
>
> Robert A. Morse, Ph. D.
> Science Chairman, Physics Master
> St. Albans School, Washington, DC 20016
> ramorse@cais.com
> robert_morse@cathedral.org


-----------------------------------------------------
  kyle forinash   812-941-2390
  forinas@indiana.edu
  Natural Science Division
  Indiana University Southeast
  New Albany, IN    47150
  http://Physics.ius.indiana.edu/
-----------------------------------------------------