Re: Stop using calories?

[SCIAMANDA@edinboro.edu]

Bob Sciamanda wrote:
> > We seek not truth; we seek usefullness, both empirical and conceptual.
> > Our method is the conception, testing and application of models of
> > reality. We cast these models in terms which we have ceased to question,
> > not because we understand them any better, but only because they have
> > become familiar and because they are all that we have.

Then Dewey Dykstra commented:
> I agree and all the more reason not to treat them as models beyond question
> in our teaching because our students can and do take a different meaning
> for them than expressed above if we _do_ present them as beyond question.


These ideas deserve our constant attention.  Educational fads come and go, 
and there are better ways to train a student to plug and chug, but in 
40 years I have found that there is no hope of evoking understanding unless 
I clearly and explicitly tell the student what it is I am doing:
when I am DEFINING a new concept,  when I am making a logical DEDUCTION, 
when I am appealing to an EMPIRICAL finding, when I am proposing an 
HYPOTHESIS, what ALTERNATIVE models exist, etc.

This is important not only while building mathematical models, it is 
almost the entire story where conceptual models are concerned.  This is 
because conceptual models are not right or wrong in the same sense that a 
mathematical statement relating measureable quantities will be empirically 
right or wrong. The human mind is clever enough to make 
almost any conceptual model "work",  it is only a question 
of how weird one is willing to get - a cultural concern.  It is not useful 
to call a conceptual model "wrong"; fruitful progress comes from investigating  
where it leads.

Bob Sciamanda           sciamanda@edinboro.edu
Dept of Physics         sciamanda@worldnet.att.net
Edinboro Univ of PA     http://www.edinboro.edu/~sciamanda/home.html