Re: [Phys-l] Equations

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

I've stayed out of this discussion but I feel compelled to submit my own
opinion about this (which I've submitted before) simply because I
haven't seen anyone else state it.

Like John Denker, I also avoid implications of causation.  However, my
reasons are not only semantic but also pedagogical.  I have found that
students come into my class confusing acceleration and velocity
(surprise, surprise).  When I imply that a force causes an acceleration,
they interpret that as "you apply a force and then you have a new
acceleration" because they are thinking "you apply a force and then you
have a new velocity".  You might think that it would be better to write
"Delta v = F Delta t / m" but even then it seems students interpret that
the change in velocity happens AFTER you apply the force, not WHILE you
apply the force (my students also have difficulty distinguishing between
CHANGES in velocity and INSTANTANEOUS velocity).  This seems to be a
difficult thing to address and I'm afraid that the "force causes
accelerations" just reinforces this notion.

I have the same problem with N3L.  Some students think that you exert a
force and this CAUSES a reaction force.  I'd rather they just accept
that the two act at the same time and we cannot determine which causes
which.  They can argue "you wouldn't push back unless I pushed you
first" but that inevitably leads some students to think there is a time
delay or that one force is "stronger" or more important than the other.

So, yes, students naturally start out with strong conceptions of
cause-effect.  It just isn't clear to me that we want to reinforce such
conceptions.

P.S. I think the V=IR discussion opens up another can or worms.  The
current in a circuit does not occur instantaneously with the application
of an electric field (even electrons have inertia, no?).  So, in a
sense, one can argue that the application of the battery comes before
the current.  On the other hand, I'd argue that the V=IR is NOT a
cause-effect relationship.

____________________________________________________
Robert Cohen, Chair, Department of Physics
East Stroudsburg University; E. Stroudsburg, PA 18301
570-422-3428; www.esu.edu/~bbq 

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf 
> Of John Clement
> Sent: Thursday, April 27, 2006 7:47 PM
> To: 'Forum for Physics Educators'
> Subject: Re: [Phys-l] Equations
>
> While the comments about causality and equivalence are 
> certainly true, the pedagogical analysis is off base.
>
> Students at the lower level and beginning students will be 
> completely overloaded by considerations of causality.  
> Students must start from what they already know and then work 
> towards higher levels, not the other way around.  This has 
> been proven by experiments by Lawson, Karplus, Renner...
> Students must first see force as causative and acceleration 
> as a result.
> This gives them a familiar context to begin with.
>
> Also this is in line with the way you do an experiment to 
> demonstrate constant acceleration.  Students first see an 
> experiment with constant force, and measure the acceleration. 
>  So a is the dependent variable and F the independent.  The 
> a=F/m is precisely the way many of the reformed curricula 
> formulate NTN2, and they demonstrably get better 
> understanding of physics concepts.
>
> Until students are completely comfortable with the idea of 
> variables, the idea of an equation as just being a 
> relationship is way too abstract.  They first have to see an 
> equation as a formula.  Once students have gotten to this 
> level, which is probably the theoretical level as defined by 
> Anton Lawson, they can be exposed to the idea of causality.
>
> You do not have to teach a wrong concept about the 
> mathematics, students naturally start with a wrong concept.  
> This is actually part of the natural development of a more 
> productive concept.  The recent Physics Teacher has a very 
> interesting article which bears on this point.  Redish has an 
> article where he shows that even when students are using 
> unproductive ideas, they can actually be making progress 
> toward more expert problem solving.  Part of the difficulty 
> is that when you propose this abstract concept, you are not 
> aware that students have not internalized the many concepts 
> that are required to come to this concept.
>
> John M. Clement
> Houston, TX