Re: [Phys-L] Conceptual Physics Course

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

If they don't have proportional reasoning (pr), they will be forever stuck.
Building the ability to do proportional reasoning is necessary before
introducing algebra.  So without pr they have nothing to really use.  The
algebra will fade quickly, but pr will last.

So my argument is that you have to get all students to use pr.  One thing
you have to do is point out that using proprotional reasoning is not a
matter of knowing the math, but rather a matter of recognizing when it is
needed.  You do this when a student spontaneously uses pr.  The standard
math method of teaching it has a section labeled ratios and they do them.
But seldom do they encounter mixed problems where they have to decide
between additive and proportional reasoning.  My favorite example of how
students do not use it is the Hi/Ho=Di/Do equation in optics.  I didn't
memorize it because it was obviously a ratio, but I remember thinking it was
stupid that students had to have the jingle hiho dido to remember it.  All
they had to do was draw the triangles, but the geometry lessons in
proportional triangles didn't transfer.  Again math got them to memorize
procedures rather than reason.

Teaching logic has the same fatal flaw.  Teachers tell students about the
types of logic, and get them to categorize it, but there is no gain on the
PLT (propositional logic test).  You would think that computer science
courses would produce gain on the PLT, but that doesn't happen.  So students
learn about ratios, but not how to recognize them, and students learn about
logic, but not how to use it.

Yes, it is maddening when students fail to use "simple" reasoning.  Another
form of reasoning has to also be promoted.  They need to learn to ask what
if questions or use hypothetico-deductive (HD) reasoning.  When they look at
a problem they just hunt for a solution using known equations, but often by
mentally changing conditions, one can visualize how the problem changes.
Then a method of solution often becomes obvious.

Modeling promotes pr by having students do lots of graphical analysis.  But
you have to also talk about the reasoning when it arises if you want gain in
reasoning ability.  And you can't just spring higher level reasoning
problems on them.  You have to have them again and again and build up from
simpler ones.  That is what "Thinking Science" and "Minds on Physics" do.

Notice I said they "can" use higher level thinking, but that assumes they
have developed it.  If they remain stuck without pr and other forms of
higher reasoning, nothing is possible, so that is why developing higher
reasoning should be the most important task in all physics courses.
Incidentally the ability to use propositional logic is not really important
compared to pr and HD reasoning, so there is really no need to to push it.
Lawson in his book has some very good arguments and examples of reasoning
that is needed.  Also PL clicks in much later than other forms of higher
reasoning and only a small percentage ever become adept at it.

John M. Clement
Houston, TX

>  
> > So de-emphasizing algebra is not physics minus if you use graphical
> > representations.  And don't forget that the conceptual 
> students will NEVER
> > use algebra after they leave school.  But they can use 
> higher level thinking
> > such as proportional reasoning.  Algebra courses have 
> failed to teach them
> > proportional reasoning.  
> [Bill Nettles] I assume that you mean they will use 
> proportional reasoning after they leave school.  I have found 
> very few students who can do proportional reasoning when they 
> arrive, and they are very resistive to using it to solve 
> problems.  For example studying  Kepler's Laws, having them 
> work examples using ratio & proportion in class, I ask them 
> on a test to find the period of an asteroid orbiting the Sun 
> at a distance of 3.5 AU.  They ask me what the mass of the 
> Sun is. I tell them they don't need it. They stare at me like 
> a calf looking at a new gate (that's a rural idiom for they 
> have no idea).
> > You have to start with where the students are, and not 
> where you want
> > them to be.  If you do the latter, they will memorize and 
> never understand.