Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

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

The fact that you used a different method from others is a clear
illustration that experts actually think differently and can have radically
different understanding.  It also illustrates the fact that when experts
attack a new problem they do not necessarily use sophisticated reasoning.
Actually the previous types of reasoning come out, and this happens to
everyone.  Outside of the field of expertise, experts often use very low
level thinking, which trips them up.

Just encouraging students to use other forms of reasoning helps a few, but
not the majority.  The type of reasoning has to be notivated which is what
the learning cycle does.  Also they have to be confronted with how their
usual reasoning is inadequate.  They need to have activities where the
previous type of reasoning is used and they see that it doesn't predict the
results.  This is what an ILD does.  Another factor is peer pressure.  If
they see that others are having success using a different style of
reasoning, they will be more likely to go along with it.

Yes to a certain extent number sense or numeracy is one factor.  They have
to have extensive experience with proportional and inversely proportional
reasoning.  That is precisely what Modeling does, but Modeling still does
not quite have as powerful an effect as we would like.  Thinking Science
probably does have a greater effect.  Executive functioning is also
important.  Students need to be aware of their thinking.  Once they are
aware, they are more likely to pay attention to confounding results.
Getting them to predict and come up with some reason for the prediction
should help.  This is a barrier because many students resist prediction, so
that is why the ILDs do not require them to expose their predictions in
public, but the demonstrator may put up the predictions as "This is a
prediction I have seen on some student papers."  Clicker prediction may also
be helpful with the prediction resisters.  Feuerstein IE helps students with
executive functioning, but it can't really be used in a physics class,
except for a few activities.

John M. Clement
Houston, TX

> Should I be embarrassed to admit that this was the first 
> method I used to get the answer?
>
> But a second approach:  Time required varies directly with 
> job size and inversely with job rate.  So a 20-fold increase 
> in both of those things will leave the time unchanged.  This 
> is the kind of thinking I steadily encourage my students to 
> use.  But not many of them embrace this.  I think one of the 
> barriers is actually number-sense fluency or whatever you 
> want to call it.  You have to see 100 and 5 and immediately 
> be thinking about the ratio.  That is not a universal among 
> my students.