Re: Setting up problems

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 14:31 -0400 10/9/03, Promod Pratap wrote:
> From the suggestions from
> contributors, the general consensus appears to be that if we provide
> non-plug-and-chug problems, things would improve -- i.e., we need to
> teach concepts.  OK, how does one do that?

By posing questions that are not just numerical problems--questions
that demand a qualitative answer that requires the concept be
understood in order to be able to answer. And then by demanding that
the student be able to defend their answer. By asking that they do
problems that require that they derive a particular expression, or
show in general some particular property of the concept under
discussion. For example, in the problem posed by David Marx earlier
this morning, ask the students to prove that the answer is
independent of the mass. Many of them won't be able to do it, but we
must keep asking this type of question, for if we don't, most of them
will never learn how to do them.

>   From looking back at my
> school days, I seem to think that I learned concepts by doing problems
> (e.g. Halliday and Resnick).  I had the distinct recollection that I did
> not necessarily understand the concept when I started doing problems in
> a particular topic, but that the concept came much later (in an "AHA"
> moment).  I don't remember doing anything consciously to get to this point.

But you probably got there in the process of doing all those R&H-type
problems a little at a time. I think that the ability to see problems
in their physics context rather than the literal context is a skill
that can only be learned with time, and it is not likely that there
is ever an "aha" moment in that process. The ability to reason
abstractly doesn't come to everybody, and those who do finally get it
don't always get there spontaneously--they have to be pushed, given
hints, pushed some more, given time and practice, and eventually they
might make it. But some never do.

> Also, I think it was easier because it is my instinct that, when given a
> problem, I tended to take it apart (literally and figuratively :)).  I'm
> not sure where I learned this, or whether some people are born with it
> (and are therefore condemned to become Physicists and Engineers).

I doubt anyone is born with it, but some learn it earlier than
others, and some never learn it. It has been said that one of the
important things a teacher must never forget, is what if felt like to
*not* understand a concept. Without that recollection you can never
understand what the student is struggling with.

>   This
> curiosity (maybe?) about the real world appears, to me, to be essential
> for learning Physics.

Alas, almost all children are born with that curiosity, but by the
time they get to high school or college it has been beaten out of
them, by insensitive parents, teachers, even fellow students.

> If students want you to give them plug-and-chug
> problems, does this mean that they have lost this sense of curiosity
> somewhere along the line?  (I think all humans have this at the
> beginning of life.)  Is this something they can reacquire, or is it
> something that's gone for ever?

Good question. I suspect that, giving them things they are willing to
be curious about (be careful with this!), and permission to be
curious, can go a long way toward re-instilling the feeling of
curiosity.

> An aside:  in the problem about the roller coaster by David Marx, the
> concept being taught there concerns gravitational potential energy, and
> that is why you don't need the mass (the assumption being that the
> gravitational mass and inertial mass are the same).  However, if instead
> of climbing the second hill, the cart hit a spring and compressed it,
> then you would need the mass.
That's correct, and realizing that essential difference between the
two questions is part of understanding. David's original question,
interesting though it is, is only part of the issue. Once they see
the part of the overall concept that is relevant here, they can
develop an algorithmic approach to this class of problems that will
serve them well as long as that is the only type of problem they get.
But understanding is near when the student not only knows when a
certain technique will work, but when it *won't* work. And what
changes to the approach to the problem will be needed to solve it.

This is why I find teaching physics so interesting. There are always
new things to learn, both about physics and about teaching.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

Never ask someone what computer they use. If they use a Mac, they
will tell you. If not, why embarrass them?
                       --Douglas Adams
******************************************************