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Re: AP students



Hi all-
I totally don't understand Hugh's logic. Yes, concepts do not
come easily. How in the world does this fact justify teaching students
a bunch of algorithms? Algorithms teach students to substitute numbers
into formulas - nothing more. That may be an appropriate exercise for
parts of some math classes, but what has it got to do with learning
about physics?
As for the automobile analogy - well, we argue by analogy when
we think that the audience can't grasp the real issues. I suggest that
in this forum we stick to the real issues.
Regards,
Jack

On Fri, 27 Apr 2001, Hugh Haskell wrote:

Tim Burgess wrote:

Do you think that the "set of algorithms" approach to problems solving
is limited only to the students of teachers and/or books where this
shameful approach is taken? If so then I disagree. The problem
solving you describe reflects your expertise. You may "not know how to do
problem solving without understanding" but I think many students probably
do get "answers marked correct" without understanding.

I'm not all that certain we should be so disappointed if all the
students learn the first time around is an algorithmic approach. We
all know that achieving understanding of the concepts is difficult.
If we remember what it was like before we *understood* it should come
as no surprise that concepts don't come easy. I'm not saying we
shouldn't emphasize concepts, students need to know that there is
something deeper than what they are doing. The good ones will sooner
or later realize that they can't go very far with just algorithms,
and will seek out the deeper understanding on their own. It is at
this point that the opportunity for real learning occurs.

I keep saying that I think we expect way too much in a first-year
course--maybe even a second-year course. The number of concepts the
students are introduced to in the course of a year is truly daunting.
To be able to put all these ideas together and reduce them to a few
basic concepts, like the conservation laws, Newton's laws and
Maxwell's equations, is a higher order skill and for most students
isn't going to happen the first year. But if they come away from the
course knowing that they can solve some interesting problems, even if
they don't fully understand what they are doing, they'll feel good
about physics, and realize that it, like most things academic, is a
learned skill, and if they are interested enough to pursue it
further, they, too, can learn those skills. If they're not, then at
least they come away without thinking that physics is magic, and
physicists are somehow demigods. That is a healthy attitude.

For years after most cars came equipped with automatic transmissions,
driver ed courses used manual transmission cars to teach with, the
idea being that those cars were "more fundamental" and so students
should learn on them. Then someone had a bright idea. Why are we
truing to teach two complex skills simultaneously? Shouldn't we teach
them one at a time? With automatic transmissions we can. Teach them
how to steer a car first, and let them get proficient at it. Then
after they know how to steer, and can navigate a car around a course
and in an out of traffic, let them learn how to shift manually. I did
it the old way, and ground a lot of gears, tore up one clutch and
sideswiped another car because I was too busy trying to shift to look
where I was going. Both my kids learned on automatic transmissions,
and then I took them out and in an afternoon they learned how to
shift a manual transmission. By then it was easy, because they didn't
have to concentrate on two things at once. Maybe we could learn
something from the driver's ed folks after all. I believe that the
air force teaches its students how to fly by starting with a fixed
landing gear, fixed pitch propeller, simple aircraft. Same principle.
Teach them the basics first and add the complicating features later,
after they know what to do with the airplane.

Physics isn't quite the same. The fundamental ideas, rather than
being easy are deep and difficult. But a bright student can learn how
to solve a reasonable set of problems if they have enough tools.
There is time later for them to learn how to build the tools from the
basic concepts. It may well be enough if they know by the end of the
year which tool to pull out for which problem. Understanding will
follow. Sooner or later.

Hugh
--

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

(919) 467-7610

Let's face it. People use a Mac because they want to, Windows because they
have to..
******************************************************


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Greg Nagan from "The Metamorphosis" in
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