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Re: AP students

On Fri, 27 Apr 2001, Hugh Haskell wrote:

Jack Uretsky wrote:

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?

I didn't say to just teach algorithms.
Then we are not talking about the same thing. So I need for you
to define what it is that you are talking about as "algorithmic teaching."
What I deplore is the pretend to be teaching physics while actually
just giving the student a bunch of algorithms.

What I said was don't be too
disappointed if that's how they learn, in spite of our best efforts
to the contrary. It may not be all that bad, since understanding is
much more difficult, it will usually come later, if, indeed, it ever
comes. If we try to force understanding on students before we let
them learn to solve problems, the result could be that they learn
neither.

These comments, of course, do not apply to the Feynmans of the world,
only to us lesser mortals.

Algorithms teach students to substitute numbers
into formulas - nothing more.

I disagree with your definition.

Definitions are arbitrary. Evidently you want to talk about
someething different from what I am talking about, so we are clearly
not having a dialogue.

You want to defend "algorithmic learning" as you are defining it
here. That is one way to introduce concepts, but it seems to turn off
an awful lot of students. But, as I just said, that is a different
topic.

Plug-and-chug is at the lowest skill
level. I would put algorithmic learning a step or two higher--where
they can follow a prescribed or learned route to a problem solution
that may involve some algebraic manipulation, several process steps,
and more than one stage of computation. The algorithm may be complex
and require lots of practice in order to get good at it, but in the
end, it enables the student to solve a particular class of problems
without actually understanding the process. I can think of several
advanced concepts that I first learned algorithmically and only later
came to understand what was behind them.

In fact, much of what we do every day is done algorithmically. We
have routines that we follow, methods that we invoke to solve
problems. When the methods or routines give the wrong results, we
modify them as necessary (a learning process). We don't stop to
completely analyze every situation we encounter from first
principles. We frequently try one or more learned
routines--algorithms--to see if they will work, and if they don't
then we start trying other things that may not appear to fit, or
start a more careful analysis. Some people are better at this than
others.
-----------------------------skip_____________________________

I suspect that our disagreement is over the use of the word
"algorithm."
Exactly. There are few activities less fruitful than
arguing over definitions. So the discussion should end here.

Regards,
Jack

--
Franz Kafka's novels and novella's are so Kafkaesque that one has to
wonder at the enormity of coincidence required to have produced a writer
named Kafka to write them.
Greg Nagan from "The Metamorphosis" in
<The 5-MINUTE ILIAD and Other Classics>