Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: AP students



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. 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. 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.

In many fields, flying, for instance, training for emergencies is
highly valued because it enables the practitioners to quickly choose
the correct algorithm to deal with a particular emergency. Granted,
physics isn't necessarily like flying (neither is driving, my point
there was simply to teach one skill at a time, rather than try to
have the student learn all of them at the same time), and at the
frontier of physics, we are forced to rely less on algorithms and
more on careful analysis (which itself often involves analytic
algorithms that are different for different areas of the subject),
but when first learning the subject, reliance on algorithms can
enable a student to make progress and develop confidence, even if the
deep understanding isn't there yet.

I suspect that our disagreement is over the use of the word
"algorithm." I doubt that you will deny that you follow certain
routines when attacking a problem, and then modify the routines as
necessary as you encounter obstacles. The deeper the understanding,
the easier it is to deal with the obstacles. This is what I have
always though of as algorithmic behavior, and, call it what you will,
it is, I believe, widely practiced by nearly everybody, and many
animals as well. Where we differ from the animals is that we can
often modify our algorithms as necessary, while the animals usually
cannot, their algorithms being pretty much hard-wired in.

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..
******************************************************