Re: LOGO-L> Questions and problems

[Chuck Shavit <CShavit@MagicSquare.com>]

Brian Harvey wrote:
> 
> "Olga Tuzova" <olgatu@ort.spb.ru> writes:
> >...
> >This my experience showed that the students are very poor in most
> >important points. Their ability in observation and analyzing data is
> >very-very low. When they come to the obviously erroneous results,
> >they don't see it's absurdity. And, they can't make hypothesis about
> >what is going to be even in simple cases.
> >For example, one of the girls (rather smart one) came to the fact
> >that (power distance [0 0])/(:a*:a) = 2.
> >Being asked, what we'll get if we take :a*:a+:a*:a instead of just
> >:a*:a, she accepted this as a new task, made several experiments for
> >different :a, but her program contained a bug. She wrote:
> >(power distance [0 0])/(:a*:a)+(:a*:a) You can imagine, what numbers
> >she has got, but they haven't confused her a bit.
> 
> You won't like it, but here's my answer:  This student has been ruined
> by grades, and won't get any better until she's in an environment
> without grades.
> 
> It sounds as if she doesn't think that algebraic manipulations *mean*
> anything at all.  They're just this thing you have to do in school to
> make the teacher happy.  If that's the case, perhaps she needs a detour
> into problem-solving in a non-algebraic context, things like (my latest
> fixation) logic puzzles.  Or riddles.  Make it a class about solving
> problems instead of about geometry, and once every 10 or 20 problems,
> throw in one that's related to the official curriculum.

I don't know about SPb, but in my town (Boston area), 7-th graders in
general still do not have the math background for solving such problems.

I agree to every word that Brian says.  However, I think that there is
another very important counter-motivational factor related to the use of
computers for math education.  I think that students need to feel that the
computers add value to their math education.

If you give your class graph paper and rulers, even the slowest students
will be able to come up quickly with a series of measurements of
edge/diagonal of squares, and relating that to the Pythagorean formula.
By requiring them to use a computer language for the same purpose, we
introduce unnecessary difficulties.  In this case, the difficulties are
related to operator precedence, the difference between infix and prefix
notations, and the need to remember the names of built-in primitives like
sqrt, power and quotient.  All these IMHO slow the math learning process.
They also slow the computer programming learning process.

I think that Brian's idea about logic puzzles and riddle solving using a
computer is very neat, especially since it can demonstrate to kids the
added value of a computer. 

And I think that teaching computer programming to kids is a *very*
important end in itself.  We don't typically try to teach math to student
at Biology class.  Why should we teach them math at programming class?

Chuck Shavit

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