Re: LOGO-L> Questions and problems

["Olga Tuzova" <olgatu@ort.spb.ru>]

Thank you, Brian for a strict and detailed response.

Brian Harvey writes:
> "Olga Tuzova" <olgatu@ort.spb.ru> writes:
> >I can't explain them clearly, why they should put parenthesis around 
> >distance [0 0], that is, why the line 
> >       show distance [0 0]/:a  
> >is wrong.
> 
> One approach: forget about infix and just say
> 	show quotient distance [0 0] :a
> 
> But if you don't like that, ...

Yes, I'd prefer something different, for there is a problem of 
language and the word "quotient" would sound unfamiliar for the 7th 
graders, deepening the problem. May be, it would make sense to write 
helper procedures with more familiar names?

> I guess you start by saying, what do you
> think it would mean if you'd said
> 	show some.function 3/:a
> and then explain that Logo is stupid and only has one rule about the
> precedence of infix vs. prefix operations, even when the domains don't
> make sense that way.
> 
> >2. The notations in Logo and in Algebra are different and sometimes 
> >students don't see what stands behind this or that formula. For 
> >example, when they see that (power distance [0 0] 2)/(:a*:a+:a*:a)  
> >is equal to 1, they can't formulate in words what they have come to.
> 
> Extra parentheses and/or spaces might help:
> 	(power (distance [0 0]) 2) / (:a*:a + :a*:a)
> 
> Alternatively, define helper procedures and use them:
> 	(square (distance [0 0)) / ((square :a) + (square :a))
> 
> Finally, before asking them to translate the Logo into words, what if
> you ask them to translate the Logo into traditional algebra notation
> first?  Does that help?

Well, I think, there is something wrong with my teaching, or, with 
Logo. We began with algebra notation, they translated it into Logo 
(with difficulties), then they couldn't recognize in Logo-formula 
it's algebraic equivalent.

I have no intentions to come to the final conclusions just now.  
These  were our very first lessons of that kind, and, may be the 
implementation of the initial idea wasn't the best one. But, what 
confuses me most, is the fact, that instead of concentrating on the 
problem, the students had to have a battle with notation.

> 
> >This my experience showed that the students are very poor in most 
> >important points. 
[...]


> 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.

Of course, I don't like it. Not your words, but the fact itself. 
Surely, it's true. 
> 
 > [...]
> But of course you'll never get away with this, since then you won't
> "cover" the curriculum.  :-(

Fortunately, our curriculum is very flexible and there is nobody to 
blame for it failures except me. :-( 

Thank you,
Olga.
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