LOGO-L> Questions and problems

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

Dear friends,

I've got some problems and need your help.

Some time ago our dear Yehuda has suggested interesting ideas about 
how to involve students into the exploration of the geometrical 
shapes. I liked Yehuda's proposals and developed special 
MSWLogo lessons plan for my 7th graders, who have just began to learn 
Geometry. Step by step, they have to explore squares, rectangles, 
polygons. They are performing computer experiments, making hypothesis, 
trying to prove or reject them, analyzing data.
All this turned to be more difficult, than I have expected and 
sometimes unexpected problems occur.
I can divide them into two categories -- "local" problems and 
"global" ones.

Local problems.

1. The students have to estimate the ratio diagonal/side for 
different squares. The value of the diagonal they get as an output of 
the distance function.
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.

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.

Have you any suggestions how to deal with this?

Global problems. I'm afraid, these problems are familiar to many of 
you. They are problems of the education.

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.

I'd be glad to hear any comments.

Thank you,
Olga.
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