Re: LOGO-L> Questions and problems

[KERRB@Magill.UniSA.edu.au]

 Olga wrote:-

>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.
 (snip)

 One key factor is the students sense of ownership of the problem -- you need 
to build in some choice. This also helps to cater for different ability levels.

 My favourite introductory Logo Geometry book is Turtle Confusion by Barry 
Newell. He has 40 different shapes, starting with the square (shape 1) and 
building up to some quite complex shapes. I have only ever had one year 8 
complete all 40 shapes. All of the shapes can be done with fd, bk, rt, lt and 
repeat. 
(there is no trig or pythag but I would like to see a new booklet developed 
offering lots of choice that takes students onto trig and pythag).

 This means:-
a) students have some choice
b) they can choose shapes that they think matches their ability level
c) there is something there to challenge everyone
 
I am just there to facilitate, make suggestions but I tend to let the students 
have the final say as to how they will make *their* shapes. It would be 
counterproductive to impose my *more efficient* method onto them -- even though 
I might mention it to them and ask if they want to see it.


>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.

 I'm not surprised -- this is very complex for beginners. I think the best 
research on this sort of questions (students grasping complexity fluently) has 
been done by Idit Harel. Seymour summarises her approach with the slogan, 
Project before Problem. ie. if a student immerses themselves in a complex 
Project that they want to do then over time (it may take months) they will 
begin to pose and solve quite complex problems for themselves. 

The Project approach is conceptually opposite to the directed problem solving 
approach that you seem to be using. BTW the title of Idit Harel's book is 
'Children Designers'.

 -- Bill Kerr
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