[plt-scheme] Re: HTDP - evidently not for everyone.

On Feb 12, 2010, at 12:41 PM, wooks wrote:

> We formed a human list in class. Each member was allocated a number.
>
> I asked them who is (first human-list). They told me.
> I asked them which bit is (rest human-list). They showed me.
> I asked them what is the value of (first human-list). They told me.
> I asked them when (first human-list) is being added to (sum (rest
> human-list)) what value is being passed from (sum (rest human-list)).
> They told me.
>
> I moved my way down the human list. At every stage they told me what
> constituted (rest human-list) and what the value of (sum (rest human-
> list)) was.

Sounds good.

> Is that active enough.

Probably; it may be that in this case the difficulty was the leap  
from human-list to Scheme-list.  So the next thing I would do is  
write a Scheme list with the exact same numbers in the exact same  
order and ask the exact same questions.  Then write a different  
Scheme list with different numbers and ask the exact same questions.

Which you may well have also done.  So what is the next problem to  
give them?

count-list is fairly similar, but LOOKS different to your students  
because it doesn't actually use the elements of the list.  Another  
possibility is "concat-all", which takes in a list of strings and  
concatenates them into one long string; its solution is isomorphic to  
that of "sum", but it uses a different data type.

You could try "sum-squares", which adds up the squares of the  
numbers.  This does introduce an additional concept -- applying a  
unary function to each element before combining it with the rest --  
but it's not too hard to understand, and it still uses addition, and  
the answer to the base case is the same.

If you're working with graphics, and either 2htdp/image or my  
teachpacks, you could next write a function "beads" that takes a list  
of numbers and produces an image of a bunch of circles of the  
specified radii, side by side:
(check-expect (beads (list 3 10 8)) (beside (circle 3 "outline"  
"black") (circle 10 "outline" "black") (circle 8 "outline" "black")))
This one is isomorphic to "sum-squares"; whether your students find  
it easier or harder depends on how scared they are of "math".


Stephen Bloch
sbloch at adelphi.edu