analytical Skill for Java Development

[Ingo R. Homann]

Hi,

»...The children were using Logo to make
things happen (something moving in a circle, I think), and
he described this as seeing six-year-olds effectively
understanding differential geometry.«

Very interesting interpretation!

OK, but that lets me speculate a bit further:
<speculation>
Was it really the *task* to program somthing that draws a circle?
Or did the children play with turtle, randomly generating a simple
program - realizing that it draws a circle?
</speculation>

Note that I think that "turtle" is a good idea to let children play with
it. I also think that even 5yo childs can be *quite* clever.

But I do not think that the interpretation of the results is correct.

Ingo

 

[Ingo R. Homann]

Hi,

»...The children were using Logo to make
things happen (something moving in a circle, I think), and
he described this as seeing six-year-olds effectively
understanding differential geometry.«

Very interesting interpretation!

OK, but that lets me speculate a bit further:
<speculation>
Was it really the *task* to program somthing that draws a circle?
Or did the children play with turtle, randomly generating a simple
program - realizing that it draws a circle?
</speculation>

Note that I think that "turtle" is a good idea to let children play with
it. I also think that even 5yo childs can be *quite* clever.

But I do not think that the interpretation of the results is correct.

Ingo

 

[Stefan Ram]

Note that I think that "turtle" is a good idea to let children play with
it. I also think that even 5yo childs can be *quite* clever.

I found this in the web:

»Circle

1. We want to tell the turtle how to make a circle for us
on the screen. First watch while I pretend I am the turtle
and I am going to walk out a circle. I begin to take a
step and then turn a little. I continue these two moves
until a circle is beginning to form. As I make each
movement I am talking out loud and naming each move. I
step then turn, then step, then turn, etc. I continue this
process until I end up in the same spot I started in.

2. Now I want you to stand up and we will all pretend to
be turtles. Let's all begin making a circle in slow motion
by taking one step then a little turn. Keep doing this and
name each move as you take it. Keep going until you end up
where you started from.

3. Pair off children for the purpose of more practice.
Each child will take a turn at being the turtle and the
commander for walking and talking out of a circle.

4. Now let's see how you would make a smaller circle. Walk
it out. Which move changed: the step or the turn? That's
right, if you make a sharper turn your circle will become
tighter or smaller

5. Gather around the computer and have the children tell
the Logo turtle how to make a circle. After producing the
line fd 1 rt 1 show the children how to manually repeat
this command by pressing the "arrow up" key so that the
cursor is flashing on the fd 1 rt 1 and then hit "return."
Have the children make tally marks, draw a circle around
it to represent a bundle. When the turtle is back in its
starting position, count by tens all the bundled tally
marks the children made. Ideally, several children will
have 360 tally marks.

6. On the "flip side -- apple F," show how to write
that very tiring process in a three line program named
circle. Why would I want to call this circle?

to circle
repeat 360 [fd 1 rt 1]
end

7. Sometimes I need different size circles, so I made a
few more circles of different sizes for us to work with. I
also had to name them different things so the turtle knows
which one I want it to draw. Unknown to the children, I
changed some of the input numbers to make the turtle draw
faster.

to circle.1 to circle.3
repeat 36 [fd 1 rt 10] repeat 36 [fd 5 rt 10]
end end

to circle.2 to circle.4
repeat 36 [fd 3 rt 10] repeat 36 [fd 7 rt 10]
end end

Each circle number represents the size of the circle; 1 is
the smallest, 4 is the largest, 2 and 3 are in between. «

http://el.media.mit.edu/logo-foundation/pubs/papers/animals/logo_animals.html

 

[Chris Uppal]

Well, I am only sceptical about the story with the circle. I cannot
believe, that a normal, 5-year-old-child is able to write a program by
itself - even if the program is supposed do no more than drawing a
circle, and even if the language is very simple and (and that is the
most important point) that normal 10-year-old and normal 15-year-old
childs fail on the same task.

I suspect that one aspect of the story has become distorted in the (however
many times) retelling -- I doubt if the original studies were with children
aged {5 10 15}, the numbers are a bit too round. I tried to find primary
references, but failed. The nearest I could get is a study (referencing Kay)
using Logo with children aged "six to seven". I can't find a reference to
Kay's own studies which mentions children younger than 12.

BTW, unless you assume that the turtle graphics sub-system wasn't available to
the "10" and "15" yo-s then the anecdote does relate to the point that (I
think) Stefan wanted to illustrate. I find that assumption rather
implausible -- there seems to have been an almost automatic equation "children
+ graphics = turtles" amongst the crowd who were doing these kinds of studies,
so I'd expect the features to have been there, even if the 10&15 yo-s didn't
think to use them[*].

([*] And I wouldn't have done either -- I can't understand how /anyone/ can do
turtle graphics without getting totally confused[**]...)

([**] Unless we are talking about an almost real turtle -- one that crawls
around on a /horizontal/ surface.)

-- chris

 

[Ingo R. Homann]

Hi,

I suspect that one aspect of the story has become distorted in the (however
many times) retelling -- I doubt if the original studies were with children
aged {5 10 15}, the numbers are a bit too round. I tried to find primary
references, but failed. The nearest I could get is a study (referencing Kay)
using Logo with children aged "six to seven". I can't find a reference to
Kay's own studies which mentions children younger than 12.

Ah, OK, that sounds more convincing.

BTW, unless you assume that the turtle graphics sub-system wasn't available to
the "10" and "15" yo-s then the anecdote does relate to the point that (I
think) Stefan wanted to illustrate. I find that assumption rather
implausible -- there seems to have been an almost automatic equation "children
+ graphics = turtles" amongst the crowd who were doing these kinds of studies,
so I'd expect the features to have been there, even if the 10&15 yo-s didn't
think to use them[*].

Ah, well, but there is an interesting question:

Obviously, it is necessary to do some training with turtle for the 5yo-s
(wether they are really 5 or not) in advance.

And obviously, it is also necessary to do the same training for the 10-
and 15-yo - otherwise it is not fair.

So, one question is: Did they really get the same training?

And another question: Did the 10- and 15yo-s get another training in
another programming language as well?

I mean, when you have one group of persons and you show them how to use
a hammer and another group which you show how to use a hammer and a
tongs and a saw and screwdriver and ... then it is not astonishing that
the first group is better in handling a hammer. But I think it is unfair
to say that the second group suffers from "stuckness"!

Ciao,
Ingo

 

[Oliver Wong]

You both seem remarkably ready to impute a high degree of intellectual
dishonesty to one of the most significant figures in modern computing.

To be more honest, I should have said "When I imagine *myself*
conducting the same experiment, I picture *myself* just asking the kids to
explain etc." Perhaps this is because I have no idea what Alan Kay looks
like, so I visualize someone who looks (exactly) like myself in the same
situation, and then I project onto that person the same methodologies that I
would use.

But more to the point, I really have a hard time believing that a 5 year
old child would sit at a computer and type:

<code>
to circle
repeat 360 [fd 1 rt 1]
end
</code>

... without any guidance.

- Oliver

 

[Chris Uppal]

Ah, well, but there is an interesting question:
[...]
I mean, when you have one group of persons and you show them how to use
a hammer and another group which you show how to use a hammer and a
tongs and a saw and screwdriver and ... then it is not astonishing that
the first group is better in handling a hammer. But I think it is unfair
to say that the second group suffers from "stuckness"!

That is an interesting question. But I think that the training effect -- or
something very like it -- is what stuckness /is/. The first thing(s) that come
to mind get wedged there and prevent other ideas coming forward. If the older
children had never learned turtle graphics (or if they had learned it but knew
that it was unavailable in their current environment) then it would clearly be
incorrect to say they were "stuck" on X/Y coordinate drawing. But if they
/had/ learned about it, but had more recently learned X/Y stuff, so that when a
drawing task came up they immediately reached for the X/Y toolkit, then that is
a fair example of "stuckness". Note that it doesn't matter whether they may
have learned X/Y graphics /better/ than turtle -- we only require (for it to be
a valid example) that /if/ someone had said "Hint: turtle graphics!", that they
would have been able to solve the problem.

I was taught by a very good maths teacher who had a habit of never letting
stuff get "stale". So, even in the middle of a lesson devoted to, say
geometry, he would still throw in exercises in algebra, or calculus. And vice
versa. Kept everything fresh in (what passed for) our minds. Made it much
less likely that we would get "stuck". He was an /excellent/ teacher.

That suggests one way around stuckness. Work, wherever possible, on several
unrelated problems at the same time.

-- chris

 

[Ingo R. Homann]

Hi Chris,

That is an interesting question. But I think that the training effect -- or
something very like it -- is what stuckness /is/. The first thing(s) that come
to mind get wedged there and prevent other ideas coming forward. If the older
children had never learned turtle graphics (or if they had learned it but knew
that it was unavailable in their current environment) then it would clearly be
incorrect to say they were "stuck" on X/Y coordinate drawing. But if they
/had/ learned about it, but had more recently learned X/Y stuff, so that when a
drawing task came up they immediately reached for the X/Y toolkit, then that is
a fair example of "stuckness". Note that it doesn't matter whether they may
have learned X/Y graphics /better/ than turtle -- we only require (for it to be
a valid example) that /if/ someone had said "Hint: turtle graphics!", that they
would have been able to solve the problem.

I understand what you mean, and again, I *somehow* agree to it.

It's just like: "If you've got a hammer, everything looks like a nail." ;-)

On the other hand: If the task is "Write a program that draws a circle
with a certain radius", then this task may be harder to accomplish with
turtle than with Phytaghoras!

And so, an interesting question concerning this is:

Isn't it normal that the second part of the task ("...with a certain
radius") might be consiedered as "normal" even if it is not said
explicitely?

Ciao,
Ingo

 

[Chris Uppal]

On the other hand: If the task is "Write a program that draws a circle
with a certain radius", then this task may be harder to accomplish with
turtle than with Phytaghoras!

And so, an interesting question concerning this is:

Isn't it normal that the second part of the task ("...with a certain
radius") might be consiedered as "normal" even if it is not said
explicitely?

I'm not sure what's implicit in an instruction to draw a circle. For instance
if someone handed me a piece of paper and asked me to draw a circle on it, then
I /might/ ask "how big?" or then again I might not. I might ask "where?" or
"how accurately?". Or, if they had been claiming that (fictitious factoid
alert!) "psychotic personality types draw circles as ellipses slanted towards
the left", then I'd not see any need to ask questions, and would just draw
any old circle (or ellipse ;-).

But how a question, or problem, is phrased can certainly affect "stuckness".
For instance (going back to the example) I suspect that people might have been
more likely to remember turtle graphics if the request had been phrased "draw a
circle anti-clockwise starting at <some point>". OTOH, "draw a circle centred
at <some point> with radius <whatever>" might make a trigonometric solution
leap to mind first (or compasses).

Perhaps one could /define/ stuckness as a state where one has paraphrased a
problem statement into a form which demands a solution of the wrong (or
unproductive) type. For instance the kids in the example might have translated
the general instruction "draw a circle" into a problem in Cartesian geometry --
one that they were unable to solve fully, even though (by hypothesis) there
were other statements of the same problem that they /could/ solve.

And going back even further to the two balls example. If one paraphrases the
problem as "how can I partition the floors most effectively with the first ball
so that the overall number of drops is minimised?" then I don't think one would
get "stuck" on binary search concepts.

Rearranging/rephrasing problem statements is one of the core skills of
problem-solving. (IMO).

-- chris

 

[Ingo R. Homann]

Hi,

... [very much] ...
Rearranging/rephrasing problem statements is one of the core skills of
problem-solving. (IMO).

Full ACK [to everything]!



Ciao,
Ingo