[Squeakland] Re: suggestions for pedagogical examples in Squeak

Alan Kay Alan.Kay at squeakland.org
Tue Feb 24 03:20:47 PST 2004

Here's an email that's been waiting for me to add some examples. But 
I won't be able to get to this until next week, so am sending now.



Hi Richard and Marsha --

Here are a few suggestions for using etoys.

First, though I'm guessing (hoping) you already are using "Powerful 
Ideas in the Classroom" by BJ Allen-Conn and Kim Rose, I need to 
mention it just in case. It contains ideas and directions for about a 
dozen projects that children like to do, are "good" for them 
epistemologically, and have been thoroughly tested. Another very 
useful collection of projects that have been written up nicely are 
from our friends in Toronto in the 8th grade of Don Mills School with 
teacher Sebastian Hergott <sebastian.hergott at tel.tdsb.on.ca>.

Here are some comments on Marsha's email.

Squeak etoys are in the form of a scriptable multimedia environment, 
so what gets authored can range from presentations (such as in 
powerpoint), stories and games (such as in MS Word, Director and 
Flash), to mathematical and scientific simulations. Each of these can 
have a little (to a lot) of overlap with various kinds of educational 
goals (including good ones). This is rather like introducing a word 
processor into a classroom "plus plus". That is, the authoring system 
needs to be really open-ended to deal with all of its genre (a word 
processor in which one could only write stories but not essays about 
important ideas would be a terrible use of technology). To continue 
the analogy, writing is much much more than just putting words down 
on paper, and having paper and pencils (or hightech word processors) 
is not much help if the teachers don't know what writing is and have 
some ideas about how to teach it.

Children don't know much about writing or math or science, but they 
do know a lot of stories and games, and a bit about stories and 
games, so they tend to plunge fearlessly into using a dynamic medium 
like Squeak etoys to make representations of stories and games of 
many different kinds. This simply follows previous observations of 
children with LogoWriter and Hypercard. There is nothing wrong with 
this, it's an easy way for them to learn the mechanics of using the 
system, and they can occasionally learn something beyond stories and 
games (e.g. a little about math) in the process. There is a part of 
NSF  and the National Research Council that thinks this is worthwhile 
all by itself because learning to "do multimedia", especially with 
scripting is thought to be an important part of "technological 

At 6:06 AM -0600 2/17/04, RATZEL, MARSHA wrote:
>  I'm now working with the head of the math department on the sligh 
>to create a summer workshop....it just seems to me that I understand 
>enough that I could help them do some neat things when they teach 
>the "Moving Straight Ahead" module of the Connected Math Program 
>module.  This seems like a perfect language and integrated piece of 
>technology for helping kids to "get" linear equations.  They could 
>experiment and see the what "if"s of all that.  (I taught math and 
>science before becomeing the computer teacher).

This is a very good thing to do, and there are really two parts to 
it: "real math" and "school math", which are not the same thing in 
most school systems in the US. It is critically important for the 
children to have some "real math" and "real science" experiences  -- 
which include actually being mathematicians and scientists themselves 
-- doing the stuff -- as opposed to the "math appreciation" and 
"science appreciation" that is most of school math and science 
(analogous to the difference between playing and composing music and 
"music appreciation", which is about what other musicians have done).

Real Math is the easier of the two because "math is about itself", 
and a full experience can be had with very simple media (including 
simple computer media, such as LOGO). One really important point 
about real mathematics is that it is about completely understanding, 
deriving and reasoning about relationships. "School math" tends to be 
about "remembering results and methods" not about understanding, 
deriving and proving. So to most real mathematicians like me, "school 
math" isn't actually math in any important sense. This is a serious 
problem because it pits large systems of millions of nonmathematical 
adults who are committed to a particular theory of schooling against 
a few thousands of people who actually do and understand mathematics 
(we have been losing badly for more than a hundred years).

The two big things that have to be done to help children with 
mathematics are to (a) have the mathematical experiences be real and 
above threshold, and (b) to have the mathematical experiences be 
consonant with children's abilities and motivations to represent and 
reason in beyond commonsense ways.

So, as Papert pointed out in the 60s, one good thing about children 
learning how to program a computer is that they are actually doing 
real math: they are representing ideas in formal structures, learning 
some tricky tools (such as functions with arguments), reasoning about 
ideas using representations, using the computer to help debug their 
reasoning, and exhibiting the equivalent of constructive 
demonstrations and sometimes proofs of what they are trying to do. 
What seems to be a bit of a struggle here is actually a virtue: an 
embodiment of the real process of mathematics that requires the 
practitioners to understand the relationships and be able to say why.

However, quite a bit a computer programming can be done that, while 
"real math", is not above any worthwhile threshold. For example, the 
LOGO turtle can be used to make simple drawings (and this is real, 
though pretty trivial math), or it can be used as Papert intended to 
have children gracefully and easily learn about the differential 
geometry of vectors (the main mathematical language of science that 
is full of profound and above threshold ideas -- and is rarely even 
touched on in school math an any level). In spite of many books about 
how to teach this and other kinds of above threshold math using LOGO, 
most K-8 teachers did not understand what it was about and did not 
make the effort themselves to learn enough to help the children.

In the US, the further the children progress in school, the harder it 
is to help them learn real math, both from the interference with the 
non-math they've already learned, and also the interference with the 
high stakes tests they have to take in high school. This is why we 
concentrate most of our energies with 4-6 graders where there is 
still a little flexibility. For example, many of the most important 
ideas in mathematics -- such as counting and arithmetic, calculus, 
vectors, geometry, probablity, feedback and control theory, etc. -- 
do not require algebra to understand or work with, and important 
parts of these can be well taught much earlier than "school math" 
supposes. For many of these, a computer can really both enhance the 
experience *and* also connect motivations from stories and games, 
etc., to motivations for learning math.

What we've done in the Squeak etoys is to take as many of the ideas 
we think are great for children that have appeared over the years 
from many different sources and combine these with extensive 
multimedia to make a kind of a "superhypercard" that we hope will 
appeal to many different kinds of children and adults for their own 
reasons. This seems to have worked for our target group of 4-6th 
graders (more needs to be done for both older and younger children). 
A good project in Squeak etoys is one that first "appeals as art" and 
then has some serious nontrivial content that has to be worked out to 
get the whole above threshold. The "serious nontrivial content" could 
be mathematical, scientific, theatrical, musical, visual, etc., or 
some mixture. We've concentrated on mathematical and scientific, in 
part because these two areas are the most weakly represented in 
schools today.

For those who are interested in creating this kind of content, please 
let me point you to books and papers  by Seymour Papert and many 
other LOGOites, Jerome Bruner (especially his ruminations on trying 
to make an intellectually honest version of cultural anthropology for 
5th graders: a masterpiece), etc.


Now for Richard's email.

First, I think pretty much everything you will need for your three 
day experience is in the "Powerful ideas in the classroom" book.

In what follows, I should mention that I was the one who made up the 
unfortunate term "object-oriented" in the mid60s (I should have 
called it something else). In any case, I have some strong ideas 
about what this term means and should mean.

You say:
At 9:21 AM +0100 2/16/04, Richard Borge wrote:
>We have decided not to focus on code as we feel there is
>a risk this can get boring. Instead we are focusing on general OO 
>understanding and
>the use of a graphical tool therefore seems like the way to go.

I'm not sure what this means. 5th graders typically do the car and 
steering wheel project in less than an hour and they do it by writing 
code. And it is definitely not boring to them. My suggestion here is 
to avoid "music appreciation" ("object-oriented appreciation") and 
just have the children make interesting and above threshold things 
using objects.

Another suggestion is to take into account the way children think and 
do and know, and how these are different from adult thinking and 
doing and knowing. There is quite a bit known here, and this context 
can be found in the works of Montessori, Piaget, Vygotsky, Bruner, 
Papert, Brown (Ann), etc. For example, it seems much less important 
to me for children of this age to know *about* objects than to see 
computers as "personal powerful artistic material" for their ideas 
that they can shape using language, planning, reasoning, esthetics, 
etc. In other words, what "personal computing" was supposed to be 
about when we invented it many years ago.

It's very hard to understand a framework without having something to 
contrast it with, so I think I would avoid trying to get your 11-12 
year olds to think categorically about objects in their first 
encounter. See if you can get them to love the experience, feel the 
power of expression, delight in the reasoning, and take happiness 
from being able to track down an bug and fix it, etc. The rest will 
surely take care of itself.

As there are already many 10-12 year old Squeakers all over the 
world, another part of your experiment might be to see what they 
think they are doing. Etc.

Best wishes,



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