[IAEP] another book

mokurai at earthtreasury.org mokurai at earthtreasury.org
Sat Apr 30 16:09:28 EDT 2011

On Mon, April 25, 2011 1:06 pm, Alan Kay wrote:
> To me, the first paragraph below from Cynthia's excellent book, is at the
> heart of the matter.
> Since it took humans almost 200,000 years to discover many of these ideas
> and methods, but found plenty of less fruitful paths and directions, we
> shouldn't
> wonder that both children and teachers will have great difficulty.

The exact chronology doesn't matter, but I have a sort of OCD about such
things. The Stone Age began nearly 3 million years ago. Most discovery of
ideas in human society began after speech evolved, which we can now date
to after the invention of cooking, about 100,000 years ago. Cooking caused
major anatomical changes in muscles, bones, and throat that permitted
generation of a much wider range of sounds. Information on the
corresponding changes in human brains is much scarcer, although there is

> And it is also true that "discovery guided by fluent practitioners who
> really
> understand their subject" is one of the most powerful processes to help
> learners
> really get into the meat of what a subject is all about.
> Could a "computer helper interface" of the future be fluent and flexible
> enough to carry this off?

I have been working on how one could do this without a computer, and of
course I expect that we will work out even better methods with a computer.

My first topic is how students could be given the minimal necessary
guidance to discover the OLPC XO and its Sugar software, including Etoys,
and the process of discovery itself. It begins on the Sugar Labs Wiki page
The Undiscoverable, which sets out the limits on what we can expect
children to discover without explicit guidance (at least broad hints), and
suggests appropriate guidance on many of these points.


I have not seriously started the Etoys section, except to note its general
difficulty. I find that the tutorials provided in Etoys are almost
sufficient, up to a certain point. I hope to have time soon to explore
this issue further, and perhaps implement something to bridge the gaps I
see. But that must be a separate discussion.

The next stage of my project is in book form, but is a radical departure
from the conventional textbook that attempts to explain everything the
student is expected to learn. Instead, I present the learner with a
strategy for discovery, and then a series of selected challenges with a
few necessary hints. All of this is derived from my own experience in
documenting software without assistance from developers, a process that I
call Defensive Documentation.

I have a draft in the Sugar Labs project for Replacing Textbooks (with
Open Education Resources) alpha server site,


I would be grateful for reviewers and for assistance.

> Cheers,
> Alan
> ________________________________
> From: Steve Thomas <sthomas1 at gosargon.com>
> To: Cynthia Solomon <cynthia at media.mit.edu>
> Cc: IAEP <iaep at lists.sugarlabs.org>
> Sent: Mon, April 25, 2011 9:32:47 AM
> Subject: Re: [IAEP] another book
> Thank you.
> In your book (Davis chapter) you write:
> The following anecdote captures the root of the problem. A teacher who had
> taken
> part in a workshop on "discovery learning" came back almost in tears
> complaining
> that the students had "discovered it wrong." Bob Davis himself and his
> virtuoso
> disciples could work with a class of children, sensitively guiding the
> discovery
> process. In particular, they could pick out the germs of good insight in
> what
> the less understanding teacher saw as simply "wrong." The problem is deep:
> People brought up with a view of mathematics as discrete facts to be
> mastered do not easily discard this view.

Working mathematicians have a completely different relation with their
subject from what is conventionally taught. The greatest resource a
mathematician can have is an unanswered question where there is some hint
of how to approach it. One of the best recent examples is the proof of
Fermat's Last Theorem (which Fermat undoubtedly did not prove completely).
It had become known that the Taniyama-Shimura Conjecture implied FLT, and
there were possible tools for approaching TSC. Andrew Wiles then spent
eight years on this problem, ultimately solving enough of it to prove FLT.
The complete proof of what is now the Taniyama-Shimura Theorem followed in
work by others, based in part on the clues that Wiles provided.

I have started to write a paper on another aspect of this problem,
covering a number of instances in which many mathematicians and others
refused to admit the existence of a new branch of mathematics, denouncing
it in terms ranging through "nonsense", "blasphemy", and "corruption of
youth". Examples include irrational, negative, imaginary, and transfinite
numbers, and non-Euclidean geometry. We are currently in another round of
this, surrounding non-standard arithmetic and analysis.

> The reformer is faced with the problem:
>>We cannot tell teachers all they need to know about teaching--we must
>> choose.
>>Indeed, we must choose not merely content, but also the kind of content,
>> and in
>>fact even the media by which and form in which this "knowledge" is
>> presented.
>>The problem is compounded by what happens in the next year with
>> "untrained"

I am sorry that I have to contradict you, in part. We must teach teachers
how to have an open mind (without, of course, allowing their brains to
fall out). "Knowledge is of two kinds," wrote Samuel Johnson, "we know a
subject ourselves, or we know where to find information upon it." Yes, we
have to begin by guiding teachers. Then we need to take off the
constraints that go back the Prussian factory education system, in which
every student studies the same lesson from the same textbook on the same
day, and teachers were taught only how to present the lessons, not how to
understand the subject themselves, or to learn more about them when

Teachers must be helped to appreciate the deep philosophical questions
that every child asks (until it becomes clear that such questions are not
permitted in most schools). What is a number? What is counting? Should I
believe you? Should you believe me? Why are children who have trouble with
an idea called lazy and stupid? Why do teachers want me to follow the
rules and learn the procedures without asking Why? Why are there different
kinds of number? Why do people lie about history and economics? Why do
adults think it proper to keep all kinds of secrets from children? Why do
children not have civil rights?

Also, why are children taught that English has long and short vowels, like
Latin or Japanese, when in fact English has vowels and diphthongs, and
more of each than fits into this neat scheme? Why the insane bickering
between Phonics (bat cat sat mat...) and Whole Word (one, once, two, I,
my, you, though, rough, cough, book, boot...) for reading, when English
requires both?

And on, and on, and on, and on...

> Do you know where I can find copies of the scripts Bob Davis used as part
> of the Madison project?
> So what is the way out of this problem (that scales)?

I can only suggest parts of a solution. I am fairly certain that Replacing
Textbooks with OERs is an essential part of the solution, in part because
it scales so well, and in part because it lifts so many onerous
restrictions on education. Laptops + OERs cost much less than printed
textbooks in all but the poorest countries, which cannot afford adequate
textbooks, and also cannot afford enough schools and teachers, among other
things of importance. Laptops provide access to all of the freely
published information in the world, and should provide access to all of
the other children with laptops, if children can get around government

> Also in your book  (Papert chapter) you write:
> Papert pursues such questions as,
>>(1) What experiences and knowledge lead children to change their
>> theories, and

We need to ask the same question about adults. One of the most important
facts in the world today is that thousands of people in the United States
fall away from assorted forms of racism, bigotry, and other delusions,
millions every year, and that this is going to transform US politics as
each state or electoral district reaches the tipping point. The clearest
case at present is Gay Rights, where the US went from majority opposition
up to last year to majority approval this year. I could recite a multitude
of others where the time for change came in US and other history, and many
more where it is approaching. The same is happening in many other
countries, and we have seen many countries reach their tipping points on
tyranny over the decades. Egypt and other North African and Middle Eastern
countries are vastly hungry for information on these cases, particularly
on what happened afterwards.

>>(2) why do they learn some things without formal instruction and not
>> learn other things despite formal instruction?

There are important experimental findings on this. In particular, it has
been shown that instruction can interfere directly with understanding. One
experiment involved showing students in kindergarten how to fold paper
fans. They all got it, and did it. Then the instructor gave instructions
for folding paper fans, and the experimenters report that none of the
children could then do it.

> I also struggle with the first question a lot.  In my experience the
> answer
> depends a good deal on knowing what theories the child holds, so I guess
> my main
> question is are there any proven techniques to help the child
> a) see the hole/problem with their current theories (which to them make
> perfect
> logical sense)
> I usually attempt to cause "cognitive dissonance" by finding questions and
> examples that do not fit their model as I perceive it, or more easily as
> they
> verbalized it. That can work, but does not scale, also in an OLPC model
> where
> there may be no teacher or no teacher with subject matter expertise, what
> do you do?

As I said above, I'm working on that.

> b) what does research say about proven techniques to help kids change
> their mental models once they see the "holes"?
>>Regarding the 2nd question I would add: "Why do they learn some things
>> despite formal instruction?"


> Also in your book  (Papert chapter) you write:
> the process of doing elementary school mathematics so that it draws on
> children's intuition and everyday commonsense thinking.
>>How Papert differs from Suppes, Davis, and Dwyer might be summed up in
>> what I
>>call the Papert principle: If you want to teach arithmetic to children,
>>arithmetic might not be the best route into these ideas for an easy
>>understanding of the topic. What is needed is a way of mathematizing the
>> child; thereafter particular mathematical topics become easy.

Piaget, of course, had a lot to say about that, much of which Papert

> This reminds me of something I heard from Keith Devlin either here or in
> his Natural Math talk, which was:
> It comes down to finding new representations of mathematics.
>>So does anyone have any good examples of new representations?

Yes. Thousands, I think. I've been collecting them.

Let's start with Cartesian analytic geometry and polar coordinates and
homogeneous coordinates and projective geometry and differential geometry
and Minkowski space and Hilbert space. Lie groups, where a topological
structure and an algebraic structure map together. Noether's Theorem, that
every symmetry in the laws of physics is equivalent to a conservation law.
Matrices and tensors and spinors and such. Fourier analysis. Wave
mechanics and matrix mechanics in quantum theory. All of Category Theory
and Topose Theory and Model Theory. Gödel numbering. Church's Thesis, that
all sufficiently powerful models of computation, dozens at least, are
equivalent. The discovery that the vast multitude of string theories in
physics are all variations on the same theory under various mappings and

To name but a few.

"By relieving the brain of all unnecessary work, a good notation sets it
free to concentrate on more advanced problems, and in effect increases the
mental power of the race."

Alfred North Whitehead, quoted in Florian Cajori, A History of
Mathematical Notations" (1929), Vol. 2, p. 332

The same is more generally true of representations.

> Lastly, one of the great things from the Madison project is what I call it
> "Taking Tic-Tac-Toe to the next level", where the key rule of the game is
> you
> can't tell anyone the rules.  Kids play the game and have to figure out
> the
> rules by playing. Kids can learn about cartesian coordinates, positive and
> negative numbers and practice "a number is all the ways you can name it"
> all
> without being told what to do or how to do it.

Well done. More!

> Stephen
> If you give a child an answer,
> you solve a problem for the day.
> Teach a child to find the answers,
> you prepare her for a life.
>       - Mr. Steve's Science
> On Mon, Apr 25, 2011 at 6:38 AM, Cynthia Solomon <cynthia at media.mit.edu>
> wrote:
> I just posted my book, Computer Environments for Children: A Reflection on
> Theories of Learning and Education.
> http://computerenvironments.wikispaces.com
>>IAEP -- It's An Education Project (not a laptop project!)
>>IAEP at lists.sugarlabs.org
> _______________________________________________
> IAEP -- It's An Education Project (not a laptop project!)
> IAEP at lists.sugarlabs.org
> http://lists.sugarlabs.org/listinfo/iaep

Edward Mokurai
ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.

More information about the IAEP mailing list