[Its.an.education.project] From Piaget

[Bill Kerr]

Piaget:

When he was a small child, he was counting pebbles one day; he lined
them up in a row, counted them from left to right, and got ten. Then,
just for fun, he counted them from right to left to see what number he
would get, and was astonished that he got ten again


I think the key thing in this beautiful story about counting pebbles is the
word "astonished" in the above quote.

I have no personal recollection of being astonished by discovering the law
of conservation of pebble number. And yet experiments with young children
show that before a certain age this is something they (meaning all of us)
don't know. At some stage in our personal development we learnt this,
internalised it and then forgot that we learnt it - and can't recall any
sense of astonishment or not knowing something which as adults, seems to us
to be common sense

This is why constructionism doesn't scale (yet) - or is dependent on a
teacher being there who realises that what is obvious and common sense to
them is not obvious or common sense to children. And then finds ways to
spend time discussing and experimenting with these common sense notions with
children - rather than just assuming that everyone "gets it". Or doing
exercises which involve getting the "right answer". How many pebbles? Answer
= 10. Next question. This applies to all knowledge, not just to pebbbles or
number.

If we don't understand Piaget's genetic epistemology then constructionism or
a deeper philosophical approach to learning won't scale. This explains why
when a school leader with a deep understanding of learning leaves the site
then the whole learning environment of the school often then changes back
into something mundane. For those who remain obvious things become obvious
again and are no longer astonishing.

Not also that pebbles are free and that pebbles are not green machines.
There are some things that a green machine can't do.


On 5/16/08, Edward Cherlin <echerlin at gmail.com> wrote:

> I am reading in the literature of Constructivism, and will post my
> observations and interesting quotations from the pioneers from time to
> time to stimulate discussion. It is a curious fact, and one that seems
> quite important to me, that I come to understand my own thinking about
> a subject much better when I have to explain it to someone else.
>
> The following is the best example I have so far seen of Piaget's
> approach to Genetic Epistemology and to Constructivism. Genetic
> Epistemology suggests that to understand the nature of knowledge, we
> must understand the process by which knowledge has come about. Since
> we cannot study prehistoric humans, our best source is to study the
> origins of ideas in children. This study requires an understanding of
> human psychology, and also the current state and historical
> development of logic, mathematics, and the progress of science. Such
> interdisciplinary study has not been popular, in part because so few
> people have enough knowledge, and because people in different
> disciplines have great difficulty communicating with others.
>
> http://www.marxists.org/reference/subject/philosophy/works/fr/piaget.htm
> Jean Piaget (1968)
>
> Genetic Epistemology
>
> Source: Genetic Epistemology, a series of lectures delivered by Piaget
> at Columbia University, Published by Columbia Univesity Press,
> translated by Eleanor Duckworth. First lecture reproduced here.
>
> "This example, one we have studied quite thoroughly with many
> children, was first suggested to me by a mathematician friend who
> quoted it as the point of departure of his interest in mathematics.
> When he was a small child, he was counting pebbles one day; he lined
> them up in a row, counted them from left to right, and got ten. Then,
> just for fun, he counted them from right to left to see what number he
> would get, and was astonished that he got ten again. He put the
> pebbles in a circle and counted them, and once again there were ten.
> He went around the circle in the other way and got ten again. And no
> matter how he put the pebbles down, when he counted them, the number
> came to ten. He discovered here what is known in mathematics as
> commutativity, that is, the sum is independent of the order. But how
> did he discover this? Is this commutativity a property of the pebbles?
> It is true that the pebbles, as it were, let him arrange them in
> various ways; he could not have done the same thing with drops of
> water. So in this sense there was a physical aspect to his knowledge.
> But the order was not in the pebbles; it was he, the subject, who put
> the pebbles in a line and then in a circle. Moreover, the sum was not
> in the pebbles themselves; it was he who united them. The knowledge
> that this future mathematician discovered that day was drawn, then,
> not from the physical properties of the pebbles, but from the actions
> that he carried out on the pebbles. This knowledge is what I call
> logical mathematical knowledge and not physical knowledge."
>
> This states the importance of such ideas, and calls attention to the
> need for research. The research itself is a long, arduous, and
> contentious process, with a vast literature, as is all scientific
> observation, experiment, and theory-building, with many false leads
> and backtracks. It has not simply given us a body of definite
> knowledge in the way that we can say elementary physics does. It is
> more like the parts of physics out near the frontiers, where the
> variety of models of reality under consideration changes from year to
> year. But some lessons can be, and have been drawn from all of this,
> of which more another time.
>
> For the moment is it enough to have a powerful example of integrated
> thought, action, and discovery. This child did not only discover what
> we may call the Law of Conservation of Pebble Number. He discovered
> the existence of laws amenable to experiment and rational thought, but
> not dependent on the particular objects used in the discovery. In
> short, he discovered mathematics itself. Most children don't do this
> in this way, and of course, most don't become mathematicians as a
> result.
>
> What do children discover? How? What do they become as a result? These
> questions amply repay any amount of attention and effort aimed at the
> continued creation of ever-more-accurate understanding, because they
> allow us to explain ourselves better to ourselves and to others, a
> conversation that has always been rewarding, but never more so than
> now.
>
> Please let me know if this makes sufficient sense to you, and what
> else might need explaining. Also if you have been taught some quite
> different view of the nature of knowledge, or simply find this one
> obviously false, as some do.
>
> --
> Edward Cherlin
> End Poverty at a Profit by teaching children business
> http://www.EarthTreasury.org/
> "The best way to predict the future is to invent it."--Alan Kay
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