[Squeakland] the non universals
billkerr at gmail.com
Sun Aug 19 11:26:53 PDT 2007
On 8/19/07, Robert Parks <bobp at lightlink.com> wrote:
> 1. would learning calculus as a "powerful idea" (rather than through
> the duller algebraic approach) be counted as "using discovery or inquiry
> based learning as a substitute for hard facts"?
No (based mainly on my reading of Seymour Papert)
Papert's metaphor is that learning maths ought to be like a relationship,
similar to getting to know a person or becoming a member of a community
The idea is to restructure the learning environment to create a maths-land
where playing with the right sort of objects (eg. logo, LEGO logo) can lead
to the gradual acquisition of powerful ideas (eg. that a curve can be formed
from a series of v small straight lines) in ways that are natural for
children (eg. body syntonic - you can also make a circle by walking around
There is "discovery" and "inquiry" involved in this but I'm pretty sure that
Papert didn't describe his theories with those terms - instead he used the
term constructionist, a combination of the words constructivism (Piaget
hypothesised internal structures) and external construction (eg. with logo
or LEGO). Papert claims that its tapping into natural ways of learning.
It's more like joining a community where you learn to think in certain ways.
There is more to being a mathematician or scientist than knowing facts and
skills. Skills based learning being another approach which can be viewed
differently from either "hard facts" or "discovery / inquiry"
The critique of discovery / inquiry approaches would be that at least some
of them are either unrealistic or mundane.
Unrealistic - we can't expect children to discover unaided what has taken
the best human minds thousands of years to discover
Mundane - if we ask children to duplicate a scientific discovery like a
recipe out of a cookbook then we can't expect a high sense of personal
ownership of the process
I'm not saying that all discovery / inquiry approaches are hopeless but they
are different from what Papert was proposing.
In Ch 6 of Mindstorms Papert constructs a pretend conversation b/w Galileo
and Aristotle. Rather than refuting Aristotle by an experiment, instead
Galileo takes Aristotle's logic as his starting point and pulls that apart.
He asks ARI if we drop two one-pound weights simultaneously then how long
will they take to reach the ground. ARI says 4 seconds each. Then GAL asks
what if we connect the two weights with a gossamer thread, how long will
they take to fall then?
This dialogue illustrates the point that GAL and ARI think about objects
differently, that GAL sees them as composed of parts whereas ARI thinks of
them as undivided wholes. It's a different way of thinking, a world view -
not just based on an experiment or an inquiry or a skill
btw James Gee says that this approach (learning to become a member of a
community of thinking in certain ways) can be simulated using computer
games in his book, "What Video Games Have to Teach Us about Learning and
2. What IS a "powerful idea", and how does it become powerful? I'm
> particularly interested in asking whether ideas get their power from
> abstraction (finding similarity in structure), or generalization (finding
> similarity in features) - or from both.
Blake made a point about specificity in reply to your points of abstraction
and / or generalization, which I agree with.
One of the powerful ideas is the scientific method and I think that involves
an ongoing theory / practice spiral, which could also be seen as shifting
back and forward between abstraction and specificity
In general, I think the powerful ideas on the non universal list are the
ideas that arose with the Enlightenment / printing press / industrial
revolution etc., the overthrow of the State power of the Church, the origins
of modernity, science, rule of Law, democracy, the decline of feudalism, the
rise of capitalism, what we call modern civilisation.
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