The research develops around a technological intervention intended to
transform a peer produced reference resource into a peer produced
learning environment. The site will become a practicum and laboratory
where we can study how people learn mathematics.
Concurrent with developments in online peer production, there has been
a increase in demand for skills related to science, technology,
engineering and mathematics across society. A new peer learning
approach may move this system toward equilibrium. To fulfil this
promise, we require a viable theory of peer learning.
Examining the literature, we see that mathematics has always been a
socio-technical affair. We can draw on previous approaches that
situate learning within a socio-technical context. In particular, we
see that the fidelity of our learning model will be key to its
success. Furthermore, human participants will require cohesively
integrated meanings and incentives. We can understand this in a
preliminary way to mean a common value system.
We then propose four lines of inquiry. First, a quantitative
approach, using the legacy data from PlanetMath, aiming to find the
social factors that influence learning outcomes. Next, a qualitative,
interview- and design-based approach to understand requirements for
peer learning systems. Third, we use relationships with contemporary
philosophy of mathematics, media, and games to situate the theory
within texts. Fourth, we use participatory design to expand the model
of peer learning, and understand the implications of our learning
model in field work with PlanetMath users.
Future work with both research and development aspects may ultimately
demonstrate that PlanetMath provides a ``better'' way to learn
mathematics. Apart from applications in the mathematics context, the
theory of peer learning and the technical models we have developed
have implications for science and technology fields, and for any
system where peer learning is a viable approach.
Sunday, March 24, 2013
Monday, March 11, 2013
As wolves love lambs so lovers love their love
«They say that there dwelt at Naucratis in Egypt one of the old gods
of that country, to whom the bird they call Ibis was sacred, and the
name of the god himself was Theuth.» - Socrates
«At the end of his Charioteer speech, Socrates prays that Phaedrus
direct his life toward love accompanied by philosophical talk. Given
that Phaedrus seems most notable for his zest for prepared speech, I
take it that Socrates means "love accompanied by philosophical talk"
to be an improvement to that. (What "love accompanied by philosophical
talk" precisely means, I cannot say here, but it seems at least
something that advances the cause of love as depicted in the
Charioteer speech). Thus we could see the dozens of turns in the
Phaedrus conversation as Socrates' cumulative attempts to bring
Phaedrus, by harnessing his desire for speech, to perceive, want to
modify, and have the ability to modify his desire for prepared speech.
A full appreciation of the dialogue, from this perspective, would take
showing how each piece of conversation partially contributes to this
three-fold goal. We would see Socrates showing Phaedrus how a speech
could fail to benefit the city and its people, in particular out of
ignorance; be too long, especially by recycling its meager
ingredients; try to persuade people about what well-born and gentle
people know to be false or what's simple-minded and even impious;
persuade unreliably; obscure its precise topic; have its parts in
disarray; be vague and inconsistent; ignore the nature of the
audience; depend mistakenly on probabilities rather than knowledge; or
aim to gratify one's fellow slaves rather than one's good and well-
born masters, the gods. What we can see from this list is that
Socrates had not yet broached with Phaedrus the issues with using
prepared scripts, the hazards of depending on reading for learning,
and the narrowness of treating speech too pathetically or
aesthetically. None of these criteria for shameful speech address the
critic of speechwriting as such or, more importantly, isolate and cure
Phaedrus' desire for scripted speeches.» --
http://www.personal.psu.edu/crm21/theuth.pdf
«The famous legend of Osiris is well known: tricked into being shut up
in a trunk the size of his body, he is dismembered [by his brother
Seth], and his fourteen parts are scattered to the winds. After many
complications, he is found and reassembled by his wife Isis, all
except the phallus, which has been swallowed by an Oxyrhynchus fish.
This does not prevent [Theuth] from acting in with the cleverest and
most oblivious opportunism. Isis, transformed into a vulture, lies on
the corpse of Osiris. In that position she engenders Horus, "the
child-with-his-finger-in-his-mouth," who will attack his father's
murderer. The latter, Seth, tears out Horus's eye while Horus rips off
Seth's testicles. When Horus can get his eye back, he offers it to his
father--and this eye is also the moon: [Theuth], if you will--and the
eye brings Osiris back to life and potency. In the course of the
fight, [Theuth] separates the combatants and, in his role of
god-doctor-pharmacist-magician, sews up their wounds and heals them of
their mutilation.»
«Sly, slippery, and masked, an intriguer and a card . . . a sort of
joker, a floating signifier, a wild card, one who puts play into play
. . .»
«His propriety or property is impropriety or inappropriateness, the
floating indetermination that allows for substitution and play.»
«He would be the mediating movement of dialectics if he did not also
mimic it, indefinitely preventing it, through his ironic doubling,
from reaching some final fulfillment or eschatalogical
reappropriation. [Theuth] is never present. Nowhere does he appear in
person. No being-there can properly be his own.»
«Every act of his is marked by this unstable ambivalence»
«[Theuth] extends or opposes by repeating or replacing. By the same
token, the figure of [Theuth] takes shape and takes its shape from the
very thing it resists and substitutes for. But it thereby opposes
itself, passes into its other, and this messenger-god is truly a god
of the absolute passage between opposites. If he had any identity--but
he is precisely the god of nonidentity--he would be that coincidentia
oppositorum to which we will soon have recourse again.»
-- Derrida, quoted at
http://www.lawrence.edu/dept/english/courses/60a/handouts/jptheuth.html
of that country, to whom the bird they call Ibis was sacred, and the
name of the god himself was Theuth.» - Socrates
«At the end of his Charioteer speech, Socrates prays that Phaedrus
direct his life toward love accompanied by philosophical talk. Given
that Phaedrus seems most notable for his zest for prepared speech, I
take it that Socrates means "love accompanied by philosophical talk"
to be an improvement to that. (What "love accompanied by philosophical
talk" precisely means, I cannot say here, but it seems at least
something that advances the cause of love as depicted in the
Charioteer speech). Thus we could see the dozens of turns in the
Phaedrus conversation as Socrates' cumulative attempts to bring
Phaedrus, by harnessing his desire for speech, to perceive, want to
modify, and have the ability to modify his desire for prepared speech.
A full appreciation of the dialogue, from this perspective, would take
showing how each piece of conversation partially contributes to this
three-fold goal. We would see Socrates showing Phaedrus how a speech
could fail to benefit the city and its people, in particular out of
ignorance; be too long, especially by recycling its meager
ingredients; try to persuade people about what well-born and gentle
people know to be false or what's simple-minded and even impious;
persuade unreliably; obscure its precise topic; have its parts in
disarray; be vague and inconsistent; ignore the nature of the
audience; depend mistakenly on probabilities rather than knowledge; or
aim to gratify one's fellow slaves rather than one's good and well-
born masters, the gods. What we can see from this list is that
Socrates had not yet broached with Phaedrus the issues with using
prepared scripts, the hazards of depending on reading for learning,
and the narrowness of treating speech too pathetically or
aesthetically. None of these criteria for shameful speech address the
critic of speechwriting as such or, more importantly, isolate and cure
Phaedrus' desire for scripted speeches.» --
http://www.personal.psu.edu/crm21/theuth.pdf
«The famous legend of Osiris is well known: tricked into being shut up
in a trunk the size of his body, he is dismembered [by his brother
Seth], and his fourteen parts are scattered to the winds. After many
complications, he is found and reassembled by his wife Isis, all
except the phallus, which has been swallowed by an Oxyrhynchus fish.
This does not prevent [Theuth] from acting in with the cleverest and
most oblivious opportunism. Isis, transformed into a vulture, lies on
the corpse of Osiris. In that position she engenders Horus, "the
child-with-his-finger-in-his-mouth," who will attack his father's
murderer. The latter, Seth, tears out Horus's eye while Horus rips off
Seth's testicles. When Horus can get his eye back, he offers it to his
father--and this eye is also the moon: [Theuth], if you will--and the
eye brings Osiris back to life and potency. In the course of the
fight, [Theuth] separates the combatants and, in his role of
god-doctor-pharmacist-magician, sews up their wounds and heals them of
their mutilation.»
«Sly, slippery, and masked, an intriguer and a card . . . a sort of
joker, a floating signifier, a wild card, one who puts play into play
. . .»
«His propriety or property is impropriety or inappropriateness, the
floating indetermination that allows for substitution and play.»
«He would be the mediating movement of dialectics if he did not also
mimic it, indefinitely preventing it, through his ironic doubling,
from reaching some final fulfillment or eschatalogical
reappropriation. [Theuth] is never present. Nowhere does he appear in
person. No being-there can properly be his own.»
«Every act of his is marked by this unstable ambivalence»
«[Theuth] extends or opposes by repeating or replacing. By the same
token, the figure of [Theuth] takes shape and takes its shape from the
very thing it resists and substitutes for. But it thereby opposes
itself, passes into its other, and this messenger-god is truly a god
of the absolute passage between opposites. If he had any identity--but
he is precisely the god of nonidentity--he would be that coincidentia
oppositorum to which we will soon have recourse again.»
-- Derrida, quoted at
http://www.lawrence.edu/dept/english/courses/60a/handouts/jptheuth.html
Monday, March 4, 2013
weepnomor
No, I will weep no more. In such a night
To shut me out? Pour on; I will endure.
In such a night as this? O Regan, Goneril!
Your old kind father, whose frank heart gave all—
O, that way madness lies; let me shun that;
No more of that.
-- King Lear Act 3, scene 4, 17–22
To shut me out? Pour on; I will endure.
In such a night as this? O Regan, Goneril!
Your old kind father, whose frank heart gave all—
O, that way madness lies; let me shun that;
No more of that.
-- King Lear Act 3, scene 4, 17–22
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