[Maths-Education] Newsletter on Proof

[Ernest, Paul]

Hi David et al

I have been trying to offer a semiotic account of mathemtical sign production and use, writing from what I call a social constructivist perspective but which has many points in common with a sociocultural perspective. (My fullest treatment of this perspective is in Social Constructivism as a Philosophy of Mathematics, SUNY 1998) In my series of papers in FLM this year I have been looking at semiotic systems in their social context. One of the key features is a account of the production of compound texts, and these include sequences of signs that make up proofs. I think such an approach using semiotics comes the nearest I have seen so far in answering your question (but I may have missed something)

Best wishes

Paul
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From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu]
Sent: 18 November 2008 02:32
To: Nicolas.Balacheff at imag.fr; Mathematics Education discussion forum
Subject: RE: [Maths-Education] Newsletter on Proof

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> I would put nuances on the claim that "expertise in proof is primarily a matter of social development ", and prefer to say that from a learning perspective social interaction may be a lever and sometimes also an obstacle due to the intrinsic linguistic, cognitive and social properties of argumentation.

Yes, most theorists considering the development of proof competencies would be uncomfortable with an analysis circumscribed by the social. But are there no voices in the literature urging just such a radical departure?

David



-----Original Message-----
From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Nicolas Balacheff
Sent: Monday, November 17, 2008 2:57 PM
To: Mathematics Education discussion forum
Subject: Re: [Maths-Education] Newsletter on Proof

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Dear David
it is true, in my opinion, that Lakatos has been influencial on the
research and educational community in mathematics. My own work in this
field is largely based on the study of Proof and refutations (which I
translated in French). However, the style chosen by Lakatos in his book
is a bit misleading. The aim is not to explore or value social
interaction but to use it at best to untangle the complexity of the
relationships between proving and conceptualising.  I would put nuances
on the claim that "expertise in proof is primarily a matter of social
development ", and prefer to say that from a learning perspective social
interaction may be a lever and sometimes also an obstacle due to the
intrinsic linguistic, cognitive and social properties of argumentation.
As for references, I think that you could find many of the Proof
newsletter website : http://www.lettredelapreuve.it/ (including some
discussions on argumentation)
Best regards
Nicolas


David H Kirshner wrote:
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> Thanks, Alan.
> Both Wittgenstein and Lakatos are important influences on our contemporary conversations about the socially constituted nature of mathematical proof. What I'm looking for are some key papers in the current pedagogical literature suggesting that expertise in proof is primarily a matter of social development, best attended to by nurturing increasingly sophisticated forms of argumentation within the classroom microculture.
> David
>
>
>
> -----Original Message-----
> From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson
> Sent: Monday, November 17, 2008 9:56 AM
> To: Mathematics Education discussion forum
> Subject: Re: [Maths-Education] Newsletter on Proof
>
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> Dear David,
> I would like to recommend Wittgenstein and especially "On Certainty"
> which I think is one of the deepest and, maybe in some ways, clearest
> exposition of the language usage underpinning why we seem to need...
> clear and definitive answers....and how language functions or behaves in
> trying to meet that need.
> The other seminal work of course would be that of Lakatos, where he has
> some wonderful and trenchant things to say based on his work in the
> history and, we would have to add, the socio-cultural development of
> mathematics.: "The value of a logical proof is .... that it suggests
> doubts", "I respect conscious guessing because it comes from two of the
> best human emotions(? I am quoting from a failing memory, but the sense
> is clear I hope)... courage and humility" .
> The lessons I have learnt from these two have been of immense practical
> assistance in my teaching, over the years, of students from 5 to 55. If
> you are really interested in this line of thinking I would be happy to
> make other suggestions, especially in the fields of sociology and social
> anthropology which also seem to be very useful in "understanding" - ah
> there's the  rub - maybe "comprehending", or "apprehending" would be
> better, how we function in a social and cultural complex, in which even
> language of course is but a small element of communication and hence
> of... "meaning"!
> Best wishes
> Alan
>
>
>
>
> David H Kirshner wrote:
>
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>> Maria-Alessandra, and others.
>>
>> I would appreciate your help in finding some sociocultural references to "proof" in the literature.
>>
>> Under the influence of cognitive interpretations of thinking and learning, attaining competence in proof is frequently portrayed as a cognitive accomplishment--achievement of skills and/or concepts related to proof. Thus practice and individual reflection become the vehicles for promoting competencies in proving.
>>
>> >From a sociocultural perspective, one might regard proof as a highly refined form of argumentation practiced within the mathematics community. The associated pedagogical strategy would be nurturing of increasingly sophisticated forms of argumentation within the classroom microculture (e.g., argument from authority --> argument based on material implication --> argument based on abstract logical implication).
>>
>> I know that the sociocultural perspective is reflected in the literature on proof. If anyone can point me to a particularly clear or definitive statement of that position, I'd be most appreciative.
>>
>> David Kirshner
>> Louisiana State University
>>
>>
>>
>> -----Original Message-----
>> From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of m.a.mariotti
>> Sent: Tuesday, November 11, 2008 8:57 AM
>> To: Mathematics Education discussion forum
>> Subject: [Maths-Education] Newsletter on Proof
>>
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>> This message has been generated through the Mathematics Education email discussion list.
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>> The  new   issue of the Newsletter on proof is on-line, you can find
>> it at
>>
>> http://www.lettredelapreuve.it
>>
>>   Have a good reading!
>>   m.alessandra
>>
>> ________________________________________________________
>> Maria Alessandra Mariotti
>> Dipartimento di Scienze Matematiche ed Informatiche
>> Università di Siena
>> Piano dei Mantellini, 44
>> 53100 Siena
>> tel. + 39 0577 233707
>> Fax. + 39 0577 233701
>> e-mail mariotti.ale at unisi.it
>> ____________________________________________________
>> ****http://www.lettredelapreuve.it.****
>>
>>
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