[Maths-Education] Newsletter on Proof

Tue Nov 18 02:32:42 GMT 2008

> 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

***********************************************************************************************************
This message has been generated through the Mathematics Education email discussion list.
Hitting the REPLY key sends a message to all list members.
***********************************************************************************************************
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:
> ***********************************************************************************************************
> This message has been generated through the Mathematics Education email discussion list.
> Hitting the REPLY key sends a message to all list members.
> ***********************************************************************************************************
> 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
>
> ***********************************************************************************************************
> This message has been generated through the Mathematics Education email discussion list.
> Hitting the REPLY key sends a message to all list members.
> ***********************************************************************************************************
> 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:
>   
>> ***********************************************************************************************************
>> This message has been generated through the Mathematics Education email discussion list.
>> Hitting the REPLY key sends a message to all list members.
>> ***********************************************************************************************************
>> 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
>>
>> ***********************************************************************************************************
>> This message has been generated through the Mathematics Education email discussion list.
>> Hitting the REPLY key sends a message to all list members.
>> ***********************************************************************************************************
>> 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.****
>>
>>
>>
>>
>> +++++++++++++++++++++++++++++++++++++++++++++++++++++++
>> An international directory of mathematics educators is available on the web at www.nottingham.ac.uk/csme/directory/main.html
>> ______________________________________________
>> Maths-Education mailing list
>> Maths-Education at lists.nottingham.ac.uk
>> http://lists.nottingham.ac.uk/mailman/listinfo/maths-education
>> +++++++++++++++++++++++++++++++++++++++++++++++++++++++
>> An international directory of mathematics educators is available on the web at www.nottingham.ac.uk/csme/directory/main.html
>> ______________________________________________
>> Maths-Education mailing list
>> Maths-Education at lists.nottingham.ac.uk
>> http://lists.nottingham.ac.uk/mailman/listinfo/maths-education
>>
>>
>>   
>>     
>
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++
> An international directory of mathematics educators is available on the web at www.nottingham.ac.uk/csme/directory/main.html
> ______________________________________________
> Maths-Education mailing list
> Maths-Education at lists.nottingham.ac.uk
> http://lists.nottingham.ac.uk/mailman/listinfo/maths-education
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++
> An international directory of mathematics educators is available on the web at www.nottingham.ac.uk/csme/directory/main.html
> ______________________________________________
> Maths-Education mailing list
> Maths-Education at lists.nottingham.ac.uk
> http://lists.nottingham.ac.uk/mailman/listinfo/maths-education
>
>
>   
+++++++++++++++++++++++++++++++++++++++++++++++++++++++
An international directory of mathematics educators is available on the web at www.nottingham.ac.uk/csme/directory/main.html
______________________________________________
Maths-Education mailing list
Maths-Education at lists.nottingham.ac.uk
http://lists.nottingham.ac.uk/mailman/listinfo/maths-education