[Maths-Education] Newsletter on Proof

Tue Nov 18 11:25:56 GMT 2008

Perhaps Sfard's recent work which I read as locating all of  
mathematics (and thinking) in communication, and the cognitive  
development as the individualization of the developed shared discourse?

I would not accept that as fully accurate to, say some key Kinesthetic  
Reasoning, particularly in early childhood development, and it still  
does not quite fit the kinesthetic/visual reasoning (I would say  
proof) in undergraduate education through to my mathematics research.

Walter Whiteley

On 17-Nov-08, at 9:32 PM, David H Kirshner wrote:

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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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>>> 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
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>>>
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>>
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