[Maths-Education] Newsletter on Proof

Mon Nov 17 17:53:58 GMT 2008

Dear David,
I wish I could agree with you, I am amazed how many people now have 
never, or hardly, heard of Lakatos (nor Kuhn) much less Wittgenstein, 
and I have never met anyone, in maths education at least, who has read 
their major works in entirety, as opposed to reading a few sentences 
about them, so I am not sure what "influence" these creative thinkers 
are having.
I was reacting mostly to your mention of a "clear and definitive 
statement" which was the basis of all of Wittgenstein's early work in 
the Tractatus (following to some extent the Vienna School), but despite 
its poetic beauty, it was wholly rejected by him in all his later work.
I am not sure if the professional psychologists are any clearer now as 
to the proportion of influence of "nature or nurture" as it used to be 
called, on human development (it was 40-60 last time I looked) - it is 
difficult to say because they continuously co-exist in such an obvious 
sense.
When you say something is "primarily a matter of social development" as 
opposed to cognitive - that sounds like a very hard question to resolve, 
or even to know how it could be resolved in any experimental (as opposed 
to anecdotal) sense? Certainly the attempts I have seen have not been in 
any way convincing but I hope you have better luck!
The dominant paradigms of the 1960s and 1970s, it is true, are now being 
replaced by others, but how far this is due to progress and deep study, 
as opposed to fashion, I am not sure.
Best wishes
Alan

PS If anyone on the forum has had the pleasure of absorbing all of the 
wondrous works of Wittgenstein and/or Lakatos and would like to discuss 
them in a conflict-free way I would really love to hear from them 
privately! Last weekend my wife Margaret and I attended the annual MUED 
Group meeting in Kassel, Germany, highly recommended if you want to see 
the cutting edge of maths education innovation in schools today - and 
yes they do follow implicitely Polya, Lakatos, Freire and some other 
notables. I mention it however because we had the good fortune to meet a 
remarkable man, Mattias, who had taught both philosophy and maths all 
his life so it was a real pleasure to discuss our favourite thinkers and 
their influence on our lives.

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
>
>
>   