[Maths-Education] Newsletter on Proof

[Alan Rogerson]

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
>
>
>