[Maths-Education] CERME5- TG4

[mariotti.ale at unisi.it]

The Fifth Conference of the European Society for Research in Mathematics
Education (CERME 5)
22nd – 26th February 2007

 Working Group 4


Argumentation and Proof

Call for papers




The role and importance assigned to argumentation and proof in the last
decades has led to an enormous variety of approaches to research in this
area. Historical and epistemological issues, related to the nature of
mathematical argumentation and proof and their functions in mathematics,
represent one focus of this wide-ranging research. Focus on mathematical
aspects, concerning the didactical transposition of mathematical proof
patterns into classrooms, is another established approach, which sometimes
makes use of empirical research. Most empirical research focuses on
cognitive aspects, concerning students’ processes of production of
conjectures and construction of proofs. Other research addresses
implications for the design of curricula, sometimes based on the analysis
of students’ thinking in arguing and proving and concerns about didactical
transposition. Recent empirical research has looked at proof teaching in
classroom contexts and considered implications for the curriculum. The
social-cultural aspects revealed in these studies motivate a current
branch of research which is offering new insights. Also, some researchers
refer strongly to philosophical and logical perspectives on mathematical
proofs, which is a very active domain.

Comparative studies, trying to come to a better understanding of cultural
differences in student’s arguing and in the teaching of proof can be seen
as part of this new branch of research.

 Papers presented in the last session of CERME3 and CERME4 on
“Argumentation and Proof” illustrate this diversity.

Differences concern the focus researchers take in their approach, as well
in the methodological choices they make. This leads not only to different
perspectives, but also to different terminology when we are talking about
phenomena. Differences are not always immediately clear, as we sometimes
use the same words but assign different meanings to them. On the other
hand, different categories that we build from empirical research in order
to describe students’ processes, understandings and needs are rarely
discussed conceptually across the research field. Conceptual and
terminological work is helpful in that it allows us to progress as a
community operating with a wide range of research approaches. Differences
in interests, perspectives and terminology and their relevance become
obvious when looking at the same data together. The experience we had in
our working group, analysing the same data from different research
perspectives, turned out to be rich and fruitful. It made the diversity of
our approaches evident and simultaneously demonstrated its value.

To get a better insight of the work of our group, we invite prospective
participants to Group 4 to view the proceedings of the previous
Conferences at :
http://ermeweb.free.fr/index.php

The organisers for Group 4 invite research-based papers on argumentation
and proof, including philosophical, logical, epistemological and
historical issues, learning issues and classroom situations.
We will be particularly interested in theoretical, empirical or
developmental papers that address one or more of the following themes
(though any papers of relevance to the overall focus of the group will
also be considered):

I.  The importance of explanation, justification, and proof in mathematics
education.
II.  The interplay between logic, language and mathematics in
conceptualisation.
II. Conditions for constructing proofs in mathematics classrooms.
III. Long-term building of mathematical ideas related to proof construction.

These issues will be considered from the following points of view:
(a)  Historical and epistemological, related to the nature of mathematical
proof and its functions in mathematics.
(b)  Philosophical and logical, concerning truth and validity.
(c) Cognitive, concerning the processes of production of conjectures and
construction of proofs, and their relationship with the processes of
conceptualisation.
(d) Social-cultural aspects for student construction of proofs.
(e) Educational, based on the analysis of students' thinking in
approaching proof and proving, and implications for the design of
curricula.
(f) Didactical, concerning the development of relevant situations and
programs for improving students’ ability in argumentation and proof in
mathematics.

If you have further questions, please contact any of the leaders of the
group (e-mail addresses are given below).

Maria Alessandra Mariotti
mariotti.ale at unisi.it


Viviane Durand-Guerrier
mailto:vdurand at univ-lyon1.fr


________________________________________________________
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.****