History of the Group
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
Call for papers
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:
(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@unisi.it
Viviane Durand-Guerrier
mailto:vdurand@univ-lyon1.fr