PME 30 Research Forum (Prague 2006)  

       Exemplification: the use of examples in teaching and learning mathematics

                  Co-ordinators: Liz Bills, John Mason, Anne Watson, Orit Zaslavsky
                     Additional Contributors: Paul Goldenberg, Tim Rowland, Rina Zazkis

0. Forum Structure 1. Background Paper 2. Extended Bibliography 3. Oxford Meeting 2005 4. Other Papers 5. Other Links
Download RF Paper

0. Forum Structure

This Research Forum will focus on the contribution that attention to examples can make to the learning and teaching processes, taking as background the ways in which examples are construed within different theories of learning (details are in the following background paper). Thus the forum addresses issues at the very heart of mathematics education. Much of the forum time will be allocated to participants engaging with mathematical tasks and classroom data. Our hope is that juxtaposition of previous experience with experience of the tasks offered will stimulate them to develop and express their own theoretical understanding of exemplification, leading to a synthesis and re-expression of perspectives and directions for further research.

Goals of the research forum

The Research Forum has been designed around some key questions:

Structure of the research forum sessions

Session 1:
Examples, a teacher’s perspective
Session 2:
Examples, a learner’s perspective
     Setting the stage (Orit Zaslavsky)
First task, in small groups  (Orit Zaslavsky)    Third task, in small groups (Anne Watson)
     Commentary (Tim Rowland)     Commentary (Paul Goldenberg)
Second task, in small groups (Liz Bills) Fourth task, in small groups  (Rina Zazkis)
     Commentary (Tim Rowland)      Commentary (Paul Goldenberg)
Central issues and future research questions
(John Mason)
Issues and future research questions
(Orit Zaslavsky, John Mason)
Each session consisted of presenters offering two incidents/examples to be explored/analyzed/discussed by the audience. At the end of each session, a commentator reflected on issues raised during the session, including audiences’ comments and suggestions for further research.  Since the audiences were very much larger than expected, this was done by providing cards on which comments could be written and handed in, rather than through trying to manage full open discussion.  Comments are now all published on the Research Forum website.  The forum succeeded in allowing a large number of research questions and directions to be proposed, thus re-establishing the area as a significant field for future work.

Comments were invited from participants in both sessions and have been summarised.