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
- to acquaint PME members with
existing knowledge and experience on teachers’ and
learners’ use of examples in mathematics and with issues
involved and research findings associated with exemplification;
- to raise the profile of this
field as an important domain of research;
- to bring the issues associated
with exemplification in mathematics education into a coherent
articulation from which future directions for research may be
formulated.
The Research Forum has been designed around some key
questions:
- What makes an example effective for learning mathematics,
and in what
context?
- What things do teachers consider when selecting or
constructing
instructional examples?
- What factors influence learners’ perception of
examples, and
how do we deal with the tension that arises due to
‘mis-match’ between teacher’s intention
and learners’ attention?
- What is entailed and revealed
by the process of constructing examples
and how does construction of examples promote mathematical
understanding?
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.