Annual Conference of Didactics of Mathematics
Klagenfurt 2002
Moderated Section:
Perspectives of empirical research on proving, justifying and arguing in teaching
and learning of mathematics
with Tommy Dreyfus, Götz Krummheuer and Kristina Reiss
Moderation: Aiso Heinze, Christine Knipping
Arguing, justifying and proving are goals of mathematical instruction, which
are considered to be of great importance within mathematics education. But,
how are these goals to be interpreted? What is the difference between arguing,
justifying and proving? What do we expect of heterogeneous students, e.g. students
of different ages? What kind of abilities and capabilities can we presuppose
or hope to teach? Which features characterise justification and proving processes
in teaching? These and other questions have been raised in didactic discussions
since the 1970s, but up to now these discussions have rarely been based on empirical
research in the field of proving. For that reason this moderated section will
focus explicitly on empirical approaches and perspectives.
Different ventures that have been realized in research projects will be the
starting point for the discussion of perspectives of empirical research on proving,
justifying and arguing in teaching and learning of mathematics. At the beginning
representatives of different approaches will describe and discuss their research
interests and perspectives as experts in the field. Their standpoints not only
reflect different research interests, but imply different theoretical and methodological
assumptions and concepts. To give an example, the concept of argumentation assumed
in suggestions that consider arguing as a general requirement of mathematical
learning, is not primarily directed towards mathematical reasoning and proving.
Finally, all interested participants of the moderated section will be encouraged
to contribute to the discussion of perspectives of empirical research on proving,
justifying and arguing in teaching and learning of mathematics.