While looking at the papers collected in this volume one feels that, in spite
of their diverse themes, these seven studies have quite a lot in common
and, as a collection, seem to be signaling the existence of a distinct, relatively
new type of research in mathematics education. A comparison
with, say, a fifteen-year-old issue of Educational Studies in Mathematics
or of Journal for Research in Mathematics Education would reveal
a long series of differences. To begin with, the present articles simply
look different from their older counterparts: They are longer and have a
highly variable format, often not even remotely reminiscent of the classical
background-method-sample-findings-discussion structure that reigns
in the former research reports. Long segments of conversation transcripts
take the place of the once ubiquitous graphs and tables. As we start reading,
we discover substantial differences in vocabulary. The language of
mental schemes, misconceptions, and cognitive conflicts seems to be giving
way to a discourse on activities, patterns of interaction, and communication
failures. While the older texts speak of learning in terms of personal
acquisition, the newer ones portray it as the process of becoming a participant
in a collective doing. And last but not least, the classroom scenes
that we see as we go on reading have very little in common with what
we got used to in the older papers. To be sure, finding a detailed description
of a learning activity in a research paper was a rare occurrence until
recently, and in the majority of cases we had to rely on our own experience
while trying to imagine the life of the class in which the authors
conducted their study. In spite of this limitation, much can be said also
about the differences in the ways of learning investigated in the two types
of research: The traditional mathematical classroom featuring one blackboard,
one outspoken teacher and twenty to forty silent students seems to
belong to history.1 It has been replaced by small teams of learners talking
to each other, by groups of students voicing their opinions in whole class
discussions, and by children and grownups grappling with mathematical
problems in real-life situations