Generating examples: focus on processes

Constructing an example can be a rich and
complex activity, interesting to investigate mathematical
thinking and with many potentialities in mathematics
education. In this article, I analyse processes involved in
example generation, with particular emphasis on production
and transformation of signs representing mathematical
objects and on generation of inferences. The richness and
complexity of these processes will also be shown through
the notions of prototypes, concept image and concept
definition. This investigation reveals aspects that are significant
both in education and for the reflection on cognitive
and cultural aspects of mathematical thinking.

Keywords: Example generation, Cognitive processes,
Semiotic set, Argumentation and proof