There is an increasing trend of research in exploratory learning
environments (henceforth ELE), as opposed to traditional systems with
a clear delimitation of the domain and well-defined sequences of tasks
to be performed. ELE support a constructionist approach for learning
encouraging the learner to create their own solutions to problems.
This has shown to be particularly beneficial in terms of providing
opportunities for acquiring deep conceptual and structural knowledge.
However, there are several factors that prevent appropriate learning
within an exploratory learning, not least the 'play paradox', which
recognises the pedagogical power of playful, exploratory learning, yet
acknowledges that students may potentially learn material that was not
predicted by the designers. The key learning over many years is that a
crucial determinant of learning is the level of support of the
learning process by teachers, peers, technologies and the structure of
the activity sequences. There is a need for a certain level of support
of the learning process. These are particularly true in the case of
mathematics where, unlike physics or other science domains, knowledge
is rarely a directly observable outcome of a simulation under
exploration and therefore other more expressive tools are required to
permit students to externalise their ideas.
There are two aspects of this support that are relevant: intelligent
support and support for collaboration. Both of them provide important
challenges