Connected Mathematics 
Traditional mathematics education has proceeded from a view that
mathematics is "given" rather than
constructed and is to be transmitted to learners primarily through
formalism. As a result, mathematics is
usually taught in isolation from other domains and the role of technology
in mathematics education has
primarily been to better inculcate or animate the existing formalisms. In
contrast, the theory of Connected
Mathematics sees the fundamental activity of mathematics as that of
making and designing new mathematical
representations and connecting these representations to each other and to
other domains. The vision of
mathematics as being made and not simply received leads naturally to a
role for technology. Technology is not
there simply to animate received truth, it is an expressive medium a
medium for the making of new
mathematics. It follows that we can make better use of computational
technologies than simply running
blackbox simulations we can make mathematics by constructing
computational embodiments of mathematical
models. The true power of the computer will be seen not only in better
teaching of the old topics but in
transforming ideas about what can be learned.
Connected Mathematics is the guiding framework for the research being conducted here. The current project is based on theoretical work I undertook as part of my dissertation research. The dissertation, as well as the two projects funded by the National Science Foundation can be accessed below.

