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 black-box 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.

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