After two decades of incremental advances in the capabilities of graphing calculators, handheld
technologies have recently made a leap into a new genre of educational tool – the “microworld maker.”
One such example is the TI-Nspire handheld device that allows for the creation of dynamic documents
endowed with “hot links.” The goal of a hot link is to achieve the optimum in visual proximity,
immediacy, and transparency by providing two or more external representations linked together in such a
way that the actions performed in one representation have virtually simultaneous discernible consequences
in the others. Such hot links can provide uniquely powerful settings for exploration of connections, pattern
searching, and inductive reasoning. That is, students are presented with environments where they can
directly manipulate or take actions on mathematical objects and immediately see the mathematically
meaningful visual consequences of those actions. We offer a variety of examples of such environments
drawn from a range of mathematical areas and raise two issues of import for both teachers and developers:
mathematical fidelity (faithfulness to the mathematical representations) and cognitive fidelity (faithfulness
to the cognitive perceptions of the user).