We explore some key constructs and research themes initiated by Jim
Kaput, and attempt to illuminate them further with reference to our own
research. These ‘design principles’ focus on the evolution of digital
representations since the early 1990s, and we attempt to take forward
our collective understanding of the cognitive and cultural affordances
they offer. There are two main organising ideas for the paper. The
first centres around Kaput’s notion of outsourcing of processing power,
and explores the implications of this for mathematical learning. We
argue that a key component for design is to create visible, transparent
views of outsourcing, a transparency without which there may be as many
pitfalls as opportunities for mathematical learning. The second
organising idea is Kaput’s notion of communication and the importance
of designing for communication in ways that recognise the mutual
influence of tools for communication and for mathematical expression.
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