Symbols of Success: New Representations for Teaching and Doing Mathematics
While symbolic representations are powerful in doing mathematics, it has been known since the early 1990s that much of the difficulty people have learning mathematics is because of the symbolic interface.
The modern tablet computer ("paper on steroids") offers the possibilty of developing alternative representations.
Applications to K-12 mathematics teaching have already been developed and promise to have a significant impact on mathematics learning.
We can expect novel representations to play a role in doing (some) mathematics as well. [Indeed, it is arguable that graphing apps and the electronic spreadsheet are existing examples, albeit ones that do not make essential use of a touch screen.]