Graspable math: Towards dynamic algebra notations that support learners better than paper

Pen and paper remain the preferred tools for solving mathematical problems - despite the fact that paper derivations are very challenging to master and are limited by the static nature of paper. While traditional computer algebra systems are not geared towards the need of learners, dynamic algebra notation systems (DANS) that bring derivations into the digital space without sacrificing the user agency and directness that paper derivations provide have much to contribute to mathematics education. In this paper, we first analyze the strengths and weaknesses of pen and paper for doing algebraic derivations and discuss the potential benefits of DANS. We then present Graspable Math, our own implementation of such a system, discuss the interface design challenges solved in its development, and report on the encouraging outcomes of two user studies.