Understanding the Role of Computers in Mathematical Problem Solving

Computer Algebra Systems (CAS) have been designed to aid users by automating a class of mathematical computations. However, despite widespread availability, little is known about how usable, useful, and used computers in general and CAS in particular are in mathematicians’ work. Recently we presented a first examination of the overall work process of expert mathematicians and of the drawbacks of CAS in supporting this work process [4]. In this paper, we expand our discussion of mathematicians' work practices by highlighting two primary tasks -problem solving and project management -and discussing the different artifacts used during these primary tasks. We also show how a better understanding of mathematicians work practices can lead to the design of computational tools that better support mathematical problem solving. The study results reported here and in our recent work are the first analyses of how mathematicians work and of why current computational tools have only narrow utility in their work.