Markov Transition Matrix Analysis of Mathematical Expression Input Models

Computer software interfaces for mathematics collaboration and problem solving rely, as all interfaces do, on user identification and recognition of symbols (via icons and other contextual widgets). In this paper we examine the results of a short study which examined users interacting with mathematics software (Mathematics Classroom Communicator, MC[Formula: see text]) designed for education, real-time communication and collaboration. Videos were recorded of 14 users working through seven comprehensive problems in the MC[Formula: see text] interface. Extensive second-by-second coding was completed of the user’s actions and status throughout their work, and a set of transition matrices were tabulated, estimating transition probabilities between symbols, operators and other aspects of mathematical expressions. We discuss the results of these matrices, and their implications in the translation of abstract mathematical concepts into software interfaces, and further conclude with a brief discussion of suggestions for mathematical software interface design. This study also has applications in mathematical software usability and accessibility.