Stochastic traffic assignment provides a natural framework for looking at how travellers obtain and interpret information about their transport system, and how they apply what they learn to route choice. However, in order to model traveller learning effectively it is necessary firstly, to distinguish between-day from within-day dynamics, and secondly, to classify travellers in terms of their travel knowledge. Mast stochastic assignment models will not readily incorporate such features. In this paper a new assignment method, which includes these important elements, is described. The evolution of the transport system is modelled as a discrete time Markov Chain in which each iteration is subdivided into a between-day and a within-day stage. Theoretical properties of this model are outlined, and numerical results are obtained on the development of traffic flow over a road network under various schemes for driver learning.