Recent research has shown the importance of time horizons in models of learning in finance. The dynamics of how agents adjust to believe that the world around them is stationary may be just as crucial in the convergence to a rational expectations equilibrium as getting parameters and model specifications correct in the learning process. This paper explores the process of this evolution in learning and time horizons in a simple agent-based financial market. The results indicate that, although the simple model structure used here replicates usual rational expectations results with long-horizon agents, the route to evolving a population of both long- and short-horizon agents to long horizons alone may be difficult. Furthermore, populations with both short-and long-horizon agents increase return variability, and leave patterns in volatility and trading volume similar to actual financial markets.