We propose an active cognition approach to bounded rationality, in which agents use a calculation algorithm to improve on the forecasts provided by a purely adaptive learning rule such as least-squares learning. Agents' choices of calculation intensity depend on their estimates of the benefits of improved forecasts relative to calculation costs. Using an asset-pricing model, we show how more rapid adjustment to rational expectations and forward-looking behavior arise naturally when there are large anticipated structural changes such as policy shifts. We also give illustrative applications in which the severity of asset price bubbles and the intensity of hyperinflationary episodes are related to the cognitive ability of the agents.