In this paper, we propose a normative approach to modeling apparently human irrational decision making (cognitive biases) that makes use of inherently rational computational mechanisms. We view preferential choice tasks as sequential decision making problems and formulate them as Partially Observable Markov Decision Processes (POMDPs). The resulting sequential decision model learns what information to gather about which options, whether to calculate option values or make comparisons between options and when to make a choice. We apply the model to choice problems where context is known to influence human choice, an effect that has been taken as evidence that human cognition is irrational. Our results show that the new model approximates a bounded optimal cognitive policy and makes quantitative predictions that correspond well to evidence about human choice. Furthermore, the model uses context to help infer which option has a maximum expected value while taking into account computational cost and cognitive limits. In addition, it predicts when, and explains why, people stop evidence accumulation and make a decision. We argue that the model provides evidence that apparent human irrationalities are emergent consequences of processes that prefer higher value (rational) policies.