The SUM-to-MIN transition that children exhibit when learning to add provides an ideal domain for studying naturally occurring discovery processes. We discuss a computational model that accounts for this transition, including the appropriate intermediate strategies. In order to account for all of these shifts, the model must sometimes learn without the benefit of impasses. Our model smoothly integrates impasse-driven and impasse-free learning in a single, simple learning mechanism. The issue addressed by this paper is explaining how children discover the MIN strategy. This particular discovery presents a challenge for current theories of learning. Although a variety of learning methods have been proposed, many of them are triggered when the problem solver reaches an impasse, and yet Siegler and Jenkins found no signs of impasses during the discovery of the MIN strategy. The exact definition of 'impasse' depends on the problem-solving architecture, but roughly speaking, an impasse occurs whenever the solver has a goal that cannot be achieved by any operator that is believed to be relevent to the task at hand. The essential idea of impasse-driven learning is to resolve the impasse somehow, then store the resulting experience in such a way that future impasses will be avoided or at least handled more efficiently.