Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain knowledge. In 2 experiments, 2nd- and 3rd-grade children solved 12 novel mathematical equivalence problems and then received brief conceptual instruction. After solving each problem, they received (a) no feedback, (b) outcome feedback, or (c) strategy feedback. In both experiments, prior knowledge moderated the impact of feedback on children's learning. Children with little prior knowledge of correct solution strategies benefited from feedback during exploration, but children with some prior knowledge of a correct solution strategy benefited more from exploring without feedback. These results suggest that theories of learning need to incorporate the role of prior knowledge and that providing feedback may not always be optimal. (Contains 4 tables, 3 figures and 4 footnotes.)