Children's gains in problem-solving skills during the elementary school years are characterized by shifts in the mix of problem-solving approaches, with inefficient procedural strategies being gradually replaced with direct retrieval of domain-relevant facts. We used a well-established procedure for strategy assessment during arithmetic problem solving to investigate the neural basis of this critical transition. We indexed behavioral strategy use by focusing on the retrieval frequency and examined changes in brain activity and connectivity associated with retrieval fluency during arithmetic problem solving in second- and third-grade (7- to 9-year-old) children. Children with higher retrieval fluency showed elevated signal in the right hippocampus, parahippocampal gyrus (PHG), lingual gyrus (LG), fusiform gyrus (FG), left ventrolateral PFC (VLPFC), bilateral dorsolateral PFC (DLPFC), and posterior angular gyrus. Critically, these effects were not confounded by individual differences in problem-solving speed or accuracy. Psychophysiological interaction analysis revealed significant effective connectivity of the right hippocampus with bilateral VLPFC and DLPFC during arithmetic problem solving. Dynamic causal modeling analysis revealed strong bidirectional interactions between the hippocampus and the left VLPFC and DLPFC. Furthermore, causal influences from the left VLPFC to the hippocampus served as the main top-down component, whereas causal influences from the hippocampus to the left DLPFC served as the main bottom-up component of this retrieval network. Our study highlights the contribution of hippocampal-prefrontal circuits to the early development of retrieval fluency in arithmetic problem solving and provides a novel framework for studying dynamic developmental processes that accompany children's development of problem-solving skills.