I found this open access article via Dylan William. Sleep is important for learning, this was known already for quite some while. This research shows the importance also for very young children.

The essence: “Lacking scientific understanding of the function of naps in early childhood, policy makers may curtail preschool classroom nap opportunities due to increasing curriculum demands. Here we show evidence that classroom naps support learning in preschool children by enhancing memories acquired earlier in the day as compared with equivalent intervals spent awake.”

Abstract of the research:

Despite the fact that midday naps are characteristic of early childhood, very little is understood about the structure and function of these sleep bouts. Given that sleep benefits memory in young adults, it is possible that naps serve a similar function for young children. However, children transition from biphasic to monophasic sleep patterns in early childhood, eliminating the nap from their daily sleep schedule. As such, naps may contain mostly light sleep stages and serve little function for learning and memory during this transitional age. Lacking scientific understanding of the function of naps in early childhood, policy makers may eliminate preschool classroom nap opportunities due to increasing curriculum demands. Here we show evidence that classroom naps support learning in preschool children by enhancing memories acquired earlier in the day compared with equivalent intervals spent awake. This nap benefit is greatest for children who nap habitually, regardless of age. Performance losses when nap-deprived are not recovered during subsequent overnight sleep. Physiological recordings of naps support a role of sleep spindles in memory performance. These results suggest that distributed sleep is critical in early learning; when short-term memory stores are limited, memory consolidation must take place frequently.