In a study involving 44 young adults given a rigorous memorizing task at noon and another such task at 6pm, those who took a 90-minute nap during the interval improved their ability to learn on the later task, while those who stayed awake found it harder to learn.
The degree to which the nappers were refreshed correlated with the amount of stage 2 non-REM sleep they experienced. This sleep phase is characterized by sleep spindles, which are associated with brain activity between the hippocampus and prefrontal cortex. Spindle-rich sleep occurs mostly in the second half of the night, so those who don’t get their quota of sleep are probably getting less.
The finding confirms the idea that learning ability decreases the more time you spend awake.
 . Wake deterioration and sleep restoration of human learning. Current Biology [Internet]. 2011 ;21(5):R183-R184 - R183-R184. Available from: http://www.cell.com/current-biology/abstract/S0960-9822%2811%2900042-X