NEW YORK — Any parent knows that a daytime nap can help keep preschoolers from getting cranky. Now a small study suggests that it helps them learn, too.

The lesson for grown-ups: Don’t cut out the naps if you try to cram more learning activities into a preschooler’s day, say researchers from the University of Massachusetts Amherst.

They studied 40 children, ages 3 to 5. In the mornings of test days, the children were shown a grid with pictures of nine or 12 items like a cat or an umbrella. That afternoon and the next morning, the children were tested on how well they remembered the location of each image.

All the children were tested under two conditions, one in which they were encouraged to nap before the afternoon test, and another in which they were kept awake. Without a nap, they were about 65 percent accurate. With a nap, their accuracy reached about 75 percent.

The research shows that “naps are important for preschool children,” Rebecca Spencer, senior author of the study, said in a statement.

The study was published Monday by the Proceedings of the National Academy of Sciences.