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Winners, More or Less

AGE RANGE: 2 to 3 years

RESEARCH AREA: Cognitive development

THE EXPERIMENT

First, gather your materials. You’ll need six Dixie cups (or other small containers), two trays or plates that can each hold five of the cups, and a few sheets of stickers to use as prizes.

Begin by placing one of the cups upside down on one tray. On the other tray, place two of the cups upside down and hide a sticker under each of them.

Show each tray to your child, side by side. Then pick up the single cup on the first tray and reveal that there is nothing under it. Say, “Look, this is the loser. There’s nothing inside.” Next, pick up both cups on the second tray and reveal the stickers. Say, “Look, this is the winner, and the stickers are for you.” Now switch the position of the trays and point out that even though the trays are in different positions, the tray with two cups remains the winner and the tray with one cup remains the loser.

Now restock the stickers on the tray with two cups and ask your child to point to the winner. If she chooses correctly, allow her to retrieve the stickers from under the cups. If she chooses incorrectly, prompt her to choose again, and then let her retrieve the stickers from under the cups.

After a few rounds of this, it’s time to vary the number of cups on each tray. You might, for instance, try one cup on one tray and three cups on the other; two cups on one tray and four cups on the other; or one cup on one tray and five cups on the other. In each case, the tray with the greater number of cups on it should have stickers under each cup and should be treated as the winner. Continue to prompt your child to choose the winner.

THE HYPOTHESIS

Your child will quickly catch on that the winner is the tray with more cups on it, even if you never use the words greater, more, fewer, or less. She will probably do best when the comparison is between one and two cups, but she may also do well when you vary the number of cups.

THE RESEARCH

Researchers in a 2001 study conducted a series of experiments involving two- and three-year-olds to determine their number competence, and specifically to determine if they could infer, without being explicitly told, the rule that determined which tray was the winner, and then generalize that rule.

In one of the experiments, which involved only two-year-olds, the participants went through a series of tasks like those described here, only instead of Dixie cups the researchers used small red boxes. In the one-box versus two-box condition, children correctly chose the winner about 75 percent of the time. That’s a lot more than one would expect if they were just choosing at random, so it certainly seems as if they inferred some sort of rule.

But what rule? It couldn’t have been a position-based rule, because sometimes the winner was the tray on the left and sometimes it was the tray on the right. Maybe, though, the rule they learned was “The winner is whichever tray has exactly two boxes on it.” To rule that out, they looked at how the children performed when the number of boxes was changed. It turns out that they still performed better than chance, even in a condition involving nine boxes total (four versus five boxes), although never quite as well as with the one-box versus two-box condition.

It appears, based on these results, that the children were able to infer the “greater than” versus “less than” rule and apply it to groupings beyond what had been demonstrated.

But how did they figure out which tray had the greater number of containers?

You might think they counted them, but although two-year-olds often can recite a short counting sequence, they tend not to be able to understand how the sequence actually relates to numerosity. In other words, even if they are able to count to five, and even if they are able to point to objects as they recite the sequence, there’s still a further mental leap required to arrive at “I’ve counted to five, and that means there are five objects here.” Consistent with this, none of the two-year-olds in the study used number words or were observed counting the containers one by one.

So, if counting doesn’t explain it, what does?

One possibility is that they simply observed which tray had more of its surface area covered in containers. The researchers ran a subsequent experiment in which the size of the containers varied, but two large containers still lost out against three small containers. The children still inferred the greater-than/less-than rule, which supports the idea that they weren’t simply using surface area to make their comparison.

The researchers concluded that children as young as two years old are able to make ordinal comparisons without explicitly counting because they are able to mentally grasp the concept of numerosity, even if they haven’t yet tied that concept to counting or number words.

THE TAKEAWAY

In the field of machine learning, which is enjoying its heyday after a long period of relatively modest advances, teaching a computer to make even simple inferences about unstated game rules can be challenging. Fortunately, your toddler’s brain is able to pick up on these rules with no programming involved! (Don’t be discouraged, however, if she didn’t get all the trials right. Children in the original study picked the winner only 60 percent of the time when presented with novel number pairings.)

There are at least two practical lessons to glean from this research. The first is that at two years old, your child is already picking up on rules, even those that aren’t clearly spelled out, so now’s a great time to introduce her to simple games and puzzles. The second lesson is that if you want to motivate a two-year-old to be your science project, stickers are a terrific incentive!

Preschool Pain Scales

Can preschoolers’ numerical literacy predict how accurately they are able to self-report pain? It’s a question pain researchers would like to answer, because knowing whether a child’s self-reports are accurate can help doctors and other health care workers better address and manage that pain.

A 2011 study gave several screening tasks to preschoolers who were about to have outpatient surgery, including tasks related to numerical literacy. Although several of the screening tasks did help predict self-reported pain accuracy, none was any better as a screening tool than chronological age.

However, that doesn’t mean there are no opportunities to improve the way children are asked to rate their pain. One standard pain scale used with preschool-aged children shows six illustrations of faces whose expressions correspond to a pain scale of 0 to 10. But a 2013 study found improved results among preschoolers with a two-step simplified pain assessment. First, the child is asked, “Does it hurt?” And if she responds yes, she’s shown just three faces, representing no pain, moderate pain, and severe pain. Five-year-old children who viewed picture stories depicting painful events were able to give pain ratings with roughly the same accuracy regardless of whether they used the standard or the simplified rating system. But among three- and four-year-old participants, accuracy was higher when using the simplified rating system. If you’d like to try this with your own child, use the three-face test shown here the next time she takes a spill.