Alison Gopnik explains that your baby is smarter than you think:
Three recent experiments show that even the youngest children have sophisticated and powerful learning abilities. Last year, Fei Xu and Vashti Garcia at the University of British Columbia proved that babies could understand probabilities. Eight-month-old babies were shown a box full of mixed-up Ping-Pong balls: mostly white but with some red ones mixed in. The babies were more surprised, and looked longer and more intently at the experimenter when four red balls and one white ball out of the box — a possible, yet improbable outcome — than when four white balls and a red one were produced.In 2007, Laura Schulz and Elizabeth Baraff Bonawitz at M.I.T. demonstrated that when young children play, they are also exploring cause and effect. Preschoolers were introduced to a toy that had two levers and a duck and a puppet that popped up. One group was shown that when you pressed one lever, the duck appeared and when you pressed the other, the puppet popped up. The second group observed that when you pressed both levers at once, both objects popped up, but they never got a chance to see what the levers did separately, which left mysterious the causal relation between the levers and the pop-up objects. Then the experimenter gave the children the toys to play with. The children in the first group played with the toy much less than the children in the second group did. When the children already knew how the toy worked, they were less interested in exploring it. But the children in the second group spontaneously played with the toy, and just by playing around, they figured out how it worked.
In 2007 in my lab at Berkeley, Tamar Kushnir and I discovered that preschoolers can use probabilities to learn how things work and that this lets them imagine new possibilities. We put a yellow block and a blue block on a machine repeatedly. The blocks were likely but not certain to make the machine light up. The yellow block made the machine light up two out of three times; the blue block made it light up only two out of six times.
Then we gave the children the blocks and asked them to light up the machine. These children, who couldn’t yet add or subtract, were more likely to put the high-probability yellow block, rather than the blue one, on the machine.
We also did the same experiment, but instead of putting the high-probability block on the machine, we held it up over the machine and the machine lit up. Children had never seen a block act this way, and at the start of the experiment, they didn’t think it could. But after seeing good evidence, they were able to imagine the peculiar possibility that blocks have remote powers. These astonishing capacities for statistical reasoning, experimental discovery and probabilistic logic allow babies to rapidly learn all about the particular objects and people surrounding them.