Crackers and Buttons.

In class, we watched a video of a four- or five-year-old child sitting opposite an experimenter, each with a graham cracker in front of them. The experimenter asks if they have shared the crackers equally, and the child nods. The experimenter then breaks her own cracker in half, and then asks the child again if they have shared the crackers equally. The child shakes her head, because now she perceives the experimenter as having two crackers, and she only having one – thus, the experimenter has “more”.

In our assigned reading about the experiments done by Feigenson, Carey and Hauser (2002), we read that 10- and 12-month-old infants who were given the choice between one large cracker versus two smaller ones (that added up to less than the bigger cracker), they preferred the large cracker. When given the choice between one cracker and two halves of a cracker the same size, they chose at chance. Thus, it appeared that they perceived “more” to be a function of the total surface area of the crackers, and not the number of crackers.

What does this mean? Why do 10- and 12-month-old infants seem to be able to represent the abstract quantity of surface area better than four- and five-year-olds? Would infants then be able to succeed at conservation tasks that much older children consistently fail to do? If so, why and how do they lose this ability?

The findings of Feigenson, Carey and Hauser (2002) suggest that babies can compare object files on the basis of continuous extent. It’s not as if they don’t have the ability to compare object files on the basis of one-to-one correspondence – there have been numerous other experiments that prove they can. Babies simply preferred to use the basis of continuous extent. It is not unconceivable, therefore, that this ability to compare abstract quantities is an innate ability, along with the other counting principles that Gelman and Gellistel (1978) suggested.

In my opinion, one strong possibility for the apparent “loss” of this ability in preoperational children is perceptual narrowing. We have learnt that neuronal connections that aren’t exercised weaken and wither away, resulting in a decrease of perceptual ability. Connections that are used frequently, on the other hand, are strengthened. As children develop their cognitive abilities, one of the first things parents teach their children is how to count. Very rarely do parents put crackers in front of their children and say, “Cracker A is bigger than Cracker B, therefore there is more of Cracker A”, or “I have two crackers and you have one, but the total area of my two crackers is smaller than the area of your cracker, so you have more.” It is much more likely that parents would just go, “I have one cracker, and you have one… We both have a cracker each!”, or “I have one cracker, and you have one… two… TWO crackers!”. Thus, the counting principles are emphasized and exercised, whereas the more abstract quantitative analysis is often ignored when both bases are present.

It is interesting to note, however, that this preference for the continuous extent basis for comparison does not completely disappear for preoperational children. Consider the child in the same video we watched, who was given two rows of five buttons and then asked if one row had more buttons than the other. She counted them both out and confidently announced that they were both the same, because there were five buttons in each. The experimenter then spread the buttons in one row out, so that it appeared longer, and then asked the child if one row had more buttons than the other. The child, who had just counted out the buttons, now said that the longer row had more buttons, thus displaying a preference for the continuous extent basis over the one-to-one correspondence.

Is this phenomenon is another instance of U-shaped development, in which the capabilities of performing a particular task first decrease, and then increase with age? Is this capability for abstract quantitative comparison in infants limited to surface area? We know that preoperational children often fail at conservation tasks, and that the majority of concrete operational children succeed. It would be interesting to design and conduct conservation tasks for sensorimotor infants to see if the hypotheses mentioned above hold any truth.