Warning: I'm about to question one of developmental psychology's sacred cows.
It amazes me sometimes how influential Piaget still is, and how much he is still believed. He's still taught in my psychology classes, with caveats such as "we now know that children don't reach the same level at all different sorts of tasks at the same time," and "children move up to the next level on any task more gradually than Piaget thinks," and "children can reach xyz level a few years earlier than Piaget thought." Sometimes it seems like developmental psychology is just tweaked Piaget (even though I know that's a gross exaggeration)*. But has anyone actually looked at his famous tasks and asked whether they actually measure what everyone thinks they do?
For instance, a task of water level is often used to assess children's understanding of conservation of matter at different ages. In this task, two identical beakers are filled with the same amount of liquid. Children are asked which has more water, and respond correctly that they contain the same amount of water. When one of the beakers is emptied into a taller and thinner container, the water level appears higher. Children are again asked which has more. Before a certain age, children respond that the taller, thinner vessel has more liquid, while older children say that the amount of water remains the same. Researchers conclude that the younger children do not understand the concept of conservation of matter.
There's another possibility that seems fairly obvious, though I've never heard it mentioned. Like other everyday words, "more" has ambiguous meanings. "More" is used to describe both things that take up a larger perceptual space--like water in a tall, thin beaker, or a widely spread display of objects--and larger absolute quantities, regardless of the space they take up. The difficulty is that in most cases, larger absolute quantities take up a larger perceptual space, so it may be hard for children to know which concept the word actually means, and they may erroneously choose the larger perceptual-space meaning because it generally applies. They don't yet have enough life experience to see a lot of examples of large quantities of objects that take up a smaller perceptual space referred to as "more," so they don't realize that the experimenter really means a larger quantity. With more conversational experience, they sort out this ambiguity of usage and learn that the "real" meaning of "more" is a larger absolute quantity.
(Furthermore, I would point out that researchers might artificially bias children to give the wrong answer by first showing the identical beakers with the same water height and asking which has more. This might prime children to pay attention to the height of the water (after all, it's hard to pour evenly, so a child might rarely see two containers with exactly the same water level). Thus, they're more likely to think that the experimenter wants them to talk about the height of the water, and answer accordingly. As they get older and their executive functioning develops, they may be better able to avoid this trap and inhibit this priming).
In other words, I submit that the Piaget task, with its ambiguous wording, could as easily test a child's pragmatic language/interpretation skills as his or her concept of conservation of matter, and we need some way of separating these two variables.
Piaget's methodology involved asking children questions and recording their answers. While this method can be very powerful for eliciting children's thoughts, it can also bias them. As both common sense and experimental evidence indicate, children often want to please the experimenter and do what he or she expects of them. So it's important to pay as close attention to the questions as to the answers. It'd be interesting to know how many of Piaget's other experiments, in his own time and today, fall prey to the same basic problem as the water-level-conservation task.
*Please let me know if I have somehow misrepresented Piaget's research (or his influence today). I haven't read a lot of the neoPiagetian stuff, so it's quite possible I've missed something, or my complaints have been addressed somewhere.