The way I worded the question (using 2x2 duplo blocks) was "see, this block covers one square of the paper."
I then laid out four blocks tight together.
"this is one way to arrange them"
move the blocks apart
"this is another way. Which arrangement covers more of the paper?"
Oooh, thanks for the wording! My 7yo does not have conservation of area.
Was this tongue in cheek? I think it should have been :-) You must know the famous experiment that (my interpretation!) demolishes Piaget's ideas about when conservation of number develops by showing that children can answer correctly very much earlier if it's a "naughty teddybear" rather than the experimenter who stretches out one of the lines? IOW, it isn't that young children can't conserve - it's that they haven't learned the phenomenon of adults asking Really Silly Questions. (Well, maybe this is a personal interpretation of the experiment.) Still, I bet it's the same here. "Cover" is ambiguous in English. If a child has been drawing on the wallpaper, we do not say that the same area has been covered if the same amount of crayon has been used - we consider the bounding box of what has been drawn.
I asked my DS7, who enjoys and is used to being asked trick questions and articulating his responses to them. I used exactly the wording given above. He said, up to memory, "Well, it depends what you mean. If you just mean literally how much paper is underneath the blocks, then obviously they cover the same area. If you mean there are invisible lines joining the blocks and you're interested in the area of the invisible polygon, then this way [blocks far apart] covers more."
Here is a page that gives a story about barns build on grassland and how much grass will each of two cows have to eat, depending on whether barns are built in a cluster or scattered around. I'd expect this to be a much better test of what children actually understand about area, because the "grass for the cow to eat" manages to be unambiguous about what area we're talking about. AlexsMom, I'd bet a small amount that your DD will demonstrate fine conservation of area in that context. [The page has some bugs in the names of characters, though, so read it through and sort it out in your head before trying it on a child!]
ETA
Here is a page that summarises Piaget and objections to his work very briefly. Incidentally DS7 has no trouble answering questions about two-headed green parrots, either :-)
