Humans of all ages find it fascinating to see objects that are in the wrong scale-- much bigger or smaller than the real thing usually is. We're intrigued by those puzzles that show pictures of ordinary objects magnified. Our love for miniatures is shown in dollhouses (adults like them too!), model boats and planes, and above all, model railroad displays, complete with tiny trees, people, cows, and stop signs.
Although adults may be much taken with miniature replicas of ordinary objects, they don't confuse the two with each other. Curiously, though, toddlers do sometimes make the mistake of acting as if a miniature object is the same as its full-size counterpart. These mistakes are called "scale errors". Of course the actions we call "scale errors" don't work; for instance, a toddler might try to sit down on a doll chair, or put a foot into the open door of a toy car as if trying to get in. Scale errors have been demonstrated in laboratory studies of young children (for example, De Loache et al., Science, 2004, Vol. 304, pp. 1027-1029), when children were allowed to play with full-size objects and then had the objects replaced with miniatures. A recent study (Rosengren et al., Child Development, 2010, Vol. 80, pp.1586-1591) interviewed parents about scale errors at home and found that almost all of thirty parents of young children reported that their child had shown this kind of behavior. The greatest number of the errors reported had to do with trying to fit the child's body into or onto a miniature object like a chair, but it may be simply that those errors were more likely to be noticed by an adult than other errors where the child tried to fit another object into a miniature object. Also, it appears that the children were very persistent in some of the body errors, and in some cases became annoyed or frustrated at their failure to achieve the impossible.
It can be quite difficult to observe some scale errors, especially if the child gives up the effort quickly, or if it is hard to tell the difference between the scale error and pretend play. One of my children, as a toddler, got hold of the T-shaped end of a plastic hang-tag holder. He grasped it by the long leg and struck it against other objects, saying "ham[mer]". Was this an actual scale error or pretend? It's hard to say, because at this age he was not able to use a hammer properly and would have played with an actual hammer in the same way.
Are scale errors associated with other kinds of mistakes young children make? The developmentalist Jean Piaget described children's lack of the ability to understand that objects contain the same amount of material no matter what we do to their shape. This ability, called "conservation", allows older children and adults to know that a piece of Play-doh rolled out flat is the same amount of Play-doh as it is when squeezed into a ball, and that when a tall thin glass of water is poured into a short fat glass, the amount of water remains the same. Young children who have not achieved conservation complain loudly when they think a piece of birthday cake standing on end is different from an identical piece lying flat on the plate. Occasionally older children too will show a problem with conservation, as in the case of the 8-year-old who told his mother that if she couldn't fit a container of yoghurt into his lunchbox, she should put it in a plastic bag like the sandwich-- "then it will fit!".
Young children have trouble figuring out how to put two objects together even when the objects are of normal size. Their strategy seems to be to try first to bring into contact the two parts of the object which eventually will go together. This is why T-shirts go on backward (it seems) more than 50% of the time, as the child arranges the shirt so that the front is nearest to the front of the body before putting it on--- but of course this orientation puts the front of the shirt at the back of the body later. Similarly, watch a toddler trying to put an adult's shoe on the adult's foot. The child puts the toe of the shoe against the toe end of the foot instead of slipping the heel of the shoe past the toes until the foot is inside the shoe.
Piaget described young children as "cognitive aliens", meaning that much of their thinking is so different from ours that they might as well come from another planet. Scale errors and backward T-shirts are some indications of these differences. These things are part of the reason that young children need to learn by playing instead of by instruction. We can't think the way they do well enough to design lessons for them.