The first step is seeing that two groups identical in shape and arrangement are also the same in number. Thus, if a brown bear and a yellow canary are placed directly below another brown bear and yellow canary, both rows are the same in number (as well as in shape, color, and arrangement).The idea of same number evolves, even without adult assistance, through several stages: Also, the item that was first can become last under a new order.Īgain young children tend to rely too much on appearances to solve the problems.In a group of three objects, the second item is larger than the one preceding it but smaller than the one following it.Judgments of more or less are sufficient for many purposes, but sometimes a comparison between more than two things needs to be made. Thus the idea of order, which includes subtle ideas: "This flock of geese in the sky must be larger because it covers a greater area than does the other flock." This approach is often adequate but can lead to wrong answers and confusion. (Perhaps that’s why number was invented: the shepherd needs to know not only that he has a lot of sheep, but exactly how many.) This is what children know and what they need to learn at roughly ages three, four and five.Ĭhildren need to be able to see that there are more objects here than there. They often solve this problem not by counting but by physical appearance. Children learn most of these things on their own, without much adult help. Children often use these concepts in everyday life, for example, to determine who has more or less ice cream. Children’s concepts and procedures are useful under certain conditions but need to be enriched. Young children, even infants, develop essentially non-verbal basic concepts of quantity: more/less, order, same, and adding/subtracting.
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