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Children are born with an incredible capacity to learn about mathematics and numbers, and their play can be naturally mathematical (counting, sorting, building, comparing, measuring, etc.). Most children come to preschool with some counting ability. Adults may believe that a young child understands numbers when they hear the child counting. However, the child may only be engaging in rote counting-that is, reciting numbers without any real understanding of the underlying quantity, similar to reciting a poem, a rhyme, or the alphabet.
Counting is more than just reciting numbers-it is a very important foundation for mathematical learning and future success in mathematics! There are five aspects to counting (Gelman & Gallistel 1978):
1 Objects should be counted only once. Counting objects twice means that children do not have an understanding of the one-to-one correspondence between an object and the number.
2 Numbers have a stable order. When children count, the string of number words has a stable order (e.g., one, two, three, four, five).
3 Any set of objects can be counted. Adults do a very good job of counting different objects with young children. However, some children may not fully understand that everything in their environment can be counted.
4 The last number counted represents the total of the set. The cardinality, or total, of the set is a tricky concept for young children. A child may accurately count a set of objects without repeat counting. She may recite the counting words in the right order. However, when you ask the child "How many?," she may not understand that the last number word she said was the total of the set. Instead, the child may give you the next counting number, her age, or any other number!
5 You can start counting the objects in a set at...