From learning basic numbers to memorizing multiplication tables to solving algebraic equations, children progress through an amazing range of mathematical abilities as they grow. In this section we will explore how mathematical reasoning develops through childhood.
Mathematical Skills in Infancy
Amazing but true: Researchers have found evidence that even newborns have rudimentary mathematical skills. Humans seem to be "born with a fundamental sense of quantity" (Geary, 1994, p. 1). For example, researchers showed newborn infants less than one week old!) a card with two black dots (Antell & Keating, 1983). The newborns looked at the dots for a bit, then started looking away. Looking away signals boredom. When researchers then switched to a card that had three dots, the newborns regained interest in looking at the dots—they dishabituated. Newborns also showed dishabituation when the set size was changed from three dots to two. These patterns of habituation and dishabituation show that newborns can see the difference between two and three dots.
In the first months after birth, infants can already distinguish among small numbers of objects (e.g., among one, two, and three objects), whether the objects are similar or different, moving or still, or presented at the same time or in sequence. They can even match the number of objects they see with the number of sounds they hear. For example, when infants hear a sound track of two drumbeats, they prefer to look at a photo of two household objects rather than a photo of three objects. When they hear three drumbeats, however, their preference switches to the photo of three objects (Starkey, Spelke, & Gelman, 1983,1990). Impressive as these skills are, however, they apply only to very small sets. If researchers increase the number of objects in each set to five or more, then children don't show evidence that they recognize the quantities until they are about 3 or 4 years old (Canfield & Smith, 1996; Simon, Hespos, & Rochat, 1995; Starkey & Cooper, 1980; Strauss & Curtis, 1981; van Loosbroek & Smitsman, 1990; Wynn, 1992, 1995).
How are infants able to show such abilities? They clearly cannot count objects. They have no experience with a number system, and they don't have the language skills they would need to say the words that go with the numbers. Researchers propose that infants enumerate small sets by subitizing, a perceptual process that we all use to quickly and easily determine the basic quantity in a small set of objects. To see how subitizing works, try the following experiment. Have a friend toss three or four pennies onto a table while you have your eyes closed. Now open your eyes and, as quickly as you can, look to see how many pennies there are. Most people can "see" that there are three pennies, or four pennies, without needing to actually count each penny. There is something about the visual arrangement of the pennies that lets you know immediately how many there are. Of course we can't be sure that infants are subitizing object sets exactly the way adults do, but from the experimental evidence it does seem that they use a similar process. Somehow, without actually counting, they can determine that one set of objects has more items than another set, and they can match the number of things they see with the number of sounds they hear. Quite remarkable math skills for such a young age!
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