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 BOX 5-4 Using Fingers to Count: Cultural Differences Around the world, most children learn from their family one of the three major ways of raising (or in some cultures, lowering) fingers to show numbers. All of these methods can be seen in centers or schools with children coming from different parts of the world, as well as some less frequent methods (the Indian counting on cracks of fingers with the thumb, Japanese lowering and raising fingers). The most common way is to raise the thumb first and then the fingers in order across to the small finger. Another way is to raise the index finger, then the next fingers in order to the smallest finger, and then the thumb. The third way is to begin with the little finger and move across in order to the thumb. The first way is very frequent throughout Latin America, and the third way also is used by some children coming from Latin America. The second way is the most usual in the United States. It is the common way to show ages (for example, I am two years old by holding up the index and largest finger). This method allows children to hold down unused fingers with their thumb. But the other two methods show numbers in a regular pattern going across the fingers. Children in a center or school where children show numbers on fingers in different ways may come to use multiple methods. Because fingers are such an important tool for numerical problem solving, it is probably best not to force a child to change his or her method of showing numbers on fingers if it is well established. It is important for teachers to be aware and accepting of these differences.

kinds of patterns can also be considered in terms of addends that compose them, they are included in conceptual subitizing. Such patterns can help older children learn mathematically important groups, such as five and ten; these are discussed in the later levels and in the relations and operation core discussion of addition and subtraction composing/decomposing.

Children also learn to assign a number to sets of entities they hear but do not see, such as drum beats or ringing bells. There is relatively little research on auditory quantities, and they play a much smaller role in everyday life or in mathematics than do visual quantities. For these reasons, and because auditory quantities relate to music and rhythm and body movements, it seems sensible to have some activities in the classroom in which children repeat simple or complex sets they hear (clap clap or, later, clap clap clap pause clap clap), tell the number they hear (of bells, drumbeats, feet stamping, etc.), and produce sounds with body movements for particular quantities (Let me hear three claps).

In home and care/educational settings, it is important that early experiences with subitizing be provided with simple objects or pictures. Textbooks or worksheets often present sets that discourage subitizing and depict collections of objects that are difficult to count. Such complicating factors include embedded or overlapping pictures, complex noncompact things

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