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• #### Index 371-386

###### Counting Correspondences

At this step, children extend considerably the set size they are able to count accurately. They move from considerable inaccuracy with counting larger sets to only occasional errors, even with large sets of 15 and above, unless the sets are arranged in a disorganized way and children are not able to move objects to keep track of which have been counted (i.e., make a counted and an uncounted pile) (Fuson, 1988). As before, effort continues to be important. Children who are tired or discouraged may make many more errors than they make after a simple prompt to try hard or count slowly. Children at this step also continue to generalize what they can count.

Children at this step are working on counting linear arrangements correctly in the teens or above, and many make few errors, showing considerably more accuracy than children a year younger (Clements and Sarama, 2007; Fuson, 1988). Of course, accurate counting also depends on knowing an accurate number word list, so accuracy with these larger sets depends on three things:

1. Knowing the patterns discussed above in the number word list so that a correct number word list can be said.

2. Correctly assigning one number word to one object (1-to-1 correspondence).

3. Keeping track of which objects have already been counted so that they are not counted more than once.

Differentiating counted from uncounted entities is most easily done by moving objects into a counted set, but this is not possible with things that cannot be moved, such as pictures in a book. For pictures or objects that cannot be moved, counting objects arranged in a row is easiest because one can start at the end of a row and continue to the other end. However, if objects are arranged in a circle, children may initially count on and on around the circle. Strategies for keeping track of messy, large sets continue to develop for many years (Fuson, 1988), with even adults not being entirely accurate.

Children in kindergarten who have had adequate counting experiences earlier continue to extend their counting of objects as high as 100, often with correct correspondences (and perhaps occasional errors). There may or may not still be errors in the number word list.

###### Written Number Symbols

Children at this step continue to extend the number of written number symbols they can read, now often reading many of the numerals 1, 2, 3,

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