Unformatted text preview: rs. Fingers are symbols used in the service
of thinking.
Just as children use counters at different levels of abstraction, they use fin
gers at many different levels. The two most obvious levels are those of “countingall” and “countingon.” Countingall refers to children’s doing 4 + 3, for example,
by counting 4 fingers, then 3, and counting all 7 of them all over beginning with
“one.” In countingon, by contrast, children count up from 4 and say “fivesixseven.”
It will be explained further in Chapter 5 why countingon is so difficult for
many kindergartners and some first graders. Essentially, this difficulty stems from
the difficulty of making a partwhole relationship. In adding two numbers, chil Theoretical Foundation 30 Figure 2.7. Signs and symbols used to find out how many animals the
author loved. dren start with two wholes (4 and 3 in this example) and combine them into a
higherorder whole (7) in which the previous wholes become two parts. As ex
plained in Chapter 1, children make part...
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 Spring '14
 Writing, Numeral system, Table of mathematical symbols, theoretical foundation

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