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Unformatted text preview: iagetian
sense). Some children invented symbols to represent the correct num
ber, and others used 3 conventional letters as symbols to represent Representation 23 3 balls (such as “TIL” and “AE1,” which are not words). This is the first
type in which precise numerical ideas made an appearance.
4. Onetoone correspondence with numerals. One of the examples for
3 balls is “123,” and another example is “333.” It can be said that the
children who wrote these numerals felt the need to represent each ob
ject or their action of counting.
5. Cardinal value alone. We finally see “3” for 3 balls and “5” for 5 houses
(along with “invented” spelling in French for the spoken numerals trois,
deux, and cinq).
6. Cardinal value and objectkind. Examples of this type are “4 pencils”
and “5 houses.” (“Crèion” and “mèzone" are invented spellings for cray
ons and maisons.) These representations show a simultaneous focus on
the quantitative and qualitative aspects of...
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 Spring '14

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