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Unformatted text preview: our ones into segments of ten (c) Three tens and four ones They count in this way because they cannot yet think simultaneously about tens
and ones as shown in Figure 2.8c.
Figure 2.8c illustrates die system of tens the child has constructed out of
the system of ones, through constructive abstraction. When the child has con
structed the system of tens out of the system of ones, he or she has both systems,
which can function simultaneously. If children can think about the ones at the
same time that they think “ten, twenty, thirty,” they know when they must shift
to counting by ones. If they can think only about the tens while counting by tens,
they cannot shift to the ones because they are not thinking about the ones. Representation 33 Figure 2.8c further illustrates the relationships of order and hierarchical
inclusion that were discussed in Chapter 1. When adults count by tens, they put
both the ones and the tens into relationships of order and hierarchical inclu
sion. Just as they include “one" in “two,” “two” in “three,” and so on, adults can
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- Spring '14