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Unformatted text preview: cannot, they make two
wholes, namely “four” and “seven,” and answer “Seven” or “Eleven.” Each child
thus uses symbols at his or her level of abstraction.
The following example also illustrates children’s use of counters as sym
bols at various levels of abstraction. The problem was: I got out 4 bowls to serve
soup to 4 people. I want to put 3 crackers in each bowl. How many crackers do
I need? Many first graders align 4 counters to represent 4 bowls (or 4 people).
They then put 3 counters in front of each “bowl.” Many then count all the
counters and give the answer of 16, but others count only those they meant to
stand for crackers and answer “Twelve.” Representation 25 All 16 of the counters look identical and are often arranged in 4 columns,
each of 4. However, when children can make higher-level relationships (through
constructive abstraction), they unmistakably know which ones stand for “bowls”
and which ones were meant to be “crackers.” When they can make only vague
and fleeting relationships, they forget that some counter...
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This document was uploaded on 03/13/2014.
- Spring '14