Unformatted text preview: as a “concrete number.” The distinction Piaget made
between abstraction and representation clarifies this point. Let us return to the
conservationofnumber task, which was discussed in Chapter 1, to show what
Piaget meant by abstraction. Abstraction and Representation
When the conservation question is asked, both conservers and nonconservers have concrete objects in front of them. Conservers conserve because
they are at a higher level of abstraction (constructive abstraction). Those who
do not conserve do not do so because they do not have number concepts in their
heads. Counters are concrete and observable (physical knowledge), but the
number eight (logicomathematical knowledge) is not concrete and not observ
able. Numbers are always abstract because, as explained in Chapter 1, each child
constructs them through constructive abstraction. There is thus no such thing
as a “concrete number,” and if concrete numbers do not exist, “semiconcrete
numbers” do not exist either.
The following study clarifies how young children represent different idea...
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 Spring '14
 Writing, Numeral system, Table of mathematical symbols, theoretical foundation

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