Representation Reading ECI 314 Early Childhoodhood Mathematics

Let us return to the conservation of number task

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Unformatted text preview: as a “concrete number.” The distinction Piaget made between abstraction and representation clarifies this point. Let us return to the conservation-of-number 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 (logico-mathematical 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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