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Unformatted text preview: one ten” in “twenty,” “twenty” in “thirty,” and so on. All these relation
ships are much too complicated for most first graders to make simultaneously.
“Ones” and “tens” are discussed further in Chapter 5 in connection with
place value. If children cannot think simultaneously about tens and ones, they
cannot possibly represent these ideas simultaneously with a writing system in
volving place value. Children’s understanding of the “1” in “16” is discussed in
detail in Chapter 5.
In conclusion, base-10 blocks are not “concrete numbers” or an “embodi
ment” or a “representation” of the base-10 system. Children cannot construct
the system of ones by empirical abstraction from objects, and they cannot con
struct the system of tens by empirical abstraction from objects either. When they
see a long block, children who can make higher-level relationships (through
constructive abstraction) can represent higher-level meanings to themselves and
think “one ten” and “ten ones...
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This document was uploaded on 03/13/2014.
- Spring '14