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Representation Reading ECI 314 Early Childhoodhood Mathematics

When they see a long block children who can make

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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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