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Representation Reading ECI 314 Early Childhoodhood Mathematics

Many say ten twenty thirty as they count the groups

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Unformatted text preview: out “one ten” and “ten ones” and being able to think about both simultaneously. Figure 2.8a shows that when kindergartners and most first graders count 34 toothpicks, they think about 34 ones. They constructed these ones through con­ structive abstraction. Figure 2.8b shows the mental partitioning of these ones into segments of 10. This is the structure of base-10 blocks, as well as of Unifix cubes and toothpicks bundled together in groups of 10. The difference between being able to think simultaneously and only suc­ cessively about “tens” and “ones” can be seen when we give 34 toothpicks grouped into three groups of 10 and 4 loose ones to first graders and ask them to count them by tens. Many say “Ten, twenty, thirty” as they count the groups of 10, and “forty, fifty, sixty, seventy” as they count the ungrouped toothpicks. 32 Theoretical Foundation Figure 2.8. The difference between (a) counting by ones, (b) the parti­ tioning of ones into segments of 10 and, (c) the construction of tens out of the ones. (a) Thirty-four ones (b) Partitioning thirty-f...
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