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 base10 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) Thirtyfour ones (b) Partitioning thirtyf...
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 Spring '14
 Writing, Numeral system, Table of mathematical symbols, theoretical foundation

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