6: Lumping

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Page ID: 24120

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In 1982, thousands of students in the United States had to estimate 3.04×5.3, choosing 1.6, 16, 160, 1600, or “I don’t know.” Only 21 percent of 13-year-olds and 37 percent of 17-year-olds chose 16. As Carpenter and colleagues describe [7], the problem is not a lack of calculation skill. On questions testing exact multiplication (“multiply 2.07 by 9.3”), the 13-year-olds scored 57 percent, and the 17-year-olds scored 72 percent correct. The problem is a lack of understanding; if you earn roughly $5 per hour for roughly 3 hours, your net worth cannot grow by $1600. The students needed our next tool: rounding or, more generally, lumping.

choice	age 13	age 17
1.6	28%	21%
16	21	37
160	18	17
1600	23	11
don't know	9	12