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3♦ □« 6 1♦ □ • 5 □
□ + 1=8
♦3
=5 □ + 2 =4 36 Theoretical Foundation 40 chips. “Could you give to the doll what’s written here?” I said, running a fin
ger over the entire equation, 4 + 2 = 6. If necessary, I elaborated by saying, "The
doll is reading this [indicating the equation], and he wants this many counters
[again indicating the equation].”
About twothirds of the first graders gave 6 counters to the doll, but ap
proximately onethird gave 12. This happened because a third of the first grad
ers read the equation as “4 2 6” or “4 + 2 6.” The study was conducted in six
rather different schools in the United States and Japan, but the percentages were
surprisingly similar in all locations. Two schools were in an affluent suburb of
Birmingham, Alabama. One was in a small town in Alabama, and one was on
the south side of Chicago. The Japanese sample was interviewed in two schools
in Sapporo, the largest city in Hokkaido.
These first graders could read and define each of the signs in the equation.
They could also write the correc...
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 Spring '14

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