Resnick, L. B., Cauzinille-Marmeche, E., & Mathieu, J. (1987).
Understanding algebra. In J. A. Sloboda & D. Rogers (Eds.),
Cognitive processes in mathematics. Oxford: Oxford University Press.
David Kirshner
Judy Diamondstone <diamonju who-is-at rci.rutgers.edu> on 07/11/99 02:41:07 PM
Please respond to xmca who-is-at weber.ucsd.edu
To: xmca who-is-at weber.ucsd.edu
cc: (bcc: David H Kirshner/dkirsh/LSU)
Subject: arithmetic query
from the chapter:
>Inversion is the arithmetic principle that adding and subtracting the same
number leaves the original quantity unchanged. They presented problems of
the form "a 1 b 2 b" (for example, 10 1 8 2 8) to subjects ranging
>in age from 6 years to adulthood..... SNIP some
>of the children did not seem to grasp inversion. Instead of creating a
shortcut based on the inversion principle, they would dutifully
>add the second number to the first and then subtract the third number from
the sum. The larger the second and third numbers, the
>longer it took them to get an answer (it required more time to figure out
the answer to 4 1 9 2 9, for example, than to solve 4 1 5 2 5).
I am at least as arithmetically proficient as most readers, but I need help
here. Where in any of the series of numbers above is there a sign for
subtraction? Is there a context for this problem that I missed in the
chapter? -- What do unpuzzled readers know that I don't, that helps them
make sense of what the children/adults did/didn't do and the Coles'
explanation of it?
Judith Diamondstone (732) 932-7496 Ext. 352
Graduate School of Education
Rutgers, the State University of New Jersey
10 Seminary Place
New Brunswick, NJ 08901-1183
Eternity is in love with the productions of time - Wm Blake