id: 05878666
dt: j
an: 2011c.00445
au: Bishop, Jessica Pierson; Lamb, Lisa L.C.; Philipp, Randolph A.; Schappelle,
Bonnie P.; Whitacre, Ian
ti: First graders outwit a famous mathematician.
so: Teach. Child. Math. 17, No. 6, 350-358 (2011).
py: 2011
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F42
ut: negative numbers; grade 1; equations; number concepts; mathematical logic;
elementary school mathematics
ci:
li: http://www.nctm.org/eresources/article_summary.asp?URI=TCM2011-02-350a&from=B
ab: Summary: In the third century, Diophantus, the "Father of Algebra" no less,
described equations of the form x + 20 = 4 as "absurd." The absurdity
stemmed from the fact that the result of four is obviously less than
the addend of twenty. And more than 1300 years later, Pascal argued
that subtracting four from zero leaves zero because of the
impossibility of taking something from nothing. Surely, then, ideas
this challenging are too complex for first graders‒or are they?
Recent research shows that children as young as six years of age can,
in fact, reason about negative numbers and even perform basic
calculations using them (Behrend and Mohs 2006; Wilcox 2008). The
authors’ goal was to build on this research to further explore young
children’s ideas about negative numbers. This article describes the
background of their study, provides an overview of the tasks they used,
discusses children’s responses to these tasks, and identifies two
ways that students in their study reasoned about and approached
problems involving negative numbers. (Contains 1 table and 2 figures.)
(ERIC)
rv: