id: 06079396
dt: j
an: 2012e.00524
au: Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L. C.; Philipp, Randolph
A.; Schappelle, Bonnie P.; Lewis, Melinda L.
ti: Happy and sad thoughts: an exploration of children’s integer reasoning.
so: J. Math. Behav. 31, No. 3, 356-365 (2012).
py: 2012
pu: Elsevier, New York, NY
la: EN
cc: F32 C32
ut: number concepts; primary education; mathematical concepts; concept
formation; thinking skills; educational research
ci:
li: doi:10.1016/j.jmathb.2012.03.001
ab: Summary: The purpose of this study was to investigate elementary
children’s conceptions that might serve as foundations for integer
reasoning. Working from an abstract algebraic perspective and using an
opposite-magnitudes context that is relevant to children, we analyzed
the reasoning of 33 children in grades K-5. We focus our report on
three prominent ways of reasoning. We do this by describing and
analyzing the responses of three particular children (in grades 1, 3,
and 5) who exemplify these ways of reasoning. We view each of the three
ways of reasoning as rich and interesting, and we see relationships of
each to formal integer reasoning. At the same time, we view these ways
of reasoning in terms of increasing levels of sophistication,
potentially belonging to a single learning trajectory. Thus, we see the
roots of more sophisticated integer reasoning in children’s early
intuitions about opposite magnitudes.
rv: