id: 06295232
dt: j
an: 2014c.00591
au: Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre,
Ian; Schappelle, Bonnie P.
ti: Using order to reason about negative numbers: the case of Violet.
so: Educ. Stud. Math. 86, No. 1, 39-59 (2014).
py: 2014
pu: Springer Netherlands, Dordrecht
la: EN
cc: F42 F22 C22
ut: integers; children’s thinking; negative numbers; case study;
developmental milestones; ordinal numbers
ci:
li: doi:10.1007/s10649-013-9519-x
ab: Summary: This case study illustrates how a 2nd-grade child, Violet, used an
ordinal view of number to reason about positive and negative integers
and arithmetic involving integers. Violet’s ordinal view of number
facilitated her ability to reason about and correctly solve some
integer-related problems and constrained her solutions to others. We
demonstrate how Violet’s thinking evolved over time while she
extended the properties of whole numbers and addition and subtraction
to the integers. Using this case study as a basis, we propose a series
of developmental milestones that build toward one’s understanding of
integers and integer arithmetic in an order-based way. We believe that
understanding Violet’s order-based reasoning can help us listen to
other children.
rv: