
06295232
j
2014c.00591
Pierson Bishop, Jessica
Lamb, Lisa L.
Philipp, Randolph A.
Whitacre, Ian
Schappelle, Bonnie P.
Using order to reason about negative numbers: the case of Violet.
Educ. Stud. Math. 86, No. 1, 3959 (2014).
2014
Springer Netherlands, Dordrecht
EN
F42
F22
C22
integers
children's thinking
negative numbers
case study
developmental milestones
ordinal numbers
doi:10.1007/s106490139519x
Summary: This case study illustrates how a 2ndgrade 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 integerrelated 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 orderbased way. We believe that understanding Violet's orderbased reasoning can help us listen to other children.