\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014c.00591}
\itemau{Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.}
\itemti{Using order to reason about negative numbers: the case of Violet.}
\itemso{Educ. Stud. Math. 86, No. 1, 39-59 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{F42 F22 C22}
\itemut{integers; children's thinking; negative numbers; case study; developmental milestones; ordinal numbers}
\itemli{doi:10.1007/s10649-013-9519-x}
\end