Tasks to Support Preservice Teachers' Understanding of Decimal Quantities

In this article, we present some mathematical tasks designed to support pre-service teachers (PSTs) in obtaining a broader, more connected understanding of decimal numbers and quantities. We describe classroom scenarios from a content course in which PSTs experienced these cognitively demanding decimal tasks, enacted in ways that maintain high demand. We present evidence of shifts in quality of representations and explanations from pre- and post-test responses of PSTs to unique decimal comparison tasks. Prior to a unit on decimal fractions, several PSTs utilized incorrect decimal notation for amounts such as "0.16" for "16-tenths," relying on symbolic representations they may not fully understand. Written explanations of decimal comparisons commonly referred to procedural rules. After the decimals unit, responses to comparison tasks showed an increase in use of meaningful, connected representations and richer, more robust justifications. [For the complete proceedings, see ED584443.]