Building Understanding of Decimal Fractions

Asked to complete a decimal-ordering task, several preservice teachers were unable to arrange the values from smallest to largest. Even more surprising to the authors were the number who could solve this task correctly but could not justify their solution by representing each decimal in an area model using a decimal grid. Their preservice teachers committed all the errors familiar to any educator working with students in the upper elementary or middle school grades. These errors, typical of children, have been well documented in the research literature. In this article, the authors describe the challenges their adult learners faced when they used grids to represent decimals and what they learned about their understanding of decimals from analyzing their work. (Contains 4 figures.)