Representations are used throughout the study of mathematics to organize, record, and communicate ideas. They can be a way to access abstract ideas through familiar models or metaphors and to explain or justify one’s mathematical thinking by referring to common processes, materials, or symbols in everyday life. Children’s fragile understanding of decimal numbers and their representations have been well-documented in the literature . Many pre-service elementary teachers also lack the thorough, in-depth understanding of decimals needed to teach the subject and related ideas of whole number place value.
This poster presentation will investigate some of the representations that pre-service teachers utilize in their attempts to make sense (both for themselves and for their future students) of the values of decimal numbers. We will look at connections future teachers make between decimal numbers and common fraction meanings, whole number place value concepts, and decimal names. We will also explore how pre-service teachers construct and utilize models to support their learning of decimal fractions. A comparison of the merits and drawbacks of several pictorial and manipulative models will be made. Ultimately, we are interested in determining which physical or mental representations that pre-service teachers find to be robust and helpful in creating understanding of decimal notation and quantities.

Owens, D. T. and Super, D. B. (1993). Teaching and learning decimal fractions. In D.Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp.137-158). NewYork: Macmillan.