Children’s Mappings of Part-Whole Construct of Fractions

The representation of part-whole relations that are embodied in fractional numbers continues to be a problematic area of learning for many children. In this study I examine this problem with a ten-year old child by analyzing his mappings between the language of fractions, area models and symbols. The visual models in this study were built and modified with computer manipulatives called Javabars. Results of analysis showed that the participant experienced difficulty in mapping symbolic representation of selected fractions to the area analogs. Fractions provide teachers with insight into developments in children's understanding of numbers and relations among numbers. These understandings are built on both children's personal experiences, intuitions and formal knowledge taught in the classroom. Fractional numbers provide important prerequisite conceptual foundations for the growth and understanding of other number types and algebraic thinking in later years of their school and adult life. The complex nature of fractions continues to present difficulties fo