Title: The effects of a grouping by tens manipulative on children's strategy use, base ten understanding and mathematical knowledge
Description: Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do not encourage children to perceive higher-order units in multi-digit numbers. The aim of this study was to closely examine the affordances of a novel grouping by tens virtual manipulative. Seventy-nine first grade students were randomly assigned to one of two math software comparison groups or a reading software control group. In the math comparison groups, children received scaffolding and feedback while playing a computerized enumeration game that required them to use the novel grouping by tens manipulative. Children in the Transformation group used a manipulative that transformed from a unitized to a continuous model, while children in the Unitized group used a manipulative that remained discrete.

Researchers recorded children's strategy use and accuracy when determining how many objects appeared on the screen, and the data were examined microgenetically. Children's counting on abilities, base ten understanding, and number sense were tested at posttest to examine group differences. The results showed that using the transforming manipulative significantly improved children's ability to count on at posttest. The math software also improved girls' base ten understanding at posttest. Children who used the math software in both conditions improved in their advanced strategy use and accuracy over time. These findings suggest that virtual manipulatives have the potential to improve children's strategy use and base ten understanding in ways that physical manipulatives may not. Suggestions for future research are discussed.