Effects of Using One or More Manipulatives on Strategy Mastery and Generalization.

The present study examined whether the number of manipulatives used in arithmetic strategy instruction influences learning. First graders were randomly assigned to one of the following conditions for learning a decomposition strategy to solve arithmetic problems: intervention with a single manipulative, intervention with multiple manipulatives, and a business-as-usual control condition. Both intervention conditions produced a greater increase in the use of decomposition for mental calculation than the control condition. The pattern of results across the intervention conditions varied as a function of the outcome examined. In terms of children's mastery of strategy execution with the manipulatives, there was no difference between these conditions. In terms of generalization, children whose instruction involved two complementary manipulatives tended to generalize the base-10 strategy to mental calculation to a greater extent than children whose instruction involved a single manipulative. Most noteworthy was that the findings indicated path-dependent transfer: children who mastered decomposition in the multiple-manipulatives condition were more likely to generalize this knowledge to mental calculation than those who achieved mastery via practice with a single manipulative. The implications of these findings for better understanding the conditions under which manipulatives are likely to affect learning for different outcomes is discussed. [ABSTRACT FROM AUTHOR]