Strategy Generalization: The Advantage of Using More Than One Type of Manipulative in Instruction

• In Event: The Role of Hands-On Materials in Mathematics Education

Abstract

The present study examined whether number of manipulatives used in arithmetic strategy instruction influences learning. First graders were randomly assigned to a condition for learning a decomposition strategy: single manipulative, multiple manipulatives, or control condition. Both intervention conditions produced a greater increase in mental use of decomposition than the control. There was no difference between the single- and multiple-manipulatives conditions in children’s mastery of strategy execution with manipulatives present. In contrast, the multiple-manipulatives condition led to greater generalization to mental calculation than the single-manipulative condition. Further, the findings indicated path-dependent transfer: children who mastered decomposition with multiple manipulatives were more likely to generalize this knowledge to mental calculation than those who achieved mastery via practice with a single manipulative.

Authors

• Elida Velez Laski, Boston College

• Marina Vasilyeva, Boston College

• Anna Ermakova, Boston College

• Karina Halloran