It Works Both Ways: Transfer Difficulties between Manipulatives and Written Subtraction Solutions

Abstract

Three experiments compared performance and transfer among children aged 83-94 months after written or manipulatives instruction on two-digit subtraction. In Experiment 1, all children completed the posttest in a written format, while in Experiment 2, all children took a posttest using manipulatives. Experiment 3 investigated how altered surface features of the blocks affected posttest performance, subtraction strategies and mathematical behaviors. In the first two experiments, children demonstrated performance gains when the posttest format was identical to the instructed format, but failed to demonstrate transfer from the instructed format to an incongruent posttest. Posttest performance in these two experiments provides evidence for bidirectional challenges in transfer between manipulatives and written instruction. In the third experiment, children who learned with standard, unaltered blocks more often used productive problem-solving strategies and engaged in mathematical behaviors significantly more often than children who used blocks with altered surface features. Flexibility and the need to provide explicit links between written and manipulatives instruction are discussed.