Virtual Manipulative Materials in Secondary Mathematics: A Theoretical Discussion

With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This article reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials must be broadened to include new forms of materials such as virtual manipulatives which are also useful tools in a larger collection of learning tools. applying a theoretical lens to a specific material—polynomial tiles—this article demonstrates the following: (a) a complementary relationships between virtual and concrete manipulatives, (b) two or more theories can appropriately justify the same material, and (c) exploration of a specific manipulative may generate novel theoretical rationales. This exploration has proven to be helpful in the process of designing, selecting, categorizing and evaluating learning tool