Transfer of Mathematical Knowledge: The Portability of Generic Instantiations

Mathematical concepts are often difficult to acquire. This difficulty is evidenced by failure of knowledge to transfer to novel analogous situations. One approach to this challenge is to present the learner with a concrete instantiation of the to-be-learned concept. Concrete instantiations communicate more information than their abstract, generic counterparts and, in doing so, they may facilitate initial learning. However, this article argues that extraneous information in concrete instantiations may distract the learner from the relevant mathematical structure and, as a result, hinder transfer. At the same time, generic instantiations, such as traditional mathematical notation, can be learned by both children and adults and can, in turn, allow for transfer, suggesting that generic instantiations result in a portable knowledge representation.