“Concreteness fading” promotes transfer of mathematical knowledge

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are “faded” into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three conditions: generic, in which the concept was instantiated using abstract symbols, concrete in which it was instantiated using meaningful images, or fading, in which itsymbols, concrete in which it was instantiated using meaningful images, or fading, in which it was instantiated using meaningful images that were “faded” into abstract symbols. After learning, undergraduates completed a transfer test immediately, one week later, and three weeks later. Undergraduates in the fading condition exhibited the best transfer performance. Additionally, undergraduates in the generic condition exhibited somewhat better transfer than those in the concrete condition, but this advantage was not robust. Results suggest that concrete instantiations should be included in the