Lisa B. Warner , Roberta Y. Schorr and Gary E. Davis have written an article called Flexible use of symbolic tools for problem solving, generalization, and explanation. The article was published online in ZDM last week. Here is the abstract of their article:
We provide evidence that student representations can serve different purposes in the context of classroom problem solving. A strategy used expressly to solve a problem might be represented in one way, and in another way when the problem is generalized or extended, and yet in another way when the solution strategy is explained to peers or a teacher. We discuss the apparent long-term memory implications this has regarding the preferences that students have for their original versus later developed representations, and how these preferences relate to the use of representational flexibility in classroom settings.