I think the catalog of misunderstandings would go nicely with the questions by Dan Suthers (overview page) that Stian highlighted in a recent blog post, namely:
What activities does a given representational notation suggest or prompt for? Do the actions that can be performed on a shared representation in this notation correspond to the potential ideas that we want learners to negotiate and distinctions we want them to attend to? Do the resulting representations express and make salient the ideas and relationships that learners should revisit and relate to new information? Are the needs that should be addressed by subsequent activity, such the lack of information, made obvious? Do the representations capture important aspects of learners’ thinking and expose conflicts between alternative solutions or perspectives? Stepping beyond the scope of the studies reported here, one might ask: does the notation provide the preferred vocabularies and representational perspectives that constitute both the target skill to be learned as an aspiring member of a community, and focus learning activity on ways of approaching a problem that are productive?