An important research objective in modelling instruction is defining what students should learn about the model-referent relationship, as when unguided, they tend to errantly think of models as literal interpretations of their referents. Restating this problem we say students should learn about structure-preserving transformations between models and referents; including: what gets transformed, how it is transformed, and directions of information flow in transformation. To define what students should learn of this triumvirate, we introduce two explanatory statements: models are abstractions and models have transferability. We then investigated how readily students could learn about abstraction and transferability, and how this learning related to literal interpretation, by comparing pre- and posttest scores of modelling knowledge for students (n = 175) who participated in a modelling activity that provided experiences with abstraction and transferability. A control group (n=49) took identical tests but received no relevant instruction. Results showed that modelling students: (1) improved their capability to generate abstract models; (2) gained in their understanding that models represented their referents under transformation; and (3) consequently, did not think of models as literal interpretations. Lack of gains in the control ruled out a testing effect. We concluded that knowledge of structure-preserving transformations is a viable and valuable object of instruction.