Developing model-based reasoning in mathematics and science

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What recent research on diagrams suggests about learning with rather than learning from visual representations in science (2016, methodology): “Closer inspection of these studies revealed that some of the diagrams did not possess the explanatory and predictive power of a scientific model (e.g. Lehrer & Schauble, 2000), suggesting that some models are diagrams, but not all diagrams are models.”
Disentangling Robust Developmental Constraints From the Instructionally Mutable: Young Children's Epistemic Reasoning About a Study of Their Own Design (2011, background): “As elaborated in the theoretical and instructional design work of Lehrer and Schauble (2000), it has many forms: from physical models, representational models, or syntactic (or analogical) models to hypothetical-deductive models.”