"When guys at MIT or Princeton had trouble doing a certain integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was contour integration, they would have found it; if it was a simple seriesexpansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s" -Richard Feynman
Metamodeling is the act of modeling our own creation, modification, and use of models for problem solving.
Metaphorical metamodels focus on the use of rich metaphors to load intuitions about how to think about models.
Concept garden:
Loads intuitions such as models evolving and changing over time, the 'garden' as needing maintenance, global vs local structure, tending as an enjoyable hobby, etc.
Tool box:
Loads intuitions such as problem-heuristic fit, specificity vs generality, the sharpening of models using other models, and the limited size of our cache for immediately accessible tools.
Pedagogical metamodels focus on how models are formed, taught, and recalled for later use.
Concept formation is the idea that the most effective means of learning concepts is to give several simple examples, ideally from different domains. The human mind naturally pays attention to invariants across situations for efficiency under the cognitive miser theory. Once the student experiences the click of noticing the similarity across the examples they will have a more cemented understanding.
Ontological metamodels focus on the use of models as sorting tools, allowing us to decide which reference class of reasoning to apply to a particular situation.
One ontological question that can be asked about a model is whether it carves reality at the joints. Related to the notion of leaky vs tight abstractions.