This is excellent, Christian! One complication/elaboration that comes to mind in relation to the part about students thinking "perfectly rationally with the meaning they've made." This strikes me as a place where enactivism might usefully be brought into dialogue w/ modern critical theory.

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From a practical perspective, I agree that it's useful to work from the premise that the way students are thinking makes sense in terms of the system of meaning they have.

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At the same time, though, I'd suggest that it's useful to consider the ways in which systems of meaning tend to be multiple, ambiguous, and internally conflicted and contradictory, as well as historically (etc.) situated. Critical theory can be helpful here.

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as is the case with all the addition/subtraction-patterns, and one can have one "meta-pattern" that deals with all of THEM, but NOT with multiplication/division. The same for your list: the triangle can be used for a=b*c-form, but there are other formulas which would need another "meta-pattern".

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You may also see now, why I was very inspired to see your "triangle", as it is similar to the "Whole-Part"-Scheme - you have "patterns", "familiarities", when dealing with formulas roughly following a=b*c (or: c=a/b),

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