So maybe there should be level 2a: conceptual understanding, and level 2b: quantitative + conceptual understanding.
The fact that nobody quite falls perfectly into a discrete level doesn’t mean it isn’t a useful heuristic though. Even in your case you could say that you’re “on your way” to level 2.
Even in your case you could say that you’re “on your way” to level 2.
Right—but that’s what I think is wrong with the definition of levels 2 and 3. Since I could get to the equation, if I had to, shouldn’t that also be a valid description of level 3? Requiring me to know the equation in order to be level 2, yet not requiring it at level 3, kind of makes the point that this is not really a linear progression.
[Edit to add: I don’t necessarily mean that understanding itself isn’t linear, just that this particular set of definitions does not seem to be.]
So maybe there should be level 2a: conceptual understanding, and level 2b: quantitative + conceptual understanding.
The fact that nobody quite falls perfectly into a discrete level doesn’t mean it isn’t a useful heuristic though. Even in your case you could say that you’re “on your way” to level 2.
Right—but that’s what I think is wrong with the definition of levels 2 and 3. Since I could get to the equation, if I had to, shouldn’t that also be a valid description of level 3? Requiring me to know the equation in order to be level 2, yet not requiring it at level 3, kind of makes the point that this is not really a linear progression.
[Edit to add: I don’t necessarily mean that understanding itself isn’t linear, just that this particular set of definitions does not seem to be.]