I think that the “teaching” benchmark you claim here is actually a bit weaker than a Level 2 understanding. To successfully teach a topic, you don’t need to know lots of connections between your topic and everything else; you only need to know enough such connections to convey the idea. I really think this lies somewhere between Level 1 and Level 2.
I’ll claim to have Level 2 understanding on the core topics of my graduate research, some mathematics, and some core algorithmic reasoning. I’m sure I don’t have all of the connections between these things and the rest of my world model, but I do have many, and they pervade my understanding.
I think that the “teaching” benchmark you claim here is actually a bit weaker than a Level 2 understanding. To successfully teach a topic, you don’t need to know lots of connections between your topic and everything else; you only need to know enough such connections to convey the idea. I really think this lies somewhere between Level 1 and Level 2.
I agree in the sense that full completion of Level 2 isn’t necessary to do what I’ve described, as that implies a very deeply-connected set of models, truly pervading everything you know about.
But at the same time, I don’t think you appreciate some of the hurdles to the teaching task I described: remember, the only assumption is that the student has lay knowledge and is reasonably intelligent. Therefore, you do not get to assume that they find any particular chain of inference easy, or that they already know any particular domain above the lay level. This means you would have to be able to generate alternate inferential paths, and fall back to more basic levels “on the fly”, which requires healthy progress into Level 2 in order to achieve—enough that it’s fair to say you “round to” Level 2.
I’ll claim to have Level 2 understanding on the core topics of my graduate research, some mathematics, and some core algorithmic reasoning. I’m sure I don’t have all of the connections between these things and the rest of my world model, but I do have many, and they pervade my understanding.
If so, I deeply respect you and find that you are the exception and not the rule. Do you find yourself critical of how people in the field (i.e. through textbooks, for example) present it to newcomers (who have undergrad prerequisites), present it to laypeople, and use excessive or unintuitive jargon?
Therefore, you do not get to assume that they find any particular chain of inference easy, or that they already know any particular domain above the lay level. This means you would have to be able to generate alternate inferential paths, and fall back to more basic levels “on the fly”, which requires healthy progress into Level 2 in order to achieve—enough that it’s fair to say you “round to” Level 2.
I agree that the teaching task does require a thick bundle of connections, and not just a single chain of inferences. So much so, actually, that I’ve found that teaching, and preparing to teach, is a pretty good way to learn new connections between my Level 1 knowledge and my world model. That this “rounds” to Level 2 depends, I suppose, on how intelligent you assume the student is.
If so, I deeply respect you and find that you are the exception and not the rule. Do you find yourself critical of how people in the field (i.e. through textbooks) present it to newcomers (who have undergrad prerequisites), present it to laypeople, and use excessive or unintuitive jargon?
Yes, constantly. Frequently, I’m frustrated by such presentations to the point of anger at the author’s apparent disregard for the reader, even when I understand what they’re saying.
I think that the “teaching” benchmark you claim here is actually a bit weaker than a Level 2 understanding. To successfully teach a topic, you don’t need to know lots of connections between your topic and everything else; you only need to know enough such connections to convey the idea. I really think this lies somewhere between Level 1 and Level 2.
I’ll claim to have Level 2 understanding on the core topics of my graduate research, some mathematics, and some core algorithmic reasoning. I’m sure I don’t have all of the connections between these things and the rest of my world model, but I do have many, and they pervade my understanding.
I agree in the sense that full completion of Level 2 isn’t necessary to do what I’ve described, as that implies a very deeply-connected set of models, truly pervading everything you know about.
But at the same time, I don’t think you appreciate some of the hurdles to the teaching task I described: remember, the only assumption is that the student has lay knowledge and is reasonably intelligent. Therefore, you do not get to assume that they find any particular chain of inference easy, or that they already know any particular domain above the lay level. This means you would have to be able to generate alternate inferential paths, and fall back to more basic levels “on the fly”, which requires healthy progress into Level 2 in order to achieve—enough that it’s fair to say you “round to” Level 2.
If so, I deeply respect you and find that you are the exception and not the rule. Do you find yourself critical of how people in the field (i.e. through textbooks, for example) present it to newcomers (who have undergrad prerequisites), present it to laypeople, and use excessive or unintuitive jargon?
I agree that the teaching task does require a thick bundle of connections, and not just a single chain of inferences. So much so, actually, that I’ve found that teaching, and preparing to teach, is a pretty good way to learn new connections between my Level 1 knowledge and my world model. That this “rounds” to Level 2 depends, I suppose, on how intelligent you assume the student is.
Yes, constantly. Frequently, I’m frustrated by such presentations to the point of anger at the author’s apparent disregard for the reader, even when I understand what they’re saying.