I've been thinking a lot about your point b) over the years.
I'm conceptualizing a piece of knowledge as an interface that can be `implemented` but with different classes (explanations renderings for different audiences).
For example, the "derivative interface" represents knowledge of the concept of derivative operations and basic skills to compute derivatives of various functions. The interface doesn't specify HOW to teach this topic or HOW DEEP, so there are multiple implementations:
- basic visual explanations (for kids)
- basic algebra steps (for high school)
- standard explanation (for undergraduate students)
- compact explanation (a reviee for grad students)
The above implementation are polymorphism due to the "reader level of knowledge," but there could be other, e.g. derivatives explained using code like in Sec 4.1 in this calculus tutorial[1].
It would be A LOT of work to produce all these explanations but it would make for a kick ass math textbook that you can pick up and learn, no matter what your level is (instead of getting lost or bored and looking for another resource).
[1] https://minireference.com/static/tutorials/calculus_tutorial...
I'm conceptualizing a piece of knowledge as an interface that can be `implemented` but with different classes (explanations renderings for different audiences).
For example, the "derivative interface" represents knowledge of the concept of derivative operations and basic skills to compute derivatives of various functions. The interface doesn't specify HOW to teach this topic or HOW DEEP, so there are multiple implementations:
The above implementation are polymorphism due to the "reader level of knowledge," but there could be other, e.g. derivatives explained using code like in Sec 4.1 in this calculus tutorial[1].It would be A LOT of work to produce all these explanations but it would make for a kick ass math textbook that you can pick up and learn, no matter what your level is (instead of getting lost or bored and looking for another resource).
[1] https://minireference.com/static/tutorials/calculus_tutorial...