Learning through exercises
One of the best aspects of mathematics is that it is possible for a student to reconstruct much of it on their own, given the relevant axioms, definitions, and some hints. Indeed, this style of education is usually encouraged for training mathematicians. Relatedly, it is also possible for a mathematician to give a quick impression of the relevance of their particular field by choosing an example of an interesting problem which can be efficiently solved using the methods of that specific specialty of mathematics.
To what extent do other academic fields share this property? How well can physics, chemistry, biology, etc. be taught “through exercises”?
EDIT: Note that the “exercises” I am referring to are not just matters of applying learned principles for solving random problems but rather are devices to lead the student to “rediscover” important principles in the field.
It seems like the question that is really being asked is whether you can impart knowledge by creating scenarios for the student to apply knowledge in a novel way in order to guide them to conclusions. The answer seems rather trivially to be yes. This arguably extends to all fields.
I can construct a history assignment that requires a student to reason to a conclusion based on the present evidence. I can construct an artificial scenario that can prod the student in to deriving some conclusions about physical phenomena. I could devise a problem that requires the student to rely on geometrical insight to derive a proof.
As far as I can tell this is a fairly standard teaching device.
Maybe you’re asking to what degree methods of requiring the students to apply learned information could be reduced to axiom and definition pushing? Science requires external input, although you can derive reasonable and necessary conclusions by taking existing regularities as axioms. Perhaps in effect this is very similar to doing mathematical exercises (and physics problems, for instance, boil down to pure mathematical puzzles once you’ve determined how you can use the given information to derive the solution), but this doesn’t totally embody the discovery process. Conducting simple (and complex) experiments and deriving regularities from the recorded data seems more appropriate in terms of accurately resembling physical discovery (and indeed this is a strong component in the science classroom, especially in a field like chemistry).
So, to be clear, the reason it seems that this cannot not induce a good discussion is that your suggestions have been in practice at institutions of higher learning for many, many years.