Teaching for understanding versus teaching for creation

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(there might be a more standard term for this distinction)

Teaching for understanding versus teaching for creation refers to the distinction between teaching a learner to simply understand the material (which allows them to use the material in simple applications) versus teaching the learner to create new ideas in the subject.

Here is a rough categorization (not necessarily very accurate):

Teaching for understanding Teaching for creation
Undergraduate curriculum (teaches standard topics in a field) Graduate school (is supposed to teach students to advance the field)
Teaching the object-level skill/material Teaching a meta-level skill (note: there is more than one way to "go meta" from the object level, e.g. one could also "go meta" by learning about how to learn, rather than learning how to create)
Teaching of material that has been systematized (e.g. linear algebra has been systematized and is well-understood) Teaching of material/skills that have not been systematized (e.g. the act of inventing linear algebra from scratch has not been systematized, and is not well-understood)
Both positive and negative examples are available Positive examples are hard to convey, while negative examples are available