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) (note: this does not mean that the act of teaching itself has been systematized; linear algebra is systematized even if people have not figured out how to teach it) 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

The meta levels are somewhat confusing, so let me try listing them:

  1. object level (linear algebra): this is what a typical student taking a linear algebra course does
  2. (how to invent linear algebra): this is what the people who invented linear algebra did, or what a highly-above-average student taking a linear algebra course might do, if they were trying to really understand the subject
  3. (how to teach linear algebra): this is what a graduate student figuring out how to teach a linear algebra course does
  4. (how to teach how to invent linear algebra): this is what Jeffreyssai (i.e. someone who wants to teach his students how to invent) must figure out[1]
  5. (how to invent how to teach linear algebra): what an unusual instructor of linear algebra does, if they want to figure out how to best teach linear algebra

Differential teaching strategies

Why does the "teaching for understanding" vs "teaching for creation" distinction matter? One reason is that depending on the audience/goal, it makes sense to alter the teaching strategy.

For example, if the goal is to create, it makes sense to prove as many theorems as possible without looking at the proofs in the book. It might make sense (after empirical investigation) to also do this even if the goal is just to understand the material (see pre-testing effect).