Dilemma of the day: teaching vs learning

[timelets]

Cognition early in training is fundamentally different from cognition late in training.

...information in an expert’s long-term memory...is organized differently from the information in a novice’s long-term memory. Experts don’t think in terms of surface features, as novices do; they think in terms of functions, or deep structure.

The novices ...[generate]... categories based on the objects in the problems.

...transfer [using known info to apply to new problems] is so difficult because novices tend to focus on surface features and are not very good at seeing the abstract, functional relationships among problems that are key to solving them.

...experts are able to ignore unimportant details and home in on useful information; thinking functionally makes it obvious what’s important.

--- Willingham. Why students don't like school? 2009.

Here's the teaching/learning dilemma:
- On the one hand, you want to teach "objects", i.e surface features, so that novices can learn.
- On the other hand, you want to teach functional relationships, i.e. abstract, deep structures, so that learners acquire useful skills.

In other words, if you are an expert you can't teach novices "the real thing" and must dumb down the material, so that it becomes learnable.

As a side note, Category Theory can be a good teaching/learning tool for experts because it focuses on functional relationships, instead of objects.