Is there a single word meaning figuratively 'separate wheat from chaff' (good from bad), about teaching ideas?

Solution 1:

There are lots of candidate words, but the appropriate choice of word depends hugely on what is being said about the distribution of the quality of ideas:

• cull/ filter/ prune/ triage (if some ideas are outright terrible and need to be summarily rejected, e.g. Earth was colonized from the dark side of the moon)
• sift (if ideas seem plausible, and we need to discern better from worse, more helpful from less)
• distill/ craft/ develop/ refine/ finesse/ amalgamate/ synthesize (if ideas are ok but need to developed, clarified, articulated better and possibly put together to make a more useful idea
• select, or its hip cousin curate, say nothing about the wider set of ideas, and merely say you (possibly arbitrarily) picked some to discuss/ focus on/ illustrate
• similarly separate (/ categorize) e.g. in physics, we can separate ideas in forces and mechanics from ideas in heat and light from ideas in radiation, but that merely says they can be split into different categories, it says nothing about whether some are worse than others, or interconnected or not
• generalize/ reduce/ condense/ summarize/ canonicalize Perhaps goes beyond your intended scope, but this applies where multiple ideas from the same or different categories are the same fundamental principle

To your second question: "(Does it seem odd such a word would not be common? Is is because separate, and it's synonyms, already imply the reason for division is already, always, about good and bad?)"

That is because there are multiple different candidates, as above. Yes it depends on what the verb implies about quality, if anything, and how much effort the discernment process takes. separate is not necessarily good from bad, it could be simple from complex, advanced from introductory, scalar from vector, general or common from special-case or rare, well-known from little-known etc.

Solution 2:

The word I would use is distill:

extract the essential meaning or most important aspects of. –NOAD

Moreover it’s so common and fitting that you yourself used it in your post.

Solution 3:

cull vocabulary.com

verb: remove something that has been rejected; look for and gather

noun: the person or thing that is rejected or set aside as inferior in quality

As in:

If you decide to make a literary anthology, you must cull the best possible stories and then arrange them in a pleasing manner.

Though we are encouraged to use our own words to explain answers, I can do no better than to quote my reference:

When you use cull as a verb, the things you gather can be the good or bad ones from a group. In your garden, you can cull the good vegetables for dinner, or the rotten ones for the compost pile. In fact, often no judgment of quality is made, as when you cull information from the Internet for your next research project. The sorting through will come later. However, if you use the word as a noun, a cull is a selection of things you intend to reject, often in reference to a group of animals. An outbreak of a disease such as foot-and-mouth disease can cause authorities to order a cull of farm pigs.

Solution 4:

The technical terms are thresh or winnow but I have never heard these used metaphorically. The metaphorical term is separate the wheat from the chaff.

Edit Having looked at other people's suggestions, I see that some suggestions, such as prune, involve taking out the bad bits. Others, such as distil, involve taking out the good bits. Separating the wheat from the chaff involves going through everything and sorting into two piles. It also seems to me that it is more specifically sorting the wanted from the unwanted, rather than making a judgment about good and bad. A typical example would be going through job applications where you go through them sorting into a pile of rejects and a pile that you will invite for interview.