The most common and most likely answer to this crossword clue is the 8 letter word PEDAGOGY
I've seen this crossword clue in Financial Times
P
E
D
A
G
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Y
More clues leading to the result PEDAGOGY
Buddy explains!

The straight part
We know that "teaching theory" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case teaching theory = pedagogy.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PEDAGOGY mean?
PEDAGOGY noun- The profession of teaching.
- The activities of educating, teaching or instructing.
- The strategies of instruction.