Crossword Genius

You'd be a fool to wear this (6,3)

Ross

I believe the answer is:

dunces cap

I'm a little stuck... Click here to teach me more about this clue!

'you'd be a fool to wear this' is the definition.
The definition suggests a singular noun which matches the answer.

'fool to wear this' is the wordplay.
I cannot really understand how this works, but
'fool' could be 'dunce' (both can mean a stupid person) and 'dunce' is located in the answer.
'wear' could be 'cap' (cap is a kind of wear) and 'cap' is found within the answer.
A single letter 's' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for dunces cap that I've seen before include "Headgear used to humiliate slow learners" , "Classroom idiot's headgear" , "Ignorant boy's headgear" .)

I've seen this clue in The Sun.
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