Crossword Genius

A foolish assumption of the old school (6,3)

Ross

I believe the answer is:

dunces cap

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

'a foolish assumption of' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'old school' is the wordplay.
I cannot really see how this works, but
'school' could be 's' and 's' is found in the answer.
The remaining letters 'duncecap' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'the' is the link.

Can you help me to learn more?

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

I've seen this clue in The Globe and Mail and The Guardian.
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