Cowed, disheartened schoolgirl (2-2)

I believe the answer is:

co-ed

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'schoolgirl' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'cowed disheartened' is the wordplay.
'disheartened' suggests removing the centre.
'cowed' with its middle removed is 'CO-ED'.

Can you help me to learn more?

(Other definitions for co-ed that I've seen before include "School for boys and girls, in short" , "School for both sexes" , "Teaching both girls and boys" , "Teaching attended by both sexes" .)

I've seen this clue in the Evening Standard.

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