Posed problem, knowing Japanese pottery (7,4)

I believe the answer is:

satsuma ware

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

'japanese pottery' is the definition.
The definition suggests a singular noun which matches the answer.

'posed problem knowing' is the wordplay.
'posed' becomes 'sat' (posed or sat for an artist).
'problem' becomes 'sum' (as in a mathematical problem).
'knowing' becomes 'aware' (I've seen this before).
'sat'+'sum'+'aware'='SATSUMA WARE'

Can you help me to learn more?

I've seen this clue in The Times.

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