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Can I say,

(a) We performed some songs. The children liked the songs. They joined in the singing and clapped the hands.

(b) They joined in to sing a song.
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Vincent TeoCan I say,

(a) We performed some songs. The children liked the songs. They joined in the singing and clapped their hands.

(b) They joined in to sing a song. [Y]

Comments  
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Feebs, would you consider "joined in the singing" incorrect?
No - it's perfectly normal.