Dozens of pupils at Marr College in Troon are to study the subjects, leading to calls for a meeting to discuss the move with South Ayrshire Council's education director.
SNP councillor Nan McFarlane, the deputy leader of her party on the council, said: "I have been approached by several parents who have had to pay for their children, mostly in fourth, fifth and sixth years, to have private tutors in English and maths.
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"This is a huge issue, and given the amount of parents who have spoken to me, there are dozens of families who have had to resort to private tuition because of the lack of, for instance, a principal English teacher at the school.
"None of the parents want to go public with their complaints, because they fear that their kids will be singled out because they are seen as being dumb and needing private tuition or, alternatively, too posh."
She questioned why people should have to pay for their children to be taught privately.
One parent of a child at the school said: "We are paying the local authority to give our children a proper education and they are failing us to the extent that we have to employ former teachers to give them lessons in the two most vital subjects - maths and English."
Douglas Hutchison, South Ayrshire's head of education, said a temporary shortage of English teachers due to staff absences was being addressed. He added: "We made sure all parents were aware of this. All parents want their children get the best opportunities and some will go further, paying to put their children through private education."