Cover supervisors should have to pass a specially designed national qualification before they can be placed in front of a class, the Association of Teachers and Lecturers (ATL) has heard.
The role has boomed since the introduction of the "rarely cover" rule, prompting calls for more regulation of the educational standard of those entering the job.
At present, cover supervisors are not officially required to have any qualifications, despite covering for eachers. In recent months, reports have emerged of nightclub bouncers being hired because they are "good at crowd control".
Higher level teaching assistants (HLTAs), who may also take whole classes and deliver work prepared in conjunction with the class teacher, must complete a rigorous course to gain their status.
Delegates at the ATL's annual conference this week called for a similar qualification to provide a basic level of training for cover supervisors.
The role has been heavily criticised in recent years, with claims that it amounts to "teaching on the cheap".
Official guidance says cover supervisors should be used only to provide cover for regular teachers for restricted periods of time and that they should only oversee the delivery of that teacher's work.
But critics complain that schools employing large teams of cover supervisors are overusing them in a bid to save money.
Florence Farahani, an HLTA and pupil support manager at the inclusion unit of Barnwood Park Arts College in Gloucester, told the conference: "Cover supervisors should have to pass a national qualification comparable to that for HLTA status."
She also expressed concern that there was little legislation regulating the educational standards of teaching assistants in general, many of whom move up the rankings through experience rather than paper qualifications.
Ms Farahani told The TES: "I know teaching assistants who have been employed just to push wheelchairs who are in front of classes in a matter of years."
Glyn Kenyon, a maths teacher at Buttershaw Business and Enterprise College in Bradford, said schools had a "duty of care" to parents to let them know who was teaching their children and what qualifications they had.
He told the conference: "Is it right that primary schools timetable HLTAs to take literacy and numeracy groups? Is it right that they use them as form tutors?"
But he added: "This is not about the capabilities of support staff; it's about using them correctly."
Concerns about cover supervisors not being allowed to "teach", despite being placed in front of whole classes, were also highlighted by Janet Blanchard, a supply teaching assistant in Nottinghamshire.
She told delegates: "I have been employed as a cover supervisor where I'm often asked questions as a teacher that I can't answer because I'm not qualified."
The call for increased regulation of cover supervisors' role comes as supply teachers claim they are taking their work.
Supply teachers are holding a protest in central London on April 9. They will also call for more access to continuing professional development to enable them to gain the planned "licence to practise" and gain access to the Teachers' Pension Scheme.
Debate the issue further on our Rarely Cover forum