School caretakers could also take football lessons, they added.
Heads at the training session in Wirral said it was absurd and beyond comprehension to rely on volunteers with no experience of teaching, no training and no track record in raising educational standards.
Brian McNutt, head of Eastway primary school, said: "If you are just taking people who are unqualified and putting them in classes from day one, chaos could ensue."
It was doubtful that there were enough willing and able volunteers or coaches to fill the gap at 24,000 schools, heads said. They also said schools face a budget shortfall of around 6 per cent in implementing the agreement and called on the Government to fully fund it.
Tim McBeath, head of St Anne's Catholic primary school, in Birkenhead, said: "I am fully in favour of members of staff getting some time to do their work, rather than doing it on Sunday afternoons. But it has to be funded properly."
The controversy comes as the National Association of Headteachers is due to vote next week on whether it will withdraw from the agreement, which guarantees that 10 per cent of a teacher's time will be set aside for preparation.
David Hart, the association's general secretary, said he supported the workforce agreement but said ill-judged suggestions like this threatened to undermine it.
"These seem to be rather laughable suggestions. Just because one school can find the right person doesn't mean every school in the country can go to the WI, grab somebody and put them in a classroom," he said.
WI members agreed. Doris Dinham, a former primary head and WI member from Haslemere, in Surrey, said: "We went on strike in the 1960s because we didn't want untrained staff teaching. I feel very angry that it could happen now."
Others said few of them would want to face classes of 30 children alone.
Judy Avens, president of the Haslemere branch, said: "It's not every child, but in most schools so many children are badly behaved. There's no parental control."
The example of WI members taking design and technology had already been successful at a school in Cumbria, the heads were told, although the local education authority could find no evidence.
A spokeswoman for the National Remodelling Team distanced themselves from the suggestions, saying they were "for discussion purposes only".