Mrs Gillespie, development manager with the Scottish Parent Teacher Council, warned the party's People's Assembly in Edinburgh. that it would be impossible to find representative people, "You would actually have different groups in education at each other's throats, fighting for power positions of being on the committee," she said.
But Nicola Sturgeon, SNP education spokesperson, disagreed. "We do not have closed minds on this but it's important to establish the principle that the education committee will not be a closed shop. I think it would be possible to find representative people," she said.
In a key address to the SNP's open forum on education and the parliament, Mrs Gillespie said the committee should be open to take advice and soundings from various groups but be comprised solely of elected members. If non-members were appointed, they should sit as individuals and not representatives.
Mrs Gillespie hoped the education committee would restrain itself and avoid "too much" legislation since Scotland had made progress by guidelines.
Nevertheless, the parliament needed to remove opting out legislation, tidy up placing requests, increase the flexibility of school boards to make them more attractive to parents and stipulate rules for free school travel.
Parents also needed more programmed time to talk to teachers about their children.
More broadly, any initiatives should be part of a national development plan, a long-standing plea of the Educational Institute of Scotland. Key Government schemes could be limited to one a year in each sector.
Secondaries, for example, had this year to cope with S1S2 reform, modern languages, target-setting and Higher Still. No-one could check developments.
Higher Still was like a "locomotive out of control" and nobody had listened to the views of people on the ground. "A national development plan would protect teachers from over-enthusiastic politicians," Mrs Gillespie continued.
Ian McCalman, EIS past president, agreed and said matching resources to implementation schemes was equally important to control the pace of change.
Mrs Gillespie further called for more balanced views on education, singling out nursery and higher education. There was a danger that babies from three months would be pitched into whole-day care. Nursery education was valuable but limited.
"The only people not looking after children could be parents," she suggested. "Some parents have very good reasons for needing childcare but let's not make it such that it's impossible for parents to bring up their own children. "
Similarly, not every school-leaver was suited to university education. Choice was being removed from some 18-year-olds. "Let us offer respect for people who want to become plumbers, car mechanics and electricians because the world would crumble if we did not have such valuable people doing such incredibly useful work," she said.
Spelling out the SNP's agenda, Ms Sturgeon pointed out that whatever Government controlled the parliament after next May, the same amount of money would be available for education. Only independence would deliver a properly funded system.
She said an SNP-run administration would seek to govern through a "social partnership" and plan education "from the bottom up, rather than top down".
The education committee would have teachers, parents, church representatives and others on it to reflect wider opinion.
"Politicians do not have a monopoly on ideas or wisdom," she said.
She praised the Government's work on early intervention but criticised target-setting for external purposes as it misled parents.
Ms Sturgeon promised a review of Higher Still, a continuation of national pay bargaining, more money for school-buildings, further progress on pre-school places, abolition of student tuition fees and a "working towards restoration of student grants".