Mr Turnbull had just visited a defence supplies company in the Labor-held Melbourne seat of Hotham when the woman approached him.
The woman, identified only as Melinda, told Mr Turnbull she wanted the Federal Government to offer more help to mothers such as herself.
“I’m worried,” she said. “I’m a single mum, I have two teenage boys, now the cost of schooling is going up and up and up and yet we’re not getting any more money.”
Mr Turnbull responding by referring to what he said was the Government’s record spending on education.
“We are absolutely committed to your boys having the best education opportunities,” he said.
“We’re spending more on school education than we ever have in the history of the Commonwealth.
“Our expenditure per student in state schools, like your boys’ schools, has been rising rapidly, far faster, than the state governments’.”
However Melinda said: “That’s not what the schools are saying”.
“Give the kids a chance, give them a fighting chance please,” she said.
Asked off camera by the ABC if she was a member of any political party, Melinda shook her head.