The health and education ministers were asked to expand the service provision available for detecting problems at the early stages of a child's education, on 23 April 2012.
Proposing the UUP motion, Roy Beggs said he wanted multi-agency support teams to be available for every child.
He said there were effective partnerships in place between the health service and schools to address the needs of children but that there was a lack of provision in certain areas of Northern Ireland.
Mr Beggs used the example of Larne where 17 out of 18 schools did not have this extra support.
"We want to ensure that no-one slips through the gaps of the system," he said.
Pam Brown of the DUP said early detection was vital for those children who were showing signs of difficulty.
"Multi-agency support teams or multi-disciplinary teams play a central role in the detection and treatment of such problems children may begin to show when in school," she said.
"They offer an excellent model for tackling need, in bringing together professionals from within both the education and health sectors."
Sinn Fein's Michaela Boyle said the work the multi-agencies did was of vital importance to families but felt more needed to be done to make parents aware of the help and support available.
Mark Durkan of the SDLP said he supported the motion with "the sentiment that much more must be done".
He said that since 2007, 137 schools had received services from the scheme, with others indicating an interest in adopting the model.
The Green Party leader, Steven Agnew, also supported the motion but said he did not want the quantity increased if it would put the quality at risk.
The second part of the debate can be viewed