In parliamentary exchanges last week, Jack McConnell was confronted by Kate MacLean, MSP and former leader of Dundee City Council, who told him that early intervention "is not necessarily closing the gap in achievement of all children, but seems to be raising standards in general, with children who are ahead when they start school remaining ahead".
Mr McConnell did not diagnose the dilemma, replying that it was important attainment levels went up for everyone but that those with a less good start in life should see their levels increae "significantly".
He added: "One of the challenges we face in discussion with local authorities is to ensure that the work we are doing to expand pre-school education and the early intervention work in the early stages of primary school can be linked into what then happens in the later stages of primary school."
The recent HMI report on primary maths found that learning in the later stages had not kept pace with good performance in the early years.
Mr McConnell said he wanted to discuss with the authorities how resources can be better targeted to iron out these problems. But he added that he would be awaiting the report from Moray House Institute and KPMG, which are evaluating the early intervention programme, before taking decisions on the future of the initiative.