Children at risk do not appear to do as well if they continue to stay at home with their parents, he has found.
Dr Connelly also disputes the impact of Scottish Executive funding on looked-after children.
In his analysis of the educational fortunes of these pupils, Dr Connelly says 5-14 and Standard grade results tell only part of the complex story.
"For example, the evidence throughout the UK is that accommodated children perform better than those who live with their own families. This may in part be due to the stability of foster care and to the improvements which have taken place in residential schools.
"The evidence from residential schools shows that 10 years ago they had a narrow curriculum; today, with a much broader curriculum, the attainment figures are dramatically improved, flying in the face of the received wisdom that kids who underperform should study fewer subjects."
Dr Connelly adds that Glasgow's Standard grade results for children looked after by relatives (often grandparents) show they outperform those living with their parents.
But results are only one dimension, Dr Connelly suggests. "A young person of 15 or 16 whose developing sense of self is hampered by confusion and anger resulting from abuse or neglect is not in the best frame of mind to take public exams," he says.
"The agencies working with these kids can often point to positive results a few years later when, for example, a young person returns to FE."
He also believes schools which exclude a pupil for a second time should seriously consider moving him or her to a residential school sooner than is current practice.
"Understandably, all efforts are made to keep children out of residential care but this may be counterproductive," he argues. Drawing on the official figures, Dr Connelly found that looked-after children are four times more likely to be excluded than their peers. Their exclusion rate fell over the past six years but started rising again two years ago.
Ministers point to the pound;16 million they say has been spent on the education of looked-after children as evidence that they are beginning to address the problem.
But Dr Connelly said the first tranche of pound;10m in 2001 was "quick-spend money" to launch the Executive's initiative on looked-after children. "Authorities got about two months to spend the money," he says.
"It is not surprising that much of it went on computers. The money was welcome, but it could only make very limited impact."
In 2004, a further pound;6m was announced but this is only now in the process of being allocated to pilot initiatives.
The Executive, stung by criticism of the way the first tranche was spent, came up with a more elaborate bidding process which has taken time to introduce. Two secondees appointed to oversee the project have only just started work.
Dr Connelly said: "These more considered projects should give us a better understanding of what might lead to improvements, but it's not quite accurate for ministers to say that pound;16 million has been spent already without impacting on attainment."
Only 18 of the 32 local authorities responded to the Executive's pound;6m offer of cash, leading to a stern rebuke last year from Jack McConnell, the First Minister. Of the 18, just seven were approved initially because their bids were judged not good enough.
Figures also show wide variations across the country. All 10 care-leavers in the Borders had at least an Access or Standard grade 56 award, in contrast with only one in five of the 45 such leavers in East Ayrshire.