In its report, published yesterday, the commission commended the city council for its rate of improvement and commitment to change, but its best-value report on Scotland's largest authority warns that it should take "particular care" to improve performance and outcomes within education and social work.
The commission acknowledges the council's achievements in addressing the issues of its school estate and measures to improve the health of pupils, but finds that it needs to ensure it has sufficient capacity to deliver its challenging and ambitious agenda.
"There are indications that this will not be easy, although Glasgow spends more than any other mainland Scottish council in both primary and secondary schools," it says.
The report cites the creation of the post of executive director (education, training and young people), held by Ronnie O'Connor, as evidence that the council considers education and, more generally, children's services, as central to the social renewal agenda.
While acknowledging that attainment has improved in some areas in the last year, the report adds that exam results remain below the Scottish average.
It also points out that improvement trends mask "considerable variation in attainment levels between schools, even taking account of levels of free meal entitlement as an indicator of deprivation".
Copeland primary in Govan is given special mention as an example of a school of high achievement, despite having 73 per cent of pupils with free school meal entitlement.
Councillor Steven Purcell, the council leader, said: "This is a very positive report which highlights the significant advances made in Glasgow, but I am acutely aware that there is still much to do."
He cites the commission of leading experts set up by the council as evidence of its efforts "to examine how we can transform the prospects of our children".