The Scottish Conservatives are today calling for Scottish Attainment Challenge money - designed to close the gap between rich and poor pupils - to follow the pupils who need it.
Following a visit to Leith Walk Primary school in Edinburgh, party leader Ruth Davidson said Ministers needed to re-think the £100m fund.
Under it, ministers have picked seven local authorities for funding - based on the fact they have a higher level of deprivation than other local authority regions.
However, with the evidence showing that most poorer families are spread right across Scotland, the Scottish Conservatives are calling for the money to go direct to less well-off pupils, no matter where they happen to live.
Calls for change have been aired by experts who have pointed out the need to support children no matter where they live.
Scottish Conservatives leader Ruth Davidson said:
"We support the Scottish Government's aim of reducing the attainment gap in Scotland's schools. The problem is the way in which they are going about it.
"Rather than have central government in Edinburgh dictate which councils get money and which ones don't, we should simply redesign the scheme so the money follows the child.
"That way, extra help goes where it is needed and schools - not government officials - can decide how best to use it to support children from deprived backgrounds.”
Last week, First Minister Nicola Sturgeon insisted that she would retain the current model of funding - under which the Scottish index of multiple deprivation is used to pick out seven local authority areas which have the greatest number of homes with deprived children.
The local authorities then decide which schools are funded.
The First Minister then declared last week that a further 57 schools from 14 authorities would also be picked for extra funding.
However, education experts have questioned the methodology.
A Reform Scotland paper last year concluded: "There is, as yet, no programme directed at those children living in poverty, but attending schools that do not serve particularly deprived areas.
"The recent research suggests that these may be the majority of all children experiencing deprivation. This is, therefore, a very substantial gap in policy."
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