In a speech to the London School of Economics, the Scottish Tory leader will call on the First Minister to honour her promise to make education, not the constitution, her top priority.
Scots pupils are slipping behind their international counterparts in maths, reading and science, according to recent reports.
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An analysis last week by the Sutton Trust said there were “major weaknesses” in Scotland, including a "prolonged and sustained decline in able pupils' performance in science".
The educational charity’s report, which drew on data from 2015, also said Scotland was “trailing behind the performance of able pupils in England in most subject areas".
It said: "Scotland has few stand-out strengths when it comes to the performance of its most able pupils... there is no specific area where able children in Scotland really excel."
SNP ministers have announced an extra £120m to help close the attainment gap.
However Ms Davidson will argue that if Ms Sturgeon calls a second referendum, her focus will inevitably be diverted onto campaigning, away from the hard grind of government.
She will say: “I believe the First Minister now faces a choice. Either to focus on her own priority, and ensure our schools are turned around. Or to push ahead with a second referendum. I say, Scotland’s children won’t get a second chance.
“Either she focuses on her own-stated priority of education. Or she betrays that pledge in favour of the SNP’s constitutional obsession. She simply cannot have it both ways.
“Simply put, I do not think the majority of people in Scotland will tolerate the SNP setting all things aside over the coming two years to re-fight a campaign on independence.”
An SNP spokesman said: “The Tories are desperately trying to distract from the complete shambles that is their handling of Brexit - a situation imposed on Scotland despite our overwhelming Remain vote.
"After the Brexit vote, Ruth Davidson said that protecting our place in the single market should be the 'overriding priority'.
"Now the born-again Brexiteers in the Scottish Tories expect us to let Theresa May push on with a hard Brexit that could cost 80,000 jobs in Scotland over the next decade.
"Tackling the attainment gap is the SNP's number one priority in government - and our budget, which the Tories voted against, will give schools an additional £120m in increased resources to give all children the best start in life."