Speaking at the conference's Scottish fringe, the leader of the Scottish Conservatives talked up the education system in New Zealand, where schools were self-governing through boards of trustees, which controlled everything from pay and conditions to building maintenance.
"Those boards are elected by parents, ensuring the community has a real say in the running of their local school. They give the schools the flexibility to meet the needs of the communities they serve, the ability to attract high quality teachers and the authority to enforce the standards of discipline parents want upheld."
Ms Davidson also referred to charter schools, which also had some freedom from the rules state schools operated under, including the freedom to set their own curriculum and operating hours.
The Scottish Tory leader explained how under her preferred system children would have a guaranteed place at their local school but "if you chose to apply to a different school, the way in which admissions would be decided for those extra places would be decided by the schools themselves and they could decide that on any level they wanted; whether that's on merit, whether they have a sibling who had gone there, on location or because it's on disadvantage".
Asked directly if she was in favour of academic selection for children applying to non-local schools, she replied it would be up to the boards of those schools.
Asked if council education authorities should be scrapped, Ms Davidson replied: "Yes, you should be able to set up charter schools, free schools, whatever and schools that already exist should be able to take themselves into their own governance but we are not going to force every school to do that should they not wish to. This would be a phased change in Scotland."