What principle was the basis for the drive for the public education?

Until about 1850, Schools were only for children coming from a rich family. So of course the reformers didn't accept that, and made 3 basics for the public education: 
-Schools should be free and supported by taxes.
-Teachers in those schools should be well trained so they would be able to deliver the message to the students in a correct, well understandable way.
-All Children should be required to attend school, poor or rich.

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