I'm sure you know Jefferson was one of the big proponents of a well-informed citizenry in order to maintain a functioning democracy.

Yes, Jefferson generally expressed the opinion that an educated citizenry is beneficial to a country, and I have often expressed agreement with that opinion. But it is important to note that Jefferson did not support making school attendance compulsory, nor did he think that education should be provided solely by state governments. Jefferson received more nonparental schooling than the other three presidents depicted on Mount Rushmore combined, first at home with a hired tutor in Tuckahoe, where Jefferson's father moved when Jefferson was two to be guardian for his wife's late cousin's son. At age nine Thomas Jefferson was placed as a boarding student in the one-room "Latin school" kept by the Reverend William Douglas, minister of St. James Parish. Thomas Jefferson's later letters reveal Jefferson didn't think Reverend Douglas really knew the subject matter very well.

Thomas Jefferson's studies with that teacher ended at the age of fourteen, when his father died. Thomas Jefferson then was sent to the five-student school kept by the Reverend James Maury, whose son was one of the other students in the school. Jefferson spent many hours walking in the woods or practicing the violin while studying there. Jefferson then again stopped attending school briefly before traveling to Williamsburg to attend the College of William and Mary.

William Small was Thomas Jefferson's favorite member of the college's seven-man faculty. Jefferson was remembered in later years by his classmates for his diligence in independently reading books until late at night. After two years, Jefferson completed his studies at William and Mary and then studied law by working with a Williamsburg lawyer from 1762 to 1766.

Jefferson, after retiring from his rather trouble-plagued presidency, spent years planning a system of publicly subsidized schools in Virginia. He wrote extensively to other planners of that project, and many of his letters from that period survive and have been reprinted. He was convinced from his extensive observations of society in America and in Europe that parental control was vital for schools:

"But if it is believed that these elementary schools will be better managed by the Governor and Council, the commissioners of the literary fund, or any other general authority of the government, than by the parents within each ward, it is a belief against all experience. Try the principle one step further and amend the bill so as to commit to the Governor and Council the management of all our farms, our mills, and merchants' stores."
Letter of Thomas Jefferson to Joseph Cabell, Feb. 2, 1816, reprinted in Political Writings of Thomas Jefferson (1955), page 98 and in The Writings of Thomas Jefferson (Memorial Edition 1904), volume 14, pages 420-21.

In other words, it is as ridiculous to have governments, especially governments of broad territorial units, operate schools as it is to have governments operate grocery stores or farms. But of course socialist countries around the world have tried the experiment of governments running farms and stores, always with disastrous results, and almost every country in the world today has government-operated schools. Perhaps it is time to listen again to Jefferson's advice.

Jefferson was quite consistent on this point of preferring private operation of schools,
however much those schools were publicly funded and open to all members of the public.
In a state of the Union address during his second term as president, Jefferson noted:

"It [should not] be proposed to take ordinary branches [of education] out of the hands of private enterprise, which manages so much better all the concerns to which it is equal."
Thomas Jefferson, sixth annual message to Congress (1806), reprinted in The Writings of Thomas Jefferson (Memorial Edition 1907), volume 14, page 384.

Jefferson most definitely supported public funding of schools, but made clear he opposed compulsory attendance.

"Is it a right or a duty in society to take care of their infant members in opposition to the will of the parent? . . . It is better to tolerate the rare instance of a parent refusing to let his child be educated, than to shock the common feelings and ideas by the forcible asportation and education of the infant against the will of the father. What is proposed here is to remove the objection of expense, by offering education gratis . . .
Letter of Thomas Jefferson to Joseph Cabell, September 9, 1817, reprinted in Writings of Thomas Jefferson (Memorial Edition 1904) volume 17, page 423.