Ok, you are quite the optimist to truly believe that every kid will learn enough math by their own choice. No matter how much encouragement and good environment and teachers, there will be kids who just don't want to learn statistics, or compound interest.

So you're left with either forcing them to go, where they at least learn something exists, or letting them do their own things, and never learn anything about math at all.

Many people commenting here have this idealized view of education as "if only... xyz... then every kid would spend 12 hours a day teaching themselves!". That's absurd, and any realistic look at education has to realize that sometimes we need to teach kids skills that are useful, but not interesting.

Before 1900, curricula in schools ranging from elementary school right up through university level were prescribed with no choices left to the students.

The attitude also was one of sink or swim, with the idea being a comparatively few "educable" people would become truly learned while the rest would pursue utilitarian goals tied to earning a living.

The classes emphasized formative skills ultimately tied to the idea of learning how to think as opposed to specific instruction that was supposed to instruct in any immediately practical way.

Even the learned professions were regarded as mere utilitarian applications to be pursued only after one had become properly educated.

A very elitist and, one might say, "strongly typed" view of how education should proceed.

It is a modern concept that students should even be able to choose among electives or follow their own inclinations without rigorous guidance from instructors using a strictly prescribed format.

Of course, all this has completely changed today, with the result being an "idealized view of education" (to use your phrase) to the effect that all students are capable of learning, and will learn, if given the freedom and motivation to develop their abilities.

For a fascinating comparison of the old way with the new, read Albert Jay Nock's 1931 assessment (given as part of the Page-Barbour Lectures at the University of Virginia) of what he considered the utter failure of the modern approach to deliver on its promises of universal education. (http://mises.org/story/2765)

Nock's defense of the old way is undoubtedly narrow, even embittered, but his critique of the new way is often intriguing. At the very least, it makes us examine our assumptions about modern education in ways that we do not often do.

If anyone goes to the link, use the index up front to skip past the preliminaries and get to the substantive parts - otherwise, it is a very long read.

Knocking holes, but I'm sure there were a very large number of people who didn't attend university before 1900. Probably a lot of people also left school to get a job at some point before they turned 18.

If being ignorant of statistics is such a terrible thing, then it shouldn't be very difficult to persuade people that they should learn it. Make your case, and let them make a value judgment. I question the value of locking people in rooms and calling the truancy officer if they don't show up. That's prison, not education.