For many years now, American students have been coming in at or near the bottom in international tests of mathematics. Meanwhile, our schools have been entertaining themselves with "new math," "fuzzy math" and everything other than old-fashioned hard-work math that other countries use.

If you want to test your own knowledge of math, here is an example for you. If a school district spends $8,000 per pupil and pays $4000 for a voucher for each pupil who leaves the public school system, will the total cost of educating all the students go up or down when more students begin using vouchers to transfer out of the public schools?

Take all the time you want. I'll wait. You can even use a pocket calculator if you want to.

If you said that the total cost of educating all the students goes down, then you are a lot smarter than those people who have fallen for the teachers' union argument that vouchers will cost the taxpayers more money. If you went even further and said that the amount of money left to spend on students remaining in the public schools would enable the spending per public school pupil to rise, you are probably in the top one to two percent.

Unfortunately, the dumbing-down of American education has been going on so long that it may now be impossible for many people to see through such flimsy arguments that are made in defense of the status quo in the public schools. These schools' own educational failures in the past may insulate them from the changes they need to make for the future -- but which an under-educated public does not realize they need to make.

Seldom, if ever, do students who receive vouchers get more than half of what is spent per pupil in the public schools. Moreover, both voucher schools and charter schools have to provide their own classrooms, while school buildings are provided free to the public school system. So the real disparity in resources is even greater than two-to-one in favor of the public schools.

Despite the deck's being stacked in favor of the public schools, students in voucher schools, charter schools and home schooling almost invariably do at least as well, and usually better, by whatever tests are used.

One of the most hypocritical arguments against vouchers is that the amounts of money given to the students are insufficient to pay for an education in a private school. In reality, tuition at many parochial and other low-budget private schools will in fact be covered by half of what the public schools spend per pupil in many communities. But if those who make this argument are serious, they need only advocate larger amounts of money per voucher. But that is the last thing they will do.

The deck is stacked in favor of the public schools in other ways. Teachers' unions and the public school establishment are already organized for political combat in a way that voucher schools or charter schools cannot be this early in their history. The unions and the public schools are thus able to lobby politicians to impose restrictions and red tape on their rivals.

The education establishment wants the teachers in voucher schools and charter schools to be "certified" as having taken education courses, being unionized and surrounded with all the iron-clad job security that makes it an ordeal to fire even grossly incompetent teachers. Sometimes these restrictions and directives are justified in the name of "fairness," where similar restrictions and directives already apply to the public schools. But this "fairness" argument is completely invalid and misleading.

First, one of the main purposes of voucher schools, charter schools and home schooling is to allow alternative forms of education to escape the bureaucratic rigidities, faddish dogmas and massive red tape that have helped turn too many American public schools into educational disaster areas.

Second, "fairness" is a concept that applies to relations between human beings, not institutions. Institutions are just means to an end. Those institutions that do not serve their purpose -- for whatever reason -- need to give way to institutions that do.

This does not mean that public schools should be shut down. Rather, they should be forced to compete with alternatives, as other kinds of enterprises have to compete. Whether or not Kodak film is better than Fuji film, both are better than they would be if either had a monopoly.