Teach: students may contract to learn *stuff* from someone who is (or claims to be) knowledgeable in the field. Students may require their teachers to be certified in a particular way, as assurance they will be useful teachers. I've also seen educators offer to re-teach any course for free, assuming only those who fail the test, but believe they can do better, will take them up on the offer; it's a good selling point for the students.
Test: students may contract to be tested on their knowledge in certain fields. The testers do not need to be related to the teachers, the results do not have to be shared.
Certify: students may go slightly further and be tested with the intent to receive certification from an entity with authority to do so (or otherwise, if inclined to spend money for naught.)
[Update 2007/08/26] Mr. Hanchey suggested at lunch that he sees a difference (not yet actualized) between the entities that provide and score standardized tests, and the entities that take those scores and turn them into actual diplomas, "those who provide credit for the scores". He sees a market emerging where students will take tests, then shop around to find the entity giving them the most useful credit for their scores. [End update] I'm not sure it makes much difference in the end whether one entity evaluates your score and a employer evaluates that entity, or the employer evaluates the score directly; it seems to me it all comes down to the employe evaluating the test/score combination.
Logo: entities such as the BetterBusinessBureau may offer a logo program by which they not only certify that an entity has met their expectations, but they require (by contract with that entity) that they continue to do so. If you're disappointed in the performance of the certified entity, the certifier actually has a legal recourse to bring them back into compliance. This concept could be extended to all professional certifications, or even schools (students would promise, and be legally required to, keep up with continuing education for the rest of their life?)
Payback: if students feel they have not passed tests for no fault of their own, but rather because they were improperly educated, they are the ones who, having paid for the teaching, should complain (and sack) the teachers.
Public schools: if our government wishes to impose minimum education standards, we should be free to attain those standards by any means at our disposal, so long as we can pass the tests (be certified) to the satisfaction of the government. It makes sense, on some level, that the government should provide for free what it requires its citizens to accomplish (under penalty of law) but the act of providing a minimum service does not imply that it should be the sole provider of that service.
National testing: if the government instead wishes to provide a minimum education (for the good of the people) it should be optional; student tests reported to the government would serve only to verify that the teachers, though probably also tested themselves, are effectively communicating what they are expected to communicate. These national tests would be tests of the teachers' abilities to teach, via the students, rather than tests of the students. It's possible that students would refuse to take the tests, or refuse to perform to their potential on those tests, and the government would have to take that into consideration when deciding how these results reflected on the teachers. The basic decision needs to be made on whether public schools are required to provide a service, or required to effect a result.
Attendance: generally speaking, there is no reason for teachers (or others) to require attendance; it is up to the students to pass their tests; if attendance helps them, it is in their best interest to attend, but it is no business of teachers or schools. Schools need not be day-care centers. If parents have children who do not need to attend school to learn, but they do not wish to leave them at home by themselves, they should be free to send their kids wherever they deem best.
Teaching for the test: it is perfectly appropriate for teachers to provide tailored education to help students pass specific certification tests, if that's what the students wish to have; if the government or the market wish to impose minimum standards of education, the certification tests used should accurately reflect the education desired. If teachers "teaching for the test" do their jobs correctly, students will in fact have achieved at least the minimum desired education, fulfilling the purpose of the certification. In other words, "teaching to the test" is only a problem if the tests are incorrectly designed. (c.f. "unit tests" and "regression tests" in software engineering.)
Government-mandated minimum: it seems to me that the only education that truly concerns the government is probably that of laws -- citizens, before coming of age and graduating into being responsible for their actions, should learn as much about the laws as possible. You're expected to know the law (ignorance is no excuse), and as government is all about making sure we get along, law is its primary concern. Somehow, law seems to be the least-taught thing at schools, why? My civics classes have mostly included "how to vote". Law classes in highschool are more like journalism classes -- self-taught, discussion-oriented classes. Perhaps we could even require that children pass a civics test (but about laws proper) before they can become responsible adults, a true (if boring) rite of passage. (c.f. concept of age of consent.)
[I realize I haven't included any reasoning in this, and I don't care tonight.]