I agree with you that the way we teach school is completely ridiculous, but 58 seconds for _preschool_ on math is probably fine. Ages 3-5 are really about learning how to socialize, play and interact with the world, and it isn't until about age 6-7 when many kids even develop an aptitude for mathematics. Scandinavian countries use a concept called "Readiness to Learn" and don't teach reading or mathematics until age 7. Your children will likely be much better off playing and being kids in pre-school and learning things like how to sit still as well as fine motor control.

That said, yes, public schooling is insane. We pile children into classrooms and then expect them to all learn the same subjects at the same rate. We grade them based on arbitrary deadlines and we force them to learn more complex topics without making sure that they have mastered basic concepts. How someone can get an 'A' and not know 10% of subject matter is beyond me. Oh, and in the US we force all children into the schizophrenic "No Child Left Behind" program which encourages teachers to only teach to tests administered at arbitrary times.

In any kind of reasonable system, children would be able to learn at their own pace, and wouldn't advance to more difficult subject matter until they had achieved 100% mastery. Montessori teaching has elements of this, but I think it will really take new tools like Khan Academy and "flipping the classroom" to make it practicable.