Contrawise, if you do have a standard test, then how do you avoid the (very natural) desire of all concerned to make sure the students pass?
I'm 50 years old, so it's been 30+ years since I was in high school. But *even then* math was never taught. *Arithmetic* and *Algebra* were taught, by rote, you do A, B, and C and you get the right answer.
It took me 25 years to learn that's not mathematics. I'm a *programmer* and always dismissed "programming=math" because I never knew what math truly was. Only when I started noodling around with the reasons behind division by 0 being impossible, and threw everything out and started asking questions like "what is a number, really?" and "when it comes down to it, what is division actually doing?" that I started doing actual mathematics.
Simple math, mind you, foundational stuff. Which immediately lead to propositional calculus, multivalued logic, and all the other eldritch horrors that lay below the Math We Know.
But none of what I learned was ever on the standard tests. In programming terms it's the difference between learning to program in a high level language and writing a compiler.
Yet I've learned more about math in 5 years than I did during my entire school attendence. Some of it *very* useful, some, well, not so much.
So now what? Teach to the test? Teach "useless" fundamentals? We're trying to stuff so much data into their heads so fast they don't have any time to get good at anything. Adding fundamentals is just more data, how do we get them to make the connections? Because without those connections it's just a sea of facts they're going to drown in.
This isn't a simple issue, so blaming "no child left behind" doesn't help anything. Sure, the system sucks. So did the one it replaced.
Question is, what's the right way?




