Can all the goals of a 3rd grade education system be reduced to a purely mechanical list of stuff?Yes, I would hope that a multi-million dollar enterprise can clearly define their goals.
What are the goals? To get children to read individual words? Or to get children to read a sentence, and obtain meaning from it?
I don't know off the top of my head whether the latter should be learned by 3rd grade. Ultimately setting the goals of our educational system is up to the various bureaucrats in the school system.
However, regardless of what the goal is, you still haven't given an way to game the system apart from "teach kids to read [words/sentences]".
While schools may not have stopped teaching students to read they have cut out other parts of the curriculum to focus on what's being tested.
Indeed - if the school system is not achieving their primary goals, they should cut secondary goals and focus on the primary ones. That's a good thing.
Do you spend extra time and money on the few strugglers (some of whom are going to fail whatever you do), or do you concentrate on the majority (and get most of them through the test and thus look good)?
This depends on what the goals of the school system are. If you want to ignore the strugglers, set the goal to be maximizing this function:
student_scores.max()
If you want to help the strugglers and ignore the strivers, choose this one:
student_scores.min()
Choose this one if helping a struggler is equally important with helping a striver:
student_scores.mean()
This one is like the previous, but strugglers get a bit of extra weight:
log(student_scores).mean()
Setting a goal merely forces you to acknowledge possible tradeoffs and decide which ones should be made (if the need arises).