The Argument:
- Premise/Background: Debate has centered on financing; many claim more money improves performance.
- Main Claim: The only way to fix school systems is to inject new ideas and new approaches.
- Supporting Claim: Schools are organized to benefit adult employees rather than students.

The argument dismisses the role of funding and asserts that only new ideas/approaches can fix schools.

The Task:

We need to find the option that most weakens this argument. That means we're looking for evidence that:
- Funding does matter, OR
- New ideas/approaches are not the only fix, OR
- The supporting claim is false.

Evaluating each option:
(A) Schools that have instituted "new approaches" attract the best performing students.

This actually strengthens the argument? Wait - it says schools with new approaches attract the best students, implying the new approaches didn't cause improvement; they just drew in already high-performing students. This weakens the causal claim that new approaches fix schools - the improvement may be from selection bias. This is a solid weakener.

(B) Schools without outside playgrounds have lower levels of student performance than schools that do.

This is about facilities/funding perhaps, but doesn't directly address the "new ideas vs. money" debate. Physical facilities could be funded by money, but the connection is indirect. Weak weakener at best.
(C) Studies show that student performance corresponded most directly with the education of the students' families.

This suggests neither money nor new approaches are the main factor - family background is. This weakens the claim that new approaches are "the only way," but it equally weakens the money argument. It doesn't specifically undermine the argument's preference for new approaches over money.
(D) School employees, by an overwhelming margin, said that the system performed well.

The argument claims schools benefit employees over students. Employee satisfaction doesn't mean the system serves students well - it might actually support the argument. Employees thinking the system works doesn't weaken the claim.
(E) Researchers in education have shown that students from school districts with high per-capita spending tend to receive higher scores on standardized tests.

This directly attacks the argument's dismissal of money. If higher spending correlates with better outcomes, then money does matter - contradicting the claim that only new ideas work. This is a strong, direct weakener.

Comparing (A) and (E):
- (A) weakens by suggesting the apparent success of new approaches might be illusory (selection bias). This undercuts the evidence for new approaches but doesn't directly rehabilitate money.
- (E) directly shows that money does correlate with improved performance, which contradicts the argument's central thrust - that funding isn't the solution and only new ideas matter.

(E) is the more direct and powerful weakener because it attacks the core premise: that money doesn't fix schools. If money does correlate with better outcomes, the argument's dismissal of financing is undermined.

Answer: (E)

I picked A first, but then I realized that E is stronger.

A: new approaches draw better student so its a selection bias not something that could magically improve student academic performance
E: this explain the money and performance correlation, it is more direct. So if I had to choose only 1 answer then E seems to be the stronger one.