If you swapped poor kids from a bare-bones Chicago school with wealthy kids from a fancy North Shore school, test scores in the Chicago school would go way up, proof that learning is not a matter of money. It is, rather, a matter of the kids themselves -- about how well prepared they are for school, how involved their parents are.

There is truth to this. Schools, no matter how well-funded, can't produce miracles if the kids don't show up or if they start years behind academically. But that doesn't mean money doesn't matter. Money does matters. It matters a lot.

That point is hammered home by a new study that adds heft to the argument that extra dollars can help boost test scores.

The researchers started by documenting what we all already know: Wealthier school districts spend more per kids than poor districts do. On average, the wealthiest districts spend $4,186 more per child than the poorest ones. Broken down by dollars that go to instruction, the differential is $2,324, according to the analysis by the Center for Tax and Budget Accountability.

The researchers then tied spending to achievement. Among elementary districts with few poor students, they found a correlation between extra dollars and higher state test scores. Affluent districts that spent up to $5,000 per student on instruction produced a mix of outcomes -- about half performed below expectations on state tests, half performed above. When spending approached $7,000, almost every district posted better-than-expected test score averages. The same pattern exists with respect to high-poverty schools, though it's more tenuous because there are only a small number of poor districts that spend $7,000 per student.

This analysis has its flaws. The researchers were unable to look at the most destitute districts and didn't analyze the link between high spending and test scores.

Nonetheless, the research makes a compelling case: Money may not be everything, but it sure helps.

In Illinois, unfortunately, poor schools will never get extra money unless the state reforms the way it funds education. The point was driven home last month when the Rev. James Meeks, who is also a state senator, led a student boycott in Chicago to highlight inequities in school funding. Meeks argued, rightly, that Illinois' heavy reliance on property taxes creates unconscionable disparities in the quality of education.

Districts with the fewest poor kids, for example, have fives times as much property value as districts with the greatest number of poor kids: $446,000 per child vs. $81,000, according to the Center for Tax and Budget Accountability.

The state is supposed to help make up the difference but doesn't come close. Illinois ranks near the bottom in state contributions to the overall cost of education. Illinois pays for 28 percent of the bill for education. Nationally, the average is 47 percent.

For years, advocates have called for a change in Illinois school funding, seeking additional state support in exchange for greater accountability. This new research adds yet another layer of support for that plea.