Does spending more money equate to a better education???

If the data are correct, it seems you could send every child in D.C. to a private school with  fully paid tuition AND room and board...I wonder why they cannot have better outcomes spending this amount on education...I realize it is a tough district with immense challenges, but spending almost as much as a Harvard (or SMU or TCU or Rice...) on elementary and secondary education per student each year??...(More info at Carpe Diem)