IF American public schools generally are having trouble financing improvements and reforms, schools on Indian reservations in the United States have a special problem. They are dependent on the federal government at a time when that source of funding is being squeezed off. Maintenance of very old buildings is the most pressing concern. According to reservation school officials and congressional staffers, a slowdown of federal appropriations over the past 10 to 15 years has produced a maintenance backlog of more than $500 million. Tribal authorities have little ability to issue bonds to raise added funds for school improvements, as would public school districts elsewhere. What about income from much-publicized (and unfortunate) Indian-run gaming operations? The relatively few tribes that have substantial gambling earnings are required by law to use that money for civic purposes, including schools. But the needs on reservations include a wide range of major items - sewers and jails, for example, as well as classroom buildings. And many tribes, including those on some of the largest Western reservations, have neither the geographical location nor cultural inclination to move heavily into gambling. Over the long term, supplemental funding for Indian education may have to be found. But for now, the monies channeled through the Bureau of Indian Affairs (BIA) should be sustained at a level that can start to erase the maintenance backlog at deteriorating reservation schools. Sadly, trends are in the opposite direction. The per-student spending on reservations is already far below the prevailing level in most surrounding communities. This year the US Senate passed a budget that whacks an added $31 million off BIA funds for school repair and construction. Behind these figures lies a bitter history of broken promises by Washington. In few areas of federal spending can a better argument be made for commitment and follow-through.