CAN MORE MONEY buy better education for the nation's schoolchildren? In a speech yesterday, as at his most recent press conference, President Reagan made it clear that as far as he's concerned the answer is no--at least when the money is federal money and the schools are public. Mr. Reagan's views on this point are not beyond argument. But there is much truth in his comments about what makes schools work well for their students.

While the president is wrong in thinking that the total public education budget is "far greater than the defense budget," he is right in observing that financing education is still not primarily a federal responsibility. Despite substantial growth in federal aid, state and local taxes still account for the bulk spent on elementary and secondary education. In Mr. Reagan's view, localities have paid dearly for the meager financial help the federal government has provided.

Few would disagree that the federal government failed to provide much sound guidance on teaching practices in the permissive '60s and '70s. Neither did other parts of the education establishment. And enthusiasm for the novel equipment, innovative classroom layouts and creative curricula that federal money made possible often distracted attention from the dreary question of whether students actually learned anything useful.

Mr. Reagan also points correctly to success stories among inner-city schools as proof that money alone doesn't make the crucial difference. A good principal who elicits the best efforts of both teachers and students can work wonders in the most discouraging of settings and with the scantest of resources. Even with less talented leadership, recent experience has suggested that renewed emphasis on basic education can at least raise the average achievement of students to acceptable levels.

But some of those irritating federal rules that Mr. Reagan mentioned were needed to make school districts accept the responsibility of providing equal educational access to all the nation's children. It's easy to get nostalgic about the old red schoolhouse if you forget that most of the children it served never went on to graduation--and that some children never went to school at all. Nor would the "three Rs" have equipped most students to find a niche in a society that requires increasingly sophisticated skills even for routine jobs.

Over the last two decades the nation's schools-- prodded by federal guidelines and helped by federal money--have opened their doors to millions of students whose language, race or physical handicaps would have previously denied them entry. The pay- off shows up not just in heartwarming stories of individuals who have overcome incredible barriers on their way to educational triumphs. It also is revealed in the contributions of millions of graduates to this country's world leadership in, yes, economic productivity. The federal influence can't ensure success, but it can help make it possible.