It's noon in the clean, spacious library of a Capitol Hill junior high school that till recently was known far and wide as "Horrible Hine," and about seven adults and nine students -- the regular Wednesday lunchtime crowd -- are doing math. The kids, like virtually all those at Hine Junior High School, are black and from low-income families. The tutors are mid-level bureaucrats from the Department of Transportation.

"Let's buy a car and figure out the sales tax, same as we did last week," says Tim White, a middle-aged Federal Highway Administration employee, to the two seventh-graders at his table. "Remember how it works?" At the next table, traffic management strategist Paul Scott and 12-year-old Joslyn Mabry go over geometry exercises and talk about some real-life uses for angles, such as surveying. Joslyn is a whiz; by the end of the hour they are playing around in advanced algebra.

The unlikely pairing between Hine and the DOT -- a school and a federal agency located some blocks and worlds apart -- is the showpiece of a three-year-old White House initiative called "Partnerships in Education," which links government agencies with local public schools in need of a helping hand. Where the program has caught on, as at Hine, it highlights the strengths of the voluntary, nonprogrammatic, unfunded kind of public assistance programs this administration has been trying to promote. Elsewhere, where the chemistry is less magical, the program is a reminder of the limits of such Reagan-style voluntarism.

At Hine, principal Princess Whitfield and DOT Secretary Elizabeth Dole have become close friends; the experience "has done more for us," Dole says, "than it ever could for them." More than 200 tutors show up regularly, including a Coast Guard contingent that comes marching into school every other Wednesday in full regalia. This month, as the school year winds up, the various DOT "modes" -- maritime, Coast Guard, highways and so forth -- are taking it in two-week shifts to introduce the kids to their lines of work through field trips, presentations and "career shadowing" days, when kids follow executives around the office.

All this happens without adding a single layer of bureaucracy -- even where money is involved. Perhaps the most satisfying detail of the partnership is the way it lets the normally strapped D.C. schools become government insiders: a DOT supplier guides a Hine science teacher to the government-surplus warehouses where the DOT, like all branches of the federal government, can get office supplies. Minor items like Xerox paper now come regularly from those warehouses, along with microscopes deemed obsolete and discarded by the National Institutes of Health, and some professional-quality spotlights, otherwise unaffordable, for the Hine auditorium.

Across the city's 30 such partnerships are fascinating if uneven variations on this pattern. The General Services Administration sent 40 painters over to spruce up the interior of McKinley High School; the Federal Trade Commission found internships for graduating seniors at Coolidge High School; the White House sent over used floral centerpieces so kids at Martin Luther King Elementary could visit local nursing homes with bouquets. Most also offer tutoring and public speaking programs, but in general the intangibles work best. "Most of our kids really did not have a sense that the adult world cares about them," explains school board spokesman Janice Cromer.

This emphasis on the intangible and idiosyncratic, as well as the lack of structure or oversight, means the programs vary widely in quality. The trouble is, the real benefits flow to strong schools already helping themselves. Hine was already making a name for itself, pre-DOT, as one of the District's dramatic turnarounds; once so bad as to be a byword, it is now well-disciplined, clean and popular, its enrollment steadily rising. Whitfield, a charismatic and irrepressible principal, credits DOT with all the changes. Almost everyone else on the premises credits Whitfield.

Those schools in worse straits tend to be more defensive, intimidated by the outsiders or at a loss for ideas. That makes the agencies diffident. The Federal Trade Commission, an enthusiastic "partner," chose Coolidge High School because, out of three choices offered by the school board, Coolidge "had the most on the ball," says FTC general counsel Charles Ware. Ware loves the work, but admits that "it takes a special kind of teacher" to get results: "It's best if they're already doing things that are creative." The Veterans Administration found its association with Eastern High School lagging till recently, when a new principal expressed interest in reform. Before that, says coordinator Mary Lou Dye, "there was really only one teacher we could even talk to."

Frills and furbelows offered voluntarily, in other words, are useful as long as nobody makes the mistake of counting on them; they don't replace more impersonal, cumbersome, but ultimately reliable school aid programs. Still, the extras, properly nourished, can deepen into fundamental change. Whitfield, in praising the DOT and Dole, comes back most frequently to the new worlds of possibility the DOT's visible presence opens up for her low-income kids. Adults leading hitherto unimagined lives take them on trips, take them to lunch, tell them what kind of grades will get them into training school for the merchant marine. At a Halloween party thrown by DOT volunteers last fall, the kids got full costumes, apple bobbing, a haunted house -- "things," says Whitfield, "that they'd only seen on TV." When school is a place where things like that might happen -- a place where it's worth your while to show up in the morning -- dropout rates have a way of going down.