All over Fairfax County there are people who hate sidewalks.

Two years ago along busy Burke Lake Road a half-mile path was built linking the Kings Park public library, shopping center and housing development with the 4,100- pupil Lake Braddock Secondary School. It quickly became one of the business sidewalks in the county, constantly jammed with students, bistantly and skateboarders. Families are still fuming about it.

The county is about to build a one-mile sidewalk near the 3,500-pupil Hayfield Elementary and Secondary Schools, along Telegraph Road - a high-speed, narrow, two-lane commuter route. It will replace what now is a weed and trash-filled ditch. Many parents in nearby subdivisions are outraged.

It's not the sidewalks themselves, it's what they mean, says one angry woman.

"A sidewalk here means our children will have to walk to school instead of being bused. Telegraph Road is a dangerous road and we don't want them walking along it, even on a sidewalk," she said.

Othe parents say it's not a question of safety; they just don't want their children walking to school. They like the convenience of having them bused.

An equal but les vocal number of families, including many students themselves, think sidewalds not only are "great," but much safer than walking along the dirt shoulders of Telegraph and Burke Lake Roads - which many children have done for years.

The innocuous sidewalk has become increasingly controversial as the county attempts to cut down on the escalating $7 million a year school busing bill by requiring more children to walk to school.

For all the complaints it has generated, the sidewalk building program is small and slow. The Telegraph Road sidewalk was the school system's number one priority project in fiscal 1974, though it won't be completed until next spring. Of the $1 million in sidewalk projects proposed that year, only $250.000 worth of work was funded by the county board of supervisors. The $250,000 amount has become almost the standard annual sidewalk appropriation.

The savings and benefits of the sidewalks are significant, said school officials.

The Telegraph Road sidewalk, for example, will cost $53,640 and save an estimated $100,000 to $125,000 a year in busing costs because as many as 200 children who are now bused will walk. It also will be healthier for the children to walk, school officials said, and the sidewalk will provide the county with a paved hiking and biking path, lined with grass and trees instead of trash and weeds.

The Burke Lake Road Path forced about 650 students out of buses and onto sidewalks and is savung the county well in excess of $200,000 a year, school officials estimated.

A short, recently built sidewalk in the Camelot subdivision in Annandale is saving the county an estimated $83,000 a year, by enabling about 200 students to walk instead of bus to school, officials said.

At the crux of the issue is the traditional school regulation that stipulates that elecmentary pupils living within one mile of their schools, and secondary students (7th-12th graders) living within 1.5 miles, will walk to and from shcool if there is a safe route - meaning sidewalks and no major highways to cross on foot.

More than 82,000 students daily ride the county's 651 school buses - about 60 per cent of Fairfax's 132,500 students. Thousands of those bused lived less than a mile from their schools but are issued bus passes because there still are no sidewalks near their schools, officials said. Sidewalk construction has forced several thousand students out of buses in the past few years, but the bus fleet has remained about the same size because of new state laws on the haniicapped. The county now provides 128 school buses for the handicapped, compared to only 30 four years ago.

Most school systems have similar school walking regulations. In Arlington and Alexandria, which have sidewalks almost everywhere, virtually all children walk to nearby schools. Montgomery County last summer even increased the walking distance for its secondary school students from 15 to 1.75 miles.

The distance walked is the cause of many complaints, especially in cold and wet weather. One Kings Park resident, Pat Collier, who said "the 1.5 mile boundary form Lake Braddock School starts in my backyard" at 5417 South Hampton Dr., complains about the way the school system measures distances.

"They say it's 1.5 miles to the edge of the school property. But then it's at least 1.7 miles to the school door and my daughter's in a sub-school which is half a mile away. So she actually walks 2.4 miles each way. It's too far," she said.

Twelve-year-old Danny Goodsite, a seventh grader at Lake Braddock, who lives several houses away from the Colliers, said thatr "the walk's all right. We all walk together and we just wear a lot of clothes to keep warm."

In the Wellfleet and Hayfield Farm sub-division off Telegraph Road some residents are ecstatic about the coming sidewalk. "I'd love to see it. People now throw cans at the children and try to run them down when they walk along Telegraph Road," said Mrs. Robert Ferry, of 5818 Helmsdale La. One of her three teenage boys, Bob, a senior at Hayfield, said "I'm a runner and both the cross country and track teams run along Telegraph. So we'll be glad to have a path there."

The U.S. Coast Guard, which has given a half mile easement to the county along the front of its Telegraph road property, also favors the sidewalk because "a number of our people live nearby and walk to work," said Lt. Commander Robert Stracener, the base executive officer.

Several families said they would favor the sidewalk if the 45 mile-and-hour speed limit on Telegraph Road were reduced near the school, and idea the Virginia State Department of YTransportation is considering. Others have said they would like to see some kind of fence or barrier put up to separate traffic from children using the path.

But a few were absolutely opposed. "The sidewalk? Hell, on, I don't want that thing," said Russel Yim, who lives on Dunsmore Lane about 1.5 miles from the Hayfield schools. "I have a daughter in the seventh grade and I'm afraid for her with that 45 mile-an-hour traffic right beside it."