When Proposition 13 forced California to cut its high school day from six periods to five, a group of annoyed parents here hired Redlands High School teacher Don Dewees to teach a special summer biology course for their childrren.

"They asked me if $500 was enough to buy all the supplies and equipment I would need," Dewees said. "I was just flabbergasted. That is about as much as I get to teach five classes of biology all year long."

After three years of Proposition 13, California's great experiment in massive, forced tax reduction, some citizens here have begun to look for ways to bolster sagging public services.

In places like Redlands, people are taking money out of their own pockets. In others, they are searching for outside contributors who might help ease what is a growing fiscal crisis in the nation's most populous state:

San franciso, an older city with a declining population and heavy demands for public transportation and health services, is trying to squeeze every possible dime.

It doubled the bus fare to 50 cents, began charging visitors to the Japanese Tea Garden and the zoo and solicited corporate donations ($1 million from Chevron, $1 million from United Airlines) to save the cable cars.

In Hillsborough, one of the wealthiest towns in the country, city officials took the extraordinary step of asking for $200 from each household in voluntary contributions and raised nearly $500,000 of the $850,000 needed to offset Proposition 13's first big bite.

"Since many were enjoying at $1,500 to $4,000 tax cut, giving back $200 didn't seem so bad," said City Manager Robert M. Davidson. Later, 75 percent of the town's voters approved a new special tax on property owners to fill the revenue gap.

In Beverly Hills, the city raised several business license taxes just before Proposition 13 struck. Financial administration director Don Oblander said the city now receives nearly 60 percent of its income from hotel, rental property and other such taxes.

San Diego, faced with a possible $8.5 million deficit next year, plans to eliminate street cleaning and tree triming and sharply cut park and library services.

Lawmakers and city administrators warn that real and painful budget cuts are only beginning as the state surplus, which has cushioned the blow of Proposition 13, finally disappears.

With the state due to lose another $2 billion in federal funds under the proposed Reagan administration cuts, officials in Sacramento and in other large California cities say voters will have to decide if they really want to live with fewer police, parks, teachers and public buses or if they will pay more local taxes for them.

So far, most Californians seem to have lost none of the anti-tax fervor that led them to pass Proposition 13 in 1978. The statewide proposal cut real estate taxes to no more than 1 percent of market value and prohibited localities from raising the tax more than 2 percent a year or passing most tax increases without a two-thirds' popular vote.

A recent ballot proposal in Oakland to raise an average homeowner's tax by $50 won approval from only 45 percent of voters, even though the money was earmarked to hire more police in a city whose crime rate may be the state's worst. Officials in Los Angeles worry now about the chances of a similar proposal on next Tuesday's ballot.

Mervin Field's California poll, taken last fall, showed that 78 percent of state residents thought state and local taxes were still somewhat or much too high, compared with 70 percent who felt that way in 1977.

Like the Redlands High School parents here, Californians now show growing concern about education cuts. About 53 percent in the poll said that was the wrong place to reduce the budget. Smaller percentages of residents also opposed police and fire service cuts, while majorities favored holding the line or cutting back spending for business regulations, highways, state parks and welfare.

The burden of Proposition 13 has not fallen as heavily on suburban communities, particularly those with large shopping centers that bring in sales tax revenue. The city of San Fernando, north of Los Angeles, felt little pain, city officials explained. Money the city lost in real estate taxes returned to the city coffers, when taxpayers took their real estate tax savings and spent them at a local shopping center.

Under Proposition 13, "user fees" are the only ready source of new income that does not require voter approval, but some San Francisco officials, for example, think their well may now be going dry.

"Next year the state surplus is all gone, and that is going to be it," said Mel Wax, press secretary to San Francisco Mayor Dianne Feinstein.

The city plans to cut its government work force of 24,000 by about 1,000 next year. "I think we are going through a very difficult period," said Assemblyman Leo McCarthy. "Government leaders will be forced now to make some changes that they should hve made some time ago." But eventually, he added, something will have to be done to loosen the restraints of Proposition 13.

Asked about voluntary citizen funding like the biology class in Redlands or San Francisco's "adopt an animal" program at its zoo. McCarthy was skeptical of their impact. "You can count the number of times things like that have occurred on one hand," he said.

Kenneth Carpi, an assistant to San Diego Major Pete Wilson, said private groups have only been able to pick up funding for very small items such as the cost of putting stickers with police and fire telephone numbers into water bill envelopes.

What comes next is in doubt. Some organizations, like the California Taxpayers Association, suggest that local governments still have not eliminted inefficient operations that waste tax dollars.

Officials like McCarthy, although applauding reasonable trims in spending forced by Proposition 13, still say that "Some point soon people will say these particular services are important and we will pay for them with new taxes."