IN THE polarized city of Cambridge Francis X. Hayes has the best of both worlds. He is a student at the Harvard School of Education, taking courses in teaching mentally retarded children. He is running for school committee and his campaign manager graduated from Harvard last year.

His university ties, however, came late in life, and basically he remains a Cambridge resident, a "townie." He grew up in the poor part of the city, the son of an Irish welder. Following what has become an almost cliched Irish-American script, he went to St. Mary's High School here and took his orders as a Benedictine monk. When his father died in 1966 he left the priesthood and turned briefly to business before entering politics. He is presently Chairman of the Cambridge Model Cities program, one of the most successful in the nation.

Those are the bare facts, but as I followed Francis around the coffee circuit which is the backbone of local politics, it became clear that what looked good on paper was better in person. I suppose the word is smooth, or polished, but he really isn't. What he is is good with a wide range of people. From the eighty year old ladies on Brattle Street to the young blacks in the city he has a feeling for what people respond to and he gives it to them.

This ability to get along with so many different kinds of people isn't necessarily a blessing in Cambridge. For instance, Francis has the endorsement of the Cambridge Civic Association, the local good government society. In the Brattle Street area where City Councilors like Tom Mahoney and Barbara Ackermann get their votes this endorsement is a help. But down in East Cambridge, the home of Al Vellucci, CCA is a dirty word.

Hayes will need support both from East Cambridge and from Brattle Street to win. In the Proportional Representation (PR) system under which Cambridge operates, however, this may be a difficult combination to muster, for above all Hayes needs number one votes, the rest don't mean much.

Under Cambridge PR, a voter ranks the candidates in order of his preference by writing 1, 2, 3, etc. next to their names on the ballot. The number of votes needed to be elected is determined by dividing the total number of votes cast by the number of candidates plus one and then adding one to the quotient.

If a candidate has enough number one votes (called bullets) to be elected, his surplus ballots are redistributed according to the "number two" choices marked on them. If no one has enough number one votes for election, and few ever do, the candidate with the fewest number ones is eliminated and his ballots are redistributed.

In the School Committee election the process of counting ballots often lasts a week. Hayes plans to spend most of that week trying to calm his nerves and recover from the campaign.

ONE WAY of getting around the problem of a split constituency would, of course, be to say different things to different groups. Hayes doesn't. He doesn't ever vary his appearance-longish hair and bell bottoms. "They told me I would gain 500 votes if I cut my hair," Hayes said.

The reality of the campaign is that Hayes is trying for a Committee where two vacancies are opening up. Both were held by men who are now running for City Council. One was held by a black, Gus Solomons. Hayes is counting on a big black vote for him, for there are no other blacks running and Hayes has a good record in dealing with racial problems. Other minorities are for him too, including the Spanish-speaking people in Cambridge who seek a program for their children to learn Spanish and Latin American culture. This is one of the main planks in Hayes' program.

Much of his program is directed toward returning some kind of balance to Cambridge's schools. The tracking system is a favorite target. Cambridge school children today are in effect told in the eighth grade whether they will take the college curriculum or the business courses, which means that they won't go to college. Like most tracking systems (Washington, D.C. among other cities has one) this hurts the poor. In addition the quality of Cambridge schools varies greatly depending on what area they are in. Upper city school libraries have eight books per student while lower city schools have three.

"I would like to open the tracking system," Hayes says. "The inequities are largely because the School Committee is generally used as a stepping stone to higher political office, and members are reluctant to step on too many toes."

HAYES has a lot of ideas about how the school system can be opened up. He would like to try an Advancement School modeled on the system now in use in Philadelphia. This type of school in largely designed to fit the students. "The whole idea of passing and failing is absent in the Advancement schools. You are in this environment not to pass or fail but to acquire skills. Individuals proceed at their own pace." Hayes says that this type of school would go a long way toward reducing the dropout rate in Cambridge, which in some high schools is as high as 60 per cent.

The Advancement School is one of several innovative ideas Hayes has for Cambridge. But he insists that such experiments must be carried on under the strict supervision of the city. "I don't mind outsiders coming in if they want to help, but I don't like the idea of them using our children purely for experiments," he says.

The concept of outside agencies helping the city with education is part of Hayes' program, however. "My first term in office would be spent initiating an outside evaluation of the schools and establishing where we are at. Then we must decide for ourselves where to go."