What was going on when I was born?

FOR centuries, commercial fishermen along the shores of Long Island and Connecticut have shared the productive fishing grounds of Long Island Sound. But when Connecticut's State Department of Environmental Protection introduced a proposal last month aimed at resolving a highly controversial dispute among fishermen, the proposal and the dispute erupted into Long Island waters and onto the Island's multimillion-dollar commercial fishing industry. The dispute began two years ago in the fertile lobster nursery grounds west of Stratford, when two Connecticut fishing vessels initiated a new fishery in Long Island Sound - trawling for lobsters. The trawl fishermen, who tow a cone-shaped net over the bottom in search of fish, have always brought up lobsters as a bycatch from time to time. But the trawlers' pursuit in the Sound has been fish, not lobsters, which have traditionally been harvested from the pots of the lobstermen. The venture proved to be a success for the two lobster trawlers, which reportedly boasted a catch for a day's trawling of more than 1,000 pounds of lobsters. However, last fall the issue intensified as their efforts and their numbers increased.

The New York City Board of Education yesterday selected Deputy Mayor Robert F. Wagner Jr. to serve as the 14th chief administrator of the country's largest public school system. The vote, which followed a bitter two-month campaign that took on racial overtones, was 6 to 1 for Mr. Wagner, who was Mayor Koch's candidate to succeed Frank J. Macchiarola as Schools Chancellor. The seven-member board will meet Wednesday to adopt a resolution formally naming Mr. Wagner as Chancellor. It will also ask the State Education Commissioner to grant Mr. Wagner a waiver because the 39-year-old Deputy Mayor does not meet all the formal qualifications for chancellor as set down in state education law. Joseph G. Barkan, president of the board, announced Mr. Wagner's selection at a news conference after a morning of deliberations in private at board headquarters at 110 Livingston Street in Brooklyn.

GOVERNOR KEAN'S first term is far from its halfway mark, but ''testing the waters'' already has become the newest political ''in'' phrase. In fact, the New Jersey Election Law Enforcement Commission has scheduled a public hearing for May 11 to examine its proposed changes in the state's campaign contribution and expenditure regulations. The changes would allow ''testing the water'' bank accounts by potential opponents of Mr. Kean, should he decide to run for a second term in 1985. The term refers to the activities a potential candidate goes through before deciding whether to formally announce his or her candidacy. Among these are polling, traveling, attending conferences and distributing newsletters.

The space shuttle Challenger, bucking 18-knot headwinds, glided to a smooth landing here today for the successful conclusion of its first flight. Officials of the National Aeronautics and Space Administration hailed the virtually trouble-free performance of the nation's newest space shuttle on its five-day flight and moved to hasten its ground servicing for another flight in two months. Only such a rapid turnaround will make it possible for the agency to meet its commitments to fly four more shuttle missions this year. Previously, the shuttles have required four or more months between flights. 'A Superb Spacecraft' At a post-landing news conference, Lieut. Gen. James A. Abrahamson of the Air Force, an associate administrator of the space agency, called the Challenger ''a superb spacecraft.'' Only 22 anomalies were reported in the flight, as against 82 on the first flight of Challenger's sister ship, the Columbia.

Scholars have categorized ''All's Well That Ends Well'' as one of the Bard's ''problem plays,'' as puzzling as ''Measure for Measure'' and ''Troilus and Cressida'' yet less stimulating than either, and over the centuries actors and directors have remained faithfully aloof. ''A nasty play,'' wrote the eminent critic Sir Arthur Quiller-Couch, who edited ''All's Well'' in the definitive New Cambridge edition. Indeed, the first recorded performance of ''All's Well'' took place 125 years after its author's death, and major revivals since then can be counted on, well, a hand and a half. Enter the Royal Shakespeare company, which presented ''All's Well'' here in 1981 in a late-Edwardian setting that came complete with steam locomotives, goggled aviators, nightclub chanteuses, waltzing courtiers, bursting shells, Red Cross nurses, and much else that its author omitted to specify in his stage directions. And the result? The critics were mostly ecstatic and the houses were packed, first in Stratford, then in London. Now Broadway will have its chance to assess a production which, as it happens, comes from the same sharp and abundant imagination as the one principally responsible for ''Nicholas Nickleby'' and ''Cats.'' ''All's Well That Ends Well,'' staged by the RSC's Trevor Nunn, opens a 16-week engagement at the Martin Beck on Wednesday.

THE Island's big gambler is not a stogie-smoking sharpie in a pinstriped suit. He is more apt to wear blue jeans and carry his father's OTB charge account code in his pocket. ''The problem is rampant,'' said Elaine Brodsky, an expert on compulsive gambling who works for the New York State Office of Mental Health. ''A kid will become a runner for his bookie right in the high school in order to work off his own debts. He'll book bets from football, all sorts of sporting events. ''And it's not just the young people we're seeing in greater numbers,'' Mrs. Brodsky continued. ''More and more there are the elderly. I know of one older woman - a regular at Atlantic City -who stole her roommate's pension check. There are the housewives on limited budgets who don't tell their husbands they stock up on nofrills items at the supermarket so they can spend on lottery tickets.''

The Administration won big points last week in a running argument with Roman Catholic churchmen about the morality of its nuclear policies. A committee of bishops softened earlier support for a halt in production and deployment of nuclear arms, calling instead for a weapons ''curb.'' Joseph Cardinal Bernadin of Chicago said the new 150-page draft had been made ''more flexible'' in response to criticism but that it remained ''skeptical to the point of disbelief regarding the controlled use of nuclear weapons.'' The Cardinal and Archbishop John R. Roach of Minneapolis denied, however, that the group had yielded to White House pressure and said it still found much to fault in Mr. Reagan's policies.

CONCERNED about growing numbers of homeless people in Yonkers, three churches that established an emergency winter shelter system in February announced last week that they would extend the program indefinitely. The sponsors of the all-volunteer program, which feeds and provides beds for 25 to 50 people each night, had planned to close the operation Friday. ''I don't see any alternative for these people,'' said the Rev. S. Burtner Ulrich, rector of St. John's Episcopal Church, one of the shelter's sponsors. ''We started this program because the city of Yonkers was not doing anything,'' he said. ''We have all the problems New York City has but on a smaller scale.'' He added that the decision to keep the program going was made with the knowledge that this would require many more volunteers. The Sharing Community, as the nondenominational program is called, is sponsored by St. John's, St. Peter's Roman Catholic Church and the Yonkers Christian Assembly, a Pentecostal religious organization. It relies on a corps of 40 to 50 volunteers - students, firemen, the elderly, nuns and homemakers. Many are parishioners of the sponsoring churches but others come from several communities in the county and the Bronx.

LONG ISLAND's sandy soil and the construction methods used on many homes here have made Nassau and Suffolk Counties unusually vulnerable to termites and, according to environmental officials, to the kind of pesticide misapplication that they say led to the contamination of at least eight houses in the last 16 months. ''There's no question about that,'' said Joan Scherb, counsel to the Long Island office of the State Department of Environmental Conservation. ''We're probably the termite capital of everywhere, and when you have sandy soil and homes built on concrete slabs, you'll have problems.'' Concrete-slab home construction is an economical method that was used in Levittown and in many of the newer housing developments in Suffolk County. Basically, it means that the home is set on a slab and has no basement. But for reasons that are not fully understood, pesticides seep along the underside of the slab and, if there are holes in the slab for heating ducts, the chemicals can creep upward into the living areas.

More elementary school students are mastering the basic skills of reading, writing and arithmetic, but high school performance, especially by the brightest students, has deteriorated in recent years, educational researchers say. Data from local, state and national testing programs show that the gains have been concentrated among minority students, those from poor families and those who were the weakest academically. Moreover, they have been confined primarily to what educators call ''low-order'' skills, such as the literal comprehension of a reading passage, rather than ''high order'' skills such as interpreting an author's unstated purpose. Fewer High Scores Reported Meanwhile, despite an end last year to the 20-year decline in average scores on the Scholastic Aptitude Test, the proportion of high scores on these college entrance examinations is still much lower than it used to be. Students in the New York metropolitan area have followed the national pattern. Last year 51 percent of the pupils in the second through the ninth grades in New York City public schools were reading at or above grade level, in contrast to 43 percent in 1978. Statewide, however, the proportion of high school students making high scores on the S.A.T. fell at least 25 percent from 1972 to 1982.

More New Taxes? April 15 is not quite here, but even so, the betting is that Congress will approve a tax increase this summer. The outlook hinges on whether the Senate will pass a budget resolution, not yet a certainty. If a tax bill does go forward, Congress is expected to seek to raise about $10 billion to $15 billion in the coming fiscal year, or as much as $80 billion over three years. ''Even the White House has conceded the obvious - that there has got to be something to take care of the deficits in the far out years,'' commented Robert S. McIntyre, director of Federal tax policy for Citizens for Tax Justice. Negotiations will start in earnest once the budget resolutions are complete. The guessing is that the House might aim to put income limits on the third year of the personal tax cut, which might raise about $7 billion, and try to institute selected tax proposals to make up the difference. The House is also expected to vote to repeal tax indexing, or at least modify it. The Senate is expected to leave the personal tax cut alone, and concentrate on new excise or import taxes on oil and on further measures.

ONE afternoon last summer, the host on radio station WPKN-FM in Bridgeport began what was nominally a jazz show. First he played a series of singles by James Brown, the soul singer. Then he read a selection of newspaper editorials about the Israeli invasion of Lebanon. Only then was it on to Duke Ellington. The show was vintage WPKN, typical of the eclecticism, range and freedom on the station of the University of Bridgeport. At WPKN, a station without either advertisers or a network affiliation, radio remains a passionately individual affair.