What was going on when I was born?

Weakened by sagging demand and lower oil prices, the Exxon Corporation's net income rose 6.9 percent in the fourth quarter, while that of the Standard Oil Company of California skidded 25.6 percent, the companies reported yesterday. Both had lower earnings for the full year, and cited in part the costs resulting from their obligation to purchase oil from Saudi Arabia at that country's benchmark price of $34 a barrel for Saudi Light crude at a time when others were selling similar crude oil at lower prices. Exxon and Socal are partners in the Arabian American Oil Company, or Aramco, which produces Saudi Arabia's oil and markets most of it. The four American companies in the partnership - Exxon, Standard Oil, Texaco and Mobil - are committed to purchase Saudi oil at $34, although the price of Saudi Light oil on the spot, or noncontract market has fallen to as low as $28 a barrel. The companies process the Saudi crude and market the resulting petroleum products. Profits have been squeezed by falling retail prices for these products.

The day belonged to Karl Lagerfeld, though there was plenty of other excitement on the couture fashion scene as the spring and summer openings here continued. The German-born designer, who has been living in Paris since he was in his teens, had dared to tackle the House of Chanel - a national monument with which one does not trifle. Mr. Lagerfeld didn't trifle. Chanel clothes are the most long-lived of the 20th century. Gabrielle Chanel's styles began attracting attention after World War I and have continued ever since. They seem to have been frozen in time, but changes have not been received kindly.

New York State's Education Commissioner said today that his department was beginning to study a plan to start children in school at age 4 and have them graduate after completing the 11th grade. Under the plan outlined by the Commissioner, Gordon M. Ambach, children would enter kindergarten at 4 and the first grade at 5, a year earlier than the present system. They would graduate from high school, presumably at age 16, and then could go on to college. If enacted, the plan, which would apply to public and private schools, would begin no sooner than the mid-1980's and would be phased in over 10 years, Mr. Ambach said.

International Revised Roman Catholic canon laws were signed by Pope John Paul II. They incorporate many of the changes brought about by the Second Vatican Council, the historic ecumenical meeting that was held in the 1960's under the auspices of Pope John XXIII. The code will not officially take effect until Nov. 27, but most of the changes have been put into practice by Roman Catholics around the world. (Page A1, Column 3.) A Turk wanted in Italy for complicity in the shooting of Pope John Paul II says he has never met the man who shot the Pope in 1981. But the suspect, Bekir Celenk, said in Sofia, Bulgaria, that he had been in Bulgaria at the same time that Mehmet Ali Agca, the Turk convicted of shooting the Pope, was reportedly there. Unconfirmed Italian newspaper reports have said that Mr. Celenk offered Mr. Agca $1.25 million in German marks on behalf of the Bulgarian secret service to shoot the Pope. (A1:1.)

As the recession winds down, the statistical indicators are telling a tale of an economy that, broadly speaking, suffered less in the period since July 1981 than during the 1974-75 recession, the worst since World War II. But by some narrower measures, the toll that the latest downturn has taken on an already battered economy has been much worse. From the fourth quarter of 1973 to the end of the first quarter of 1975 -the duration of the earlier recession -the inflation-adjusted gross national product dropped 4.9 percent. The comparable figure for the recession that began in July 1981 and that economists now assume ended in December is a decline of 2.9 percent. Industrial production, which sank 15.1 percent in the 1974-75 downturn, has fallen a more modest 12.5 percent this time.

THERE are times when Pierre Franey and I, having sampled a dish in a restaurant, will attempt to reproduce it at home. These endeavors tend to have an especially gratifying quality; I think it comes both from the sense of accomplishment that results when using your own judgment in the kitchen and having the dish come out properly and from being able to duplicate a well remembered experience. If the meal in the restaurant was uncommonly good, I find that I become almost nostalgic when I successfully re-create it in my kitchen. Another aspect of this kind of cookery, of course, is the challenge. All serious cooks enjoy testing their mettle, and what better way to do so than against the chefs of fine restaurants? To choose one example, Pierre recently produced the details of a dish he had at L'Ermitage, a restaurant in Los Angeles. An appetizer, it was a terrine of langoustine and/or shrimp that he considered ''absolutely delicious.'' It was also easy to prepare. You begin by simply sauteeing some of the seafood in butter and the remaining uncooked seafood is pureed with heavy cream and then blended with the cooked. The mixture is then baked in a loaf pan and served hot or cold with or without a green sauce.

Schools Chancellor Frank J. Macchiarola yesterday afternoon proposed a plan to prevent the threatened layoff of 1,800 New York City schoolteachers and cuts in busing for pupils in kindergarten through the fourth grade. The plan, which was approved last night by the Board of Education, would raise the price of a school lunch by 5 cents and end the use of bus passes for many fifth and sixth graders. The package assumes the board will receive an additional $9 million from the State Legislature and $13 million from the city. In Albany, the State Education Commissioner, Gordon M. Ambach, and Assembly Democrats said they were in favor of the plan. But in the Republican-controlled Senate, James L. Biggane, a key fiscal aide, said the package had been referred to the Senate Education Committee. Senator James H. Donovan, Republican of Chadwicks and chairman of the committee, said he planned to table the package for the moment.

President Reagan, pressing his theme that ''America is on the mend,'' urged the new Congress in the State of the Union Message tonight to support a broad freeze in the growth of domestic spending programs. He also asked it to allow military spending to continue to rise sharply. Appealing for a ''bipartisan spirit'' in approaching the nation's economic problems, Mr. Reagan declared that President's message is on page A14; Democrats' comment, page A16. Federal deficits threatened to rise to $300 billion in the years ahead and posed ''a clear and present danger to the basic health of our Republic.'' Bid for Sustained Recovery ''To assure a sustained recovery, we must continue getting runaway spending under control to bring those deficits down,'' Mr. Reagan said. ''If we do not, the recovery will be too short, unemployment will remain too high, and we will leave an unconscionable burden of national debt for our children. This we must not do.''

The United States Steel Corporation, the nation's larget steelmaker, reported yesterday that it lost $363 million in the fourth quarter and $361 million for all of 1982, the largest one-year loss in its history. The losses were attributable primarily to the weak performance of the company's steel operations, which suffered, like others in the industry, from one of the lowest levels in demand for steel since World War II. U.S. Steel's latest figures contrasted with earnings of $101.8 million, or $1.13 a share, in the fourth quarter of 1981 and $1.08 billion, or $12.07 a share, for all of 1981. Sales in the latest quarter were $4.3 billion, up from $3.3 billion a year before, while sales for the full year totaled $18.9 billion, up from 1981's $13.9 billion.

''To assure a sustained recovery, we must continue getting runaway spending under control to bring those deficits down.

Democratic leaders in the Senate and House said today that any delays in Social Security benefits should be linked to changes in the tax cut scheduled for July, which they said favored the wealthy. Their comments cast doubt on the fate of a bipartisan compromise on financing Social Security that won the backing of President Reagan and Thomas P. O'Neill Jr., the Speaker of the House. The legislators' statements also seemed to undermine the call for a spirit of bipartisan cooperation that was a major theme of Mr. Reagan's State of the Union Message tonight. Democrats listened impassively to most of the President's speech, but gave him a standing ovation, by prearrangement, when he said, ''We in Government must take the lead in restoring the economy.''

Union County began fingerprinting schoolchildren today. Concerned about the thousands of children around the country who disappear each year, county officials set up the program to establish a record to help in the search for any missing youngster, and to identify him once found, alive or dead. ''Too many children are missing and never identified,'' said John J. Troiano, a county Undersheriff. ''Too many parents go through life never knowing what happened to their children.''