Americans have begun to lose faith in an idea that is as old as the republic: that their children will be materially better off than they are.

Nothing has been more a part of the American dream than the belief that hard work and struggle will result in rewards for future generations. Wave after wave of immigrants have come here with that in mind, and many still do.

But in a very brief period--hardly more than three years--that belief appears to have been dashed, and in its place a philosophy of lowered expectations is taking hold.

According to Washington Post and ABC News poll findings, fewer people each year expect their children to do better financially than they have done, and more expect them to do worse. Whether spurred by the zooming costs of a college education, by high unemployment or by other factors, the trend has been dramatic.

Question: "Thinking of your children when they get to be your age, would you say they will be better off financially than you are now, not as well off, or what? "

In November, 1979, when The Post first asked that of a national random sample, the economic picture was not exactly favorable. Inflation, running at an annual rate of about 18 percent, had long been the dominant problem. Interest rates were the highest ever in modern times, 15 percent or more.

Yet people were optimistic.

Yes, my children will be better off financially than I am, was the response of 60 percent of those interviewed. Only 9 percent expected their children to be worse off.

Among black families, many still in the process of entering the mainstream, enthusiasm was even greater: 74 percent said their children would be better off. Only 8 percent said their children would not.

In March, 1982, when the question was asked again,, interest rates were about the same, the inflation rate had been cut by more than half, but unemployment had reached a post-Depression high. Government programs that offer encouragement for the future, such as educational loans and grants, had been curtailed.

Forty-two percent in that survey felt their children would be better off than they were, but a strikingly high number--31 percent--expected their children to be worse off.

The greatest change occurred among blacks who, as a group, went from high expectations to bitterness. Only 36 percent of blacks saw financial improvement ahead for their children; 43 percent said their children would be worse off.

By late last month, when the poll question was repeated, President Reagan had declared that the recession was at an end. Favorable comparisons with the recent past were being drawn for automobile sales, home building and interest rates.

Ideally, these events should have brightened people's notions about the future, but they didn't. Forty-four percent in the January poll took the optimistic view toward their children's lot, but 38 percent were pessimistic--a ratio of just about 1 to 1. And for blacks, only 34 percent expected their children to be better off; 55 expected them to be worse off.