Math and science problems are confounding the nation's public schools. Both fields, vital to the new technological era, are suffering a critical shortage of teachers and equipment. Pupils are missing out on skills which are becoming more crucial every day.

It all adds up to a high-tech lag projected to last through the decade. And Congress, perhaps as concerned about trailing other nations in a critical arena as about the education gap, is looking to the private sector for some answers.

Among those being considered are: sweeter tax deductions so companies will donate computers to schools, tax credits to companies who let their high-tech experts teach math or science, and research grants to young science professors to keep them from running off to private industry.

Sen. Lloyd Bentsen (D-Tex.) said the nation faces a shortage of 2.5 million skilled workers in the current decade. Experts also note that half the math and science teachers in schools last year were not certified in their fields, and that qualified teachers in the field can double their wages in private industry.

A House Ways and Means subcommittee has approved a bill--spurred by the founder of Apple computer--that would increase the tax deduction available to companies who donate computers to schools. If the bill passes, Apple chairman Steven A. Jobbs said he will donate a new computer to every school in the country.

Sen. John Glenn (D-Ohio) and Rep. Dave McCurdy (D-Okla.) introduced two bills pushed by the National Association of Secondary School Principals.

One would provide tax credits to firms that hire public school math and science teachers during the summer--fattening their paychecks as an inducement to remain in teaching--or that let their former teachers return to the schools to teach 10 hours a week.

A companion measure would provide forgiveable 7 percent loans to potential math and science teachers. One quarter of the debt would be written off for each year the recipient teaches.

Richard A. Kruse, a lobbyist for the principals' group, said his members don't expect the Glenn tax credit bills to pass quickly, but they hope to start a public debate. His association's tax credit approach, he said, "is very much the opposite of tuition tax credits. We want to help the public schools, not betray them."

Glenn was referring to the Reagan administration's bill offering tax credits of up to $500 to parents with children in private schools.

The outlook for any tax credit proposals, to help private school parents or public schools, is doubtful this year because the congressional tax-writing committees have to raise revenues in the face of rising federal deficits.

"My God, we've got to raise taxes $21 billion," said a Republican aide. "One would think it defies logic to be looking for credits."

Several other bills also aim at closing the high- tech gap in the schools. Sen. Bentsen has introduced a package of bills to offer tax deductions to industries who donate equipment to vocational schools, and to allow tax credits for employes in skilled training programs.

In addition, the National School Boards Association is working on a bill that includes tax incentives for industries aiding the schools. Sen. Harrison Schmitt (R-N.M.) and Rep. Margaret Heckler (R-Mass.) are drafting a proposal that concentrates on providing research grant money for young college professors, and extra pay for science and math teachers who attend summer training institutes.

A Heckler aide said the idea is to make a modest proposal that will gain administration backing. Without administration support, he said, "a lot of these bills are so much fluff."

One ambitious plan backed by the National Education Association and introduced by Rep. Carl Perkins (D-Ky.), chairman of the House Education and Labor Committee, would set up a more traditional federal grant program that would cost billions of dollars.

A Perkins aide acknowledged that the current conservative political climate makes any major new federal education programs unlikely. But he also cited the need for discussing ways to address a growing national problem.

In introducing his package in May, Bentsen acknowledged the difficulty of proposing major new programs amid rising deficits. "I do not doubt that most shortages of particular labor skills will be eliminated over time by the free market process," he said. "Yet, it is not always a quick process and we do not have the luxury of time."

Describing the principals' plans, Kruse said, "We're looking for vehicles for tapping into the huge capacity industry has for helping the public schools."

Even without more generous tax advantages, industry is helping some school systems. The incentives appear to be good will and what Kruse called "enlightened self-interest" in investing now to train more qualified workers.

In Washington, for example, Control Data Corp. has donated equipment and manpower to the city schools. IBM lent the system a management expert for a year. And five corporations have agreed to be prime sponsors of high school career programs this fall.

Janis Cromer, speaking for the school system, said, "We've had extraordinary success here, but I know of other cities where the schools haven't been as fortunate." Increased tax incentives might make more companies willing to participate, she said.