Kindergarten, traditionally a playful post of entry into formal school is becoming more academic, with children being taught specific reading skills, taking tests, and occasionally even having homework.

The change to a much more structured system of teaching and learning, which affects an estimated 40,000 children in the Washington area and millions more throughout the country, results partly from the increasing number of 5-year-olds who come to kindergarten with considerable experience in nursery schools, sometimnes two or three years.

In addition, many items that used to be kindergarten staples -- learning the alphabet, counting to 10, telling the difference between big and little -- now are picked up by many children through television's "Seasame Street," the pre-school children's show which celebrated in 10th anniversary this year.

Games, songs, and art work have far from disappeared, but the deliberate teaching of specific skills, which has burgeoned since the late 1960s, has led to substantial rises in the scores on reading readiness tests given to kindergarten children throughout the country.

Similar gains have occurred on the standardized tests for first, second, and third grades in reading and mathematics.

Above the third grade, the test scores have been stable or declining throughout the 1970s, indicating that so far little long-term carry-over has occured from the children's fast start in kindergarten.

Indeed, some critics contend that the faster pace of learning concrete facts and skills may actually hinder development of the comprehension and problem-solving abilities needed for more advanced intellectual activity.

Such criticism is clearly a minority view.

Measured by its specific goals, and specific tests, the effort to teach children more things earlier has been a substantial -- though largely unheralded -- success.

For example, at Key Elementary School in Arlington recently, one group of kindergarten children was working on math problems. Their work sheets had numbers with small groups of apples or animals next to each one. The children worked methodically, solving problems such as 3+4=7 and 6-4=2.

Nearby, other children wore large headphones and leafed through small, well-illustrated books as they listened to records of short stories.

Another group was coloring small pictures of Christmas trees. Some wrote a number under each tree.

"It used to be that when we started school I had to spend most of my time consoling the children," said Mamie Spellman who has been teaching kindergarten in Arlington for 20 years."The children hadn't been away from home before. Now most of them have been to nursery school, and this year there was only one boy who cried. We can get started doing things much earlier."

At Murch Elementary School in Northwest Washington, one kingergarten class had homework on the first day of school in September. The assignment: find pictures of three things that start with the P sound and paste them onto sheet of paper.

Similar assignments for other sounds have followed regularly, and associate superintendent James T. Guines said the D.C. school system "encourages" kindergarten teachers to assign homework.

"The kids can handle it," Guines said. "Of course, their parents are supposed to help them. The purpose is to teach some things to the children and also to encourage good parenting."

Throughout the Washington area, kindergarten teachers have been given lists of skills to teach and suggested tests to check on them.

In the district of Columbia, the kindergarten curriculum is based on the theories of behaviorial psychology dedevloped by Harvard University's B. F. Skinner. The basic ideais break down complicated learning into clear simple skills that are taught step-by-step and repeated until learned.

The same approach, though with less elaboration, is used by the Fairfax school system, which has a list of more than 400 objectives for kindergarten children. It is also used for much of the instruction on "Sesame Street," which has had a substantial effect on kindergarten since it started on noncommercial stations (including WETA hre) in 1969

Funded by the U.S. Office of Education, the show was watched last year in about 80 percent of U.S. households with a child aged 2 through 5, according to ratings figures issued by the producers.

A series of research studies indicate that children learn much of the material "Seasame Street" teaches -- the alphabet, counting, shapes, and simple relationship. This is confirmed by interviews with local teachers.

Despite that success and the charm of its Big Bird and Oscar, the show has encountered serious criticism from psychologists because of its frequent shifts from segment to segment and its sometimes frenetic activity.

"Its whole message is: "Think quick, move fast, don't savor,' And that's not the strategy children need for higher-level thinking," said Dorthy Singer, codirector of the Yale University Family Television Research, and Consultation Center.

The show has been strongly defended by Gerald Lesser, a Harvard psychologist who heads the program's advisory board.

Lewis Bernstein, director of "Sesame Street's" own research staff, said Singers' contentions are refuted by other academic studies.

"Children who are young have short attention spans," Bernstein said, "and on 'Seasame Street' we try to match the material to the child's attention span -- it ranges from 10 seconds to five minutes -- there's a tremendous amount of repitition."

"Sesame Street" also has spawned a large number of educational toys and games -- including flash-cards, number books, puppets, and a monthly magazine with a circulation of about 700,000. Many of toys have become best-selling gifts for children. They earned the show $5.3 million in royalties last year. g

Irene Faubion, a kindergarten teacher at Beauvoir School, a private school in northwest Washington, suggested that besides the better toys and television, the growth of nursery schools had helped make kindergarten more academic. The nursery schools themselves have academic. The nursery schools themselves have become more academic than they used to be.

Since 1978, according to the U.S. Census Bureau, the proportion of 3-and 4-year-olds enrolled in school has risen from 16 percent to 34 percent. This partly results from the increase in working mothers. It aslo reflects the expansion of federally-financed Head Start programs that stress intellectual development for low-income youngsters.

According to researchers at the National Institute of Education, middle-class nurseries also have introduced substantial doses of academic material themselves, sometimes with games and devices orginally developed for Head Start.

Evidence of the impact of this early childhood education is considerable.

In Washington, for example, the average reading test scores of public school first-graders rose continously from 1971 to 1977, reaching national norms, even though scores at other grade-levels remained low.

In Montgomery County from 1972-1978 was a substantial gain in reading scores for third-graders, the youngest group tested, while scores were unchanged for fifth-graders, and dropped in grades seven and nine.

The same pattern is true nationwide.

For example, in the California achievement tests, published by McGraw-Hill, nationwide results for 1977 show increases in achievement in grades one to three, compared to 1970, but declines in all later grades. By high school, the drops are substantial.

Paul Copperman, author of a study of public school performance called "The Literacy Hoax," said the tests for kindergarten and early elementary grades concentrate on basic skills such as word recognition, simple vocabulary, and basic computation. By giving more academic work earlier and placing more stress on direct instruction in these particular skills, the test scores have improved, he said.

In the upper grades, however, Copperman said, the tests emphasize comprehension in reading and problem solving in mathematics. In these more analytical areas, the schools have lagged, Copperman said.

Says Hans Furth, a professor at Catholic University who is a leading interpreter of Swiss psychologist Jean Piaget: "My complaint is that most of what's going on now (in kindergarten) is information-processing rather than thinking. The school is seen as a place where children have to learn specific responses rather than become thinking persons. The tests show we are getting better learning to a certain extent. But we are not getting thinking persons, and that is a serious problem."

"It's a tragedy," he added. "Kinderarten now sometimes has the same stress as formal school. The kids used to have a lot more fun."

"The original theory of kindergarten was that a child learns through playing," said Joan Freck, the principal at Mount Vernon Woods in Fairfax County. "I think it's too bad we're moving away from that."

Others disagreed strongly.

"If the childen are capable and interested, why move them ahead?" said Faubion at Beauvoir School. "There certainly are a lot of important things for kingergarten children to do besides academic work. They have to learn how to be students in a classroom. They have to learn to manage their time . . . But when you find children who are ready to learn, to read, it wouldn't be right to deny them."