Home computers, now largely in the hands of middle- and upper-income families, could become a source of sharp dispute between schools and parents, according to a study released today by New York University.

According to the study, blame lies with the clash of "two cherished American values: achievement and equality of opportunity."

"While families generally opt, when pushed, for the achievement of their children over the equality of educational opportunity for others, the school is responsible for trying to assure equality of educational opportunity for children, sometimes, at the expense of achievement," the report said. "The problem . . . may become pronounced as effective home educational software is developed, diffused, and used by families who can afford it."

The NYU study focused on 20 upper- and middle-class families, most of them white and from the New York City area.

The study cited the experience of one family that owned two small home computers as an indication that the school-home relationship ". . . may be in for some rough sledding . . . "

When one teacher prohibited a student from submitting school work done on a home computer because other students did not have them, the girl's parents "simply refused to allow the teacher's decision to stand for their child," the study said.

"You use it for homework?" an NYU researcher asked the student." . . . . I thought your teacher didn't want you to."

"Tough," the girl replied.

"The parents, as reflected in the comments of their daughter, were saying that they would decide how their daughter was to successfully complete the assignment given by the teacher," the study concluded.

The study said, "One possible guess is that as parents come to invest more of their time, money, and energy" into their children's use of computers, "some of the traditional lines of authority between teacher at school and parents at home might be challenged or disrupted."

Sales of home educational software totaled approximately $94 million last year, with one-third of the purchases made for children under 7, according to Talmis Inc., a Chicago-based market research firm.

Joseph B. Giacquinta, a professor of educational sociology at NYU who headed the study, said despite the limited number of families studied, he had "great confidence" in the findings.

Of the 20 families studied in the initial phase of the research, 17 were white, one Jamaican, one Korean and one Hispanic. Nearly all of the parents were in their 30s and well-educated.

According to the report, most parents hope educational software will place their children "at an advantage in their competition at school and eventually at college and the world of work." But the parents also "fear" that their children will become "hooked on computers."

In other findings, the study said home computers reinforce the existing family structure. A cohesive family remains close while an individualistic family tends to undertake activities separately. However, Giacquinta said, in three of the families, the introduction of the microcomputer strained the husband-wife relationship.