The fine art of parenting is a matter of deep concern at the Department of Health and Human Services, but the subsidy of football mothers is definitely not part of the program.

This is the conclusion of the department's Board of Ethics, which has asked a top HHS official to repay the cost of trips she made at government expense to watch her son play football.

Dr. Jean Elder, an expert on the disabled, was also moved from her job as acting assistant director for Human Development Services to a position of less responsibility as special assistant to Secretary Otis R. Bowen. But Elder retained her $73,400 salary, according to an HHS spokesman.

An unrepentant Elder maintained that her attendance at the games was "part of her commitment as a parent," according to a report prepared by the HHS inspector general. "She said her staff knew that she always planned on attending every game unless government business required her to be somewhere else," the report states.

However, the report continues, "Dr. Elder emphatically denied that she ever requested any staff members to drum up" official trips that would enable her to attend her son's football games.

Sen. Gordon J. Humphrey (R-N.H.) first questioned the trips in May, after Elder was nominated to become assistant secretary for Human Development Services. Our associate Stewart Harris obtained the results of the subsequent inspector general's probe and copies of Elder's trip vouchers from 1983 through 1985.

The inspector general's investigators concluded that government business was not conducted on five out of 11 trips flagged by Humphrey; they also questioned the necessity of other trips. Examples:

On Oct. 20, 1983, Elder traveled to Lansing, Mich., to take care of business that was normally handled by telephone. An Elder aide told probers the trip was arranged because "Elder wanted to be in Lansing that weekend, and {her staffers} were to find a reason for her to be there." Elder's son Paul, a linebacker, hit the gridiron the next day at nearby Albion College. The trip cost the taxpayers $295.

The next fall, Elder's staff asked Indiana officials to "develop an agenda" for a trip to Indianapolis in late September. The report says: "Staff members stated that Dr. Elder asked that the trip be set up on Sept. 21, 1984, because her son was playing football in Indiana that weekend." Price tag: $276.

Elder returned to Michigan a month later. Wayne State University officials were informed beforehand she would be in town on Oct. 26, and that they should schedule a luncheon. The younger Elder had a home game that weekend at Albion. Cost: $357.

In a written response to Bowen, Elder challenged the inspector general's report as "inaccurate" and the result of "investigative incompetence or misrepresentation." She told us in an interview that much of the information had been provided by a disgruntled employe and that the investigation resulted from the efforts of a right-wing "cabal" that had been after her since she joined HHS in 1982.

Footnote: The case has a precedent. Two years ago we reported that deputy assistant secretary Marjory E. Mecklenburg quit after a probe began of her "official" trips, including one to Denver, where her son was playing for the Broncos.