THERE HAS been an alarming increase in child abuse and child neglect in the District. It is not limited to a few children in the poorer parts of town. It is a citywide problem of proportions that are not yet fully known. What is known is that last year the reported incidence of physical abuse of children rose by a third. In the same year, the rate of reported child neglect rose by almost two-thirds. Some of the increase may reflect the improved methods of learning that a child has been abused; for instance, anonymous callers can now report suspected abuse. But such changes in the reporting procedure are at least a couple of years old, and officials say the incidence of abuse and neglect continues to grow at an astounding rate.

According to the city's Division of Children's Protective Services, the rate of reported abuse is rising seriously again this year. Sexual maltreatment, in particular, is said to be on the increase, although no separate records of this crime against children are available. The director of a Children's Hospital program for sexually abused children says that her enterprise alone has handled 780 cases in the last three years, and almost all of those cases have been from the District.

City officials and psychiatrists have no clear idea why so many children are being maltreated. Interestingly, the doctors and city officials note that the worst time of the year for child abuse is Christmas, the family time of year. But private agencies that help children in the District say that more could be done -- all year long -- to stop the growing incidence of child abuse. These agencies lay large amounts of blame at the steps of the District Building and the Department of Human Services for sloppy, indifferent work in dealing with child-victims. The city's foster care program, for example, is often cited for its disarray. According to a recent city auditor's report on that program, the city does not even know how many children it is responsible for or where many of those children are supposed to be.

The city's attention to children's programs in the Department of Human Services needs to be sharpened. But the problem of child abuse and child neglect is not one that increased government attention can eliminate. Individuals and private groups must respond even though the financial pictur for many of these is bleak. (The Child Abuse Victim Assistance Project, for instance, is about to go out of business unless it gets some $200,000 to continue operation.)

And finally, either the city or private groups should undertake much more in the way of classes that could familarize parents with the chores and responsibilities and dangerous moments of parenthood so far as abuse in its less exotic and deranged forms is concerned. A second step for private groups or the city government would be to begin classes for parents of older children, instructing them in the care of those children and informing them of services -- food stamps, clothing centers, drug education, etc. -- that are available in the city to help them bring up children.

This is not just another" public problem. The abuse of children is a horrendous crime.