It’s the headline du jour whenever a horrific case emerges of a mother killing her kids, as Lashanda Armstrong did when she piled her children into her minivan and drove straight into the frigid Hudson River.

Our shock at such stories is, of course, understandable: They seem to go against everything we intuitively feel about the mother-child bond.

But mothers kill their children in this country much more often than most people would realize by simply reading the headlines; by conservative estimates it happens every few days, at least 100 times a year. Experts say more mothers than fathers kill their children under 5 years of age. And some say our reluctance as a society to believe mothers would be capable of killing their offspring is hindering our ability to recognize warning signs, intervene and prevent more tragedies.

And so the problem remains.

“We’ve learned how to reduce auto fatalities among kids, through seatbelt use. We’ve learned how to stop kids from strangling on the strings of their hoodies. But with this phenomenon, we struggle,” says Jill Korbin, an anthropologist at Case Western Reserve University who has studied mothers who kill children. “The solution is not so readily apparent.”

How common is filicide, or killing one’s child, among mothers? Finding accurate records is nearly impossible, experts say. One problem is classification: The legal disposition of these cases varies enormously. Also, many cases doubtless go unreported or undetected, such as very young mothers who kill their newborns by smothering them or drowning them in a toilet after hiding the entire pregnancy.

“I’d say a mother kills a child in this country once every three days, and that’s a low estimate,” says Cheryl Meyer, co-author of “Mothers Who Kill Their Children.”

Several databases track such killings but do not separate mothers from fathers or stepfathers. At the Department of Health and Human Services, the National Child Abuse and Neglect Data System reported an estimated 1,740 child fatalities — meaning when a child dies from an injury caused by abuse or neglect — in 2008.

And according to numbers compiled from 16 states by the National Violent Death Reporting System at the CDC Injury Center, 130 children were killed in those states by a parent in 2008, the last year for which numbers were available.

“The horrific stories make the headlines, so we believe it hardly ever happens,” says Meyer, a professor of psychology at Wright State University in Dayton, Ohio. “But it’s not a rare thing.”

Meyer and co-author Michelle Oberman interviewed women at the Ohio Reformatory for Women. They found that of 1,800 women at the prison, 80 were there for killing their children.

It’s also a phenomenon that defies neat patterns: It cuts across boundaries of class, race and socio-economic status. Oberman and Meyer came up with five categories: filicide related to an ignored pregnancy; abuse-related; neglect-related; assisted or coerced filicide (such as when a partner forces the killing); and purposeful filicide with the mother acting alone.

Different as these cases are, though, there are some factors that link the poor teen mother who kills her baby in a bathroom with an older, wealthier mother, and one of them, experts say, is isolation.

“These women almost always feel alone, with a total lack of emotional support,” says Lita Linzer Schwartz, a professor emeritus of psychology and women’s studies at Penn State, and co-author of “Endangered Children.”

Schwartz says women are often not checked for mental illness after their crimes, and that is unfortunate.

“Women need better treatment not only before, but after,” she says. “They get tormented in prison, when often what they need is psychological care.”

The issue of mental illness is a tricky one. Some women are obviously seriously ill — for example, Andrea Yates, who drowned her five children, one by one, in the bath in 2001, believing she was saving them from the devil. After first being convicted of capital murder, she was found innocent by reason of insanity and remains in a mental institution.

But Oberman, a law professor at Santa Clara University, says cases are not always so obvious — sometimes depression is enough to send a woman over the edge. “Almost all these women are not in their right minds (when they commit these acts),” she says. “The debate is whether they’re sick enough to be called insane.”

Besides isolation, another frequent similarity in the cases is a split with the father of the children. “So often there is an impending death or divorce or breakup,” Meyer says.

In the case of Armstrong, the 25-year-old mother had apparently argued with the father of three of her young children — about his cheating, according to the woman’s surviving son — just before driving into the river on Tuesday in Newburgh, N.Y. (Her 10-year-old son climbed out a window and survived. Three children, ages 11 months to 5 years, died.)

This was one of those cases where the mother was committing suicide and decided to take the kids with her. To rational observers, there is nothing more perverse. But in the logic of many these mothers, experts say, they are protecting their children by taking them along. Armstrong’s surviving son told a woman who helped him that his mother had told the kids: “If I’m going to die, you’re all going to die with me.”

Experts have heard that many times before.

“We see cases where the mother thinks the child would be better off in heaven than on this miserable earth,” for example with an abusive father, says Schwartz. “They think it’s a good deed, a blessing.”

A good deed — performed by a good mother. “It’s how the sick mother sees herself being a good mother,” says Oberman. “Once she decides she can’t bear the pain anymore, she thinks, ‘what would a good mother do?'”

Korbin, the anthropologist, says in prison interviews she conducted, some women who had killed their children were still certain they were good mothers. And it’s that very ideal of being a “good mother” that is holding our society back from taking preventive action or intervening in a potentially abusive situation before it’s too late, Korbin says.

“Often the people around these women will minimize a troubling instance that they see, saying, ‘Well, she’s a good mother.’ We err on the side of being supportive of women as being good mothers, where we should be taking seriously any instance where a mother OR father seems to be having trouble parenting. ANY instance of child maltreatment is serious.”

In fact, Armstrong’s aunt told reporters that her niece “was a good mother. She was going through some stuff.”

Meyer, for one, is angry that the people around Armstrong didn’t take heed of the warning signs earlier.

“To me this is a textbook case,” she says. “This woman was completely overwhelmed. Almost always, you can find people who say, ‘I knew something was wrong.’ This did not come out of the blue. I say shame on the people who saw signs and didn’t do anything. This is your responsibility, too.”

Not that it is easy to know when and how to raise an alarm bell. “I think often people just don’t know what to do,” says Korbin.

But, she adds, it doesn’t help to gape at a few of the more shocking cases and then move on, without recognizing the scope of the problem and the factors that link many of these cases.

“People focus on the spectacular cases — and they are spectacular,” she says. “But that means another few kids will die over the next few days without much notice, and that is very sad.”