A school can't correct for a class filled with poor single parent household kids who refuse to be educated
A school cannot, but society can. All it would take is a degree of ruthlessness on the part of the law-abiding and productive majority in dealing with them.
1. End no fault divorce.
2. Provide that unwed, non-custodial fathers are entitled to no welfare or public housing at all.
3. Provide that unwed mothers can never receive more than 1/3 the welfare of married mothers.
4. Inflict corporal punishment on men who abandon their children.
5. Make having two or more children out of wedlock (including outside of common law marriage) that you cannot fully support without welfare, for men or women, would be treated as a sex offense under the logic that it is sexual social parasitism.
You may not like that, but it would work. All society has to do to such people is give them a harsh ultimatum. That is, you can socialize the cost of your lifestyle, but the cost will be your freedom and autonomy since you aren't an invalid and this is by your own doing.