Unfortunately, there are way too many variables here to simply "fix" poverty. Yes, education is an issue. But the reason bad schools are bad has a great deal to do with culture. One of the key variables is illigitimacy. The OP doesn't mention how many (or few) of the families in his neighborhood have two parents. Another is gainful employment. I would bet that the average household in that neighborhood is supported by less than one full-time wage earner (whereas most middle-class families have more than one, whether it be a single earner doing OT or two workers). On the one hand, it is true that we as a society are willing to give the poor numerous subsidies, food stamps, medicaid, etc., and also to provide free public schooling which includes a bus ride each way and two meals on the public dime. But on the other, it is beyond silly for us to expect that most people in poverty are either willing or able to take advantage of those opportunities in the same way that we would be. A lot of these things are cyclical, too. It's easy to complain about the predatory shopkeepers or poor teachers in the ghetto, but far harder to convince a good teacher not to take an opening at a better workplace for the same money. Just like it's tough to get a business owner to open a store in an area with less income, more crime, etc., and charge the same prices as he would in a suburb. It almost takes a missionary mindset to go into those areas and try to help, and the burnout rate is very high. (Full disclosure--I taught and coached in the inner city for 5 years. It was both very satisfying and maddening.)
If I could only address one of these variables and get the most bang for my buck, it would be illigitimacy. Two-parent homes would contribute to household income, family culture, and education. But that issue is a terrible political third rail. I doubt very seriously that anyone who doesn't want a load of trouble would bother fighting that battle.