The Peano Axioms may work better in inner city schools because they are more exciting and interesting for the teachers as well as the students.
The Peano Axioms are a powerful way to understand the structure of math in 5 sentences that are easy to understand. Even math induction is easy, it is just spreading infection. If 0 is infected, and infection spreads to the next number, then all numbers are infected.
Drill work that has no end and no pattern is demoralizing.
Inner city schools tend to become like the movie Four Horrible Bosses. The control freak, bully, insecure, and pessimist are the 4 bosses. Sounds like the comments about Harvey Illinois schools. Iraq was better one person said.
The Peano Axioms are about student empowerment through understanding the real structure of arithmetic. This is more inspiring than just endless drill sheets. The Tower of Badges at some point becomes meaningless.
It was that way for Grassmann, Dedekind and Peano when they put them together. Mathematicians find these axioms interesting when they go back to them.
This interest carries over to the arithmetic operations when we understand them in the context of Peano Axioms as recursive operations.
Inner city students are the ones who most need to be motivated, inspired and given a feeling they can understand math, not just do a drill sheet. This is denied to them by the high stakes testing drill factories that are inner city schools. Increasingly, these are all schools.
High stakes testing is a top down approach from an imperial federal government desperate to avoid admitting that its immigration policies brought down the school systems. But given that reality, new inspiring approaches are needed. The Peano Axioms are the approach that cuts through the drill factory to real meaning for elementary math.
Any approach that ignores the Peano Axioms will be a drill factory. Any drill factory will leave inner city students eventually exhausted and disinterested. These students will be worse behavior problems for not teaching them concepts that are inspiring in math.
Not surprisingly, the stupid and evil emperor that has brought this about will ignore this. This is one reason to get free of federal involvement in schools. This emperor is not interested in human freedom, but in thrall armies of low paid workers, who spend long periods of time without employment. Its policies show that is the intent.