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Well to be honest the study suggests that public schools are as good or slightly better at teaching pre-algebra math as Catholic schools. While Catholic schools may make up a large population of private schools I don't think you can make that generalization of the results (which I know was in the source headline).
I'd be interested to see if the same results continue beyond pre-algabra mathematics (simple arithmetic) into mathematical subjects that are even less likely to be reinforced at home and in daily life (my mom drilled me in basic math but I don't recall ever getting a home explanation of why y=x^2 has two values of x for each value of y.
Interesting result, though.
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