Cost of Prison versus the cost of K12 Education

According to the Associated Press, the cost of incarcerating a prisoner in New York City is $167,731.  It costs $15,597 to educate a child in NYC. That means that prison in NYC is 10+ times greater than educating a child.

I do not understand how politicians can say that education is expensive.  It isn’t; ignorance is expensive.  We will either pay for education or the lack of education.  As a society it seems we (0r at least the politicians) would rather pay for the lack of education.