David Pakman recently interviewed Phyllis Schlafly about state-funded pre-kindergarten programs. He repeatedly badgered her about an an obscure 2005 academic study on an Oklahoma Pre-K program (pdf). She talked about other Pre-K studies, but was not prepared to comment on that one.
The study found that "Oklahoma's universal pre-K program has succeeded in enhancing the school readiness of a diverse group of children." That is, some were able to learn letters of the alphabet ahead of kindergarten, whereas otherwise they would have learned in kindergarten.
Okay, the kids learned something, but this does not prove that the program is worthwhile. I am not sure that there is any proof that kindergarten is worthwhile. The paper does not show any long-term benefits.