Any chance someone has some extra SES money to get this guy a stats tutor?
Michele McNeil explains a bit about why linking the 26-point jump to extraordinary reform is a bit silly. Comparing the average scores of round one applicants to round two applicants is hardly an apples to apples comparison - the struggling round one states didn't apply for round two, so it's not a surprise to see the average scores jump. A comparable example would be Gary Miron's recent critique of a KIPP study that pointed out KIPP doesn't fill the slots emptied by leavers. This is pretty basic stuff (and chapter 1 of a Bracey great).
Add in big jumps like AZ and you can explain some of the other gains (even though other states could have been "static" while one or two big movers shifted the entire average). And, of course, Duncan's "gains" include tying teacher evaluation to "student achievement" (code word for test scores), expanding charters, etc, not to mention criticisms that this kind of scoring systems is pretty subjective.