key differences between countries. "That is leaving out many of the important things," he warned. "They simply don't get commented on. What you are looking at is something that happens to be common. But (is it) worth looking at? PISA results are taken at face value as providing some sort of common standard across countries. But as soon as you begin to unpick it, I think that all falls apart." Queen's University Belfast mathematician Dr. Hugh Morrison stated that he found the statistical model underlying PISA to contain a fundamental, insoluble mathematical error that renders Pisa rankings "valueless". Goldstein remarked that Dr. Morrison's objection highlights "an important technical issue" if not a "profound conceptual error". However, Goldstein cautioned that PISA has been "used inappropriately", contending that some of the blame for this "lies with PISA itself. I think it tends to say too much for what it can do and it tends not to publicise the negative or the weaker aspects." Professors Morrison and Goldstein expressed dismay at the OECD's response to criticism. Morrison said that when he first published his criticisms of PISA in 2004 and also personally queried several of the OECD's "senior people" about them, his points were met with "absolute silence" and have yet to be addressed. "I was amazed at how unforthcoming they were," he told TES. "That makes me suspicious." "Pisa steadfastly ignored many of these issues," he says. "I am still concerned." Professor Svend Kreiner, of the University of Copenhagen, agreed: "One of the problems that everybody has with PISA is that they don't want to discuss things with people criticising or asking questions concerning the results. They didn't want to talk to me at all. I am sure it is because they can't defend themselves. United States Since 2012 a few states have participated in the PISA tests as separate entities. Only the 2012 and 2015 results are available on a state basis. Puerto Rico participated in 2015 as a separate US entity as well. PISA results for the United States by race and ethnicity. Research on possible causes of PISA disparities in different countries Although PISA and TIMSS officials and researchers themselves generally refrain from hypothesizing about the large and stable differences in student achievement between countries, since 2000, literature on the differences in PISA and TIMSS results and their possible causes has emerged. Data from PISA have furnished several researchers,