It's not that the existence of poor schools makes the students at good schools dumber. It's the horrible quality drop between the good and bad schools makes the statistics misleading. The report could be titled in a completely different way:

"American 8th graders significantly better at science than European 8th graders."

I went to the actual data set ( http://nces.ed.gov/timss/idetimss/dataset.aspx ), selected the 8th grade science tests, and asked for the average score from the European nations. The result was 501 +- 0.9. The American score was 520 +- 2.9.

Now, I'm a bit concerned about their averaging methodology, since I don't think that it's accounting for population density (adding the scores for each country and dividing by the number of countries gives the average returned by the dataset). Still, if we assume that the results are correct, then the United States is doing significantly better than Europe in science education.

Of course, the English and the Hungarians, with scores of 542 and 539, respectively, have nothing to fear for the average American, while Turkey, at 454, should be pretty concerned.

Which brings us back to the diversity of educational quality in the US. While the average might be 520, I wouldn't be surprised, as a Hoosier, to find Indiana down near Turkey's 454. On the other hand, I'd expect Massachusetts to compare favorably with England's 542.

You make a very good point that comparing american total aggregate scores to the best of the individual european states is misleading. We could compare total american average results against total european and show that the US does better, as you have, or even better is to present histograms showing american state by state results and comparing to european state by state results. This makes sense and is a fair way to compare since in both europe and the US, educational policy is mostly determined at the individual state level rather than at the union of states level.

I think the author of the parent post to yours meant that if an average or aggregate grade of some kind is calculated for the whole of the USA, then the resulting figure may not reflect the performance of much of the country because of a large variation between the states.

Of course, many of the countries in the study have populations smaller than some states within the USA. Perhaps the comparisons should be conducted at state level?

Which makes one wonder as to what the justification was for aggregating the data in the way it was aggregated, or aggregating it at all in the first place, other than to contrive a statistic to argue for whatever policy position the authors already support.

If the honest purpose of the study is to compare the results of various educational methodologies, I don't see that there'd be a useful unit of analysis any larger than an individual school, and even that might be too coarse. It's true that American states have de jure authority over public schools, and that there isn't any singular "American educational system" to speak of, but even within the individual states, there's still a great deal of variation from district to district and from school to school. Plus, there are plenty of schools outside the conventional public education systems, whose methodologies aren't determined by policy from any government.

Ignoring your question, I was speaking more about the whole "US kids are stupid." thing. The average is abysmal, but that doesn't mean that education is bad across the board. Often times, the media makes it out to be so.