Armstrong and Woodley argue that the documented rise in measured IQs is a result of test-takers applying rule-based approaches to tests, resulting in an increase similar to that seen in re-testing. They're arguing that in large part, it is a testing artifact. They make several predictions about what we should observe if their rule-based model is correct. For instance, that measures of crystallized intelligence (i.e. vocabulary) should not rise or not rise as robustly, and they haven't; that most obviously rule-based tests (like Raven's progressive matrices) should show the strongest effect (they do); and that we should expect the gains to appear when countries undergo demographic transition including standardized education, and the rate of increase should correspond to the rate of the transition.
To this last point, it's worth pointing out that there are many other less interesting medical explanations for why intelligence might actually be rising. Specifically, lower parasite load due to public sanitation and better nutrition in early childhood are very good candidates for why the Flynn-type gains are most pronounced in Europe, Japan and Korea in the periods when they were observed. It's hard to make the argument that lower parasite load leads to better cognitive strategies to game tests. It's also not surprising that if bombs are falling around your school and then they stop, the people tested after they stop may perform better - especially since even non-warfare jet and traffic noise has been shown to locally impair reading comprehension in students.
A second, neglected question is whether the abstract rule-based thinking required for the re-testing-type gains actually correlates to some other outcome, like personal or national per capita income, or life satisfaction. If the Flynn effect doesn't represent an increase in g but does correlate with economic growth, do we care that much?
Armstrong EL and Woodley MA. The rule-dependence model explains the commonalities between the Flynn effect and IQ gains via retesting. Learning and Individual Differences, Volume 29, January 2014, Pages 41–49.
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Haines MM, Stansfeld SA, Job RF, Berglund B, Head J. Chronic aircraft noise exposure, stress responses, mental health and cognitive performance in school children. Psychol Med. 2001 Feb;31(2):265-77.