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God that video annoyed me so much. You aren't supposed to practice for an IQ test. If you practice, whatever result you get is basically invalid as the test presumes you are approaching the problems for the first time. It wouldn't annoy me if it wasn't Veritasium, but he presents himself as a science educator and should know better.
A generous interpretation could be that it's a bad metric because you can train for it
Very generous and wrong. Any psychiatrist would tell you to not practice, and a when not practiced it's a very useful metric. We couldn't make as strong hypotheses about the effect environmental lead had on earlier generations without IQ tests. We couldn't measure the very interesting trend upwards in IQ scores over time regardless of lead, which implies anything from a structural problem with the test to a real improvement in intelligence in the general population since the test's invention. We couldn't quantify the genetic or environmental influences on intelligence without IQ either.
It's like saying a psychiatric test for depression is bad because you can practice to know the answers a depressed person would give.
Here I took part of the point being that you can practice, and to some extent you may be unwittingly doing so. That's part of the upward trend. That's part of having to localized the test for a culture. We're to some extent practicing just due to the world immediately around us.
Should you or your kid intentionally practice? Probably not, but I took practicing and mentioning that to be part of the larger point that the test can be predictive for some things, but isn't destiny.