Unstable IQ scores should provide a net zero; an average increase of half a standard deviation across the entire population already means that the norms are fucked.

Only if you make the very strong assumptions that there is no systematic bias or selection effect or regression to the mean or anything which might cause the unstability to favor an increase.

Plus you ignored my other points.

Plus we already know from the pairs of before-afters that these researchers are either incredibly incompetent or actively dishonest.

Plus we already know biases in analysis or design or data collection can be introduced much more subtly. Gould's brainpacking problems is only the latest example.

Therefore, the IQ test used simply wasn't properly normed; if we assume that it was equally improperly normed for all students in the study,

Which claim and assumption we will make because we are terminally optimistic, and to borrow from the '90s, "I want to believe!"

we still see an increase of 4 points based on teachers being told to expect more. Whether an increase of 4 points is statistically significant on that (improperly normed) test is a new question.

Wow, you still aren't giving up on the Pygmalion study? Just let it go already. You don't even have to give up on your wish for self-fulfilling expectations - there are plenty of followup studies which turned in your desired significant effects.