The switch is what is being tested yes, but it is not clear that what is being measured in the switch is "AI fried their brains" rather than "context switching in the middle of a test". If they wanted to make that point it would be useful to have the maths test run with a calculator group who also got it yanked halfway through, that way we would be able to see what proportion of the effect is over dependence on AI removing critical thinking and what amount is having your methods disrupted mid task.

Here is the paper: https://ai-project-website.github.io/AI-assistance-reduces-persistence/

No the test is not training, that’s a weird thing to claim.

The control group solved 12 questions manually and then the 3 test questions manually. The AI grouped solved 0 questions manually and the 3 test questions manually. One group had 12 more manual math tasks to prepare for the manual math test the other group had 0 and also had to context switch.

The AI-assisted group was dealt a context switch, which results in a pretty severe performance loss. A context switch causes performance loss of around 40% according to this paper, which was peer-reviewed and published and is also the most cited paper on the topic, in the APA: https://www.apa.org/pubs/journals/releases/xhp274763.pdf

The AI-assisted group also did not have 12 questions to adjust to the new context, like the control group did. If they wanted to wipe out the context switching performance loss they should have kept asking questions to see if, after 12 questions, the AI-assisted group had a similar performance.

The switch is what is tested, and you disregard that 2 other tests have shown similar results.

No, they did not switch what was tested. Here is an image from the actual paper.

They were given 12 tasks with one group using AI and another doing mental math and then 3 tasks doing mental math. One group had 12 more tasks worth of preparation than the other.

Nothing, not even the article in theOP, says that they did math and swapped to reading to test.

They did 3 different experiments, in each experiment they gave 12 tasks and then disabled the AI for one group and gave 3 more tasks as a test. At no point did they ask 12 math questions and then finish with 3 reading questions or vice versa. They did 2 experiments using math tasks and 1 experiment using reading comprehension tasks.

So one group had 15 math tasks and one group had 12 'how to ask an AI' tasks and then 3 math questions.

They also did not control for context switching losses, which is a well documented (see the APA paper) effect. The proper control would be to continue asking questions so the AI group also had 12 math tasks before the test.

There's a reason that this is published on arXiv and not in a peer-reviewed journal. Designing a poor quality experiment doesn't tell you anything useful even if you do multiple different versions of the same experiment.

This paper demonstrates a lack of a proper control group, specifically a failure to control for context switching performance loss.

Not training, no, but warm up. And no, it is not about critical thinking, it's about reading comprehension and calculations.