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Not necessarily. Test taking is a skill in its own right. The PISA test is for example 4 hours long, and students might not have the endurance to stay focused reading text that doesn’t matter and answering questions they don‘t care about for 4 whole hours.
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Not being able to focus for 4 hours seems like a bigger problem. But it’s also entirely orthogonal to your distinction of “teaching the test” vs “actually educating”. You can’t teach people to focus for 4 hours.
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I know I would not be able to focus for 4 hours on a test that doesn’t matter, while reading text I don‘t care about, so that kids are failing that seems like a non-issue to me.

The rest if your point is simply wrong. Focusing is a physical activity that you can train for. Every good chess player that plays classical trains for that. And so do (or rather so did) students in the education system. Taking mock tests before the finals is a way to train your endurance such that you will be better able to keep your focus throughout the test.

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