It should be possible to say "Children read books in order to learn something." "In order to know something" is not really correct in English. Maybe it's not a good sentence in Ukrainian, either.
I think the usage in Slavic languages is correct, even if the translation could be better. Знати is used in the sense of becoming acquainted with a subject, like connaître/conocer/cognoscere/kennen.
Yes, know is a stative verb so it can't be used like this in English. I'd translate it as learn as well.
"the books" or "books" - what is the difference in this case?
If you say "the books," it is implied that you know exactly which books the children are reading.
I gave my children some interesting books. The children read THE books to know something.
Without the definite article, the word "books" is more vague.
I would have phrased this sentence as, "Діти читають книжки щоб бути розумні/мудрі." ("Children read books to be smart/ wise.")
In the audio I can hear "щод" and not "щоб", is this how you pronounce this word?