Quick answer
Scorning correction is the definition of foolishness here, and taking it is the definition of prudence. The dividing line is not intelligence. It is teachability.
Read both lines
The verbs mark the fork. To "despise" is to hold instruction in contempt, and the NKJV footnotes "receives" as literally keeps, the guarding word, correction not merely tolerated but held onto. What makes this verse sting is that both men heard the same thing. The instruction was given; only the reception differed, which means folly here is not an inability but a posture. This is the same measurement 4:1 asked for and the same one 15:31 and 15:32 will return to at the chapter's close. Proverbs keeps circling it because it is the one skill that unlocks every other one: a person who can be corrected can eventually learn anything.
Related: Proverbs 15:31 · Proverbs 15:32 · Proverbs 4:1
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.