Scoffers and knowledge.
v.25 Correction. Don’t neglect to correct (punish/flog) the scoffer because the simple-minded will learn a lesson. Correct (rebuke) the wise and he will learn to be even wiser. See 17:10 and 21:11 for similar proverbs.
v.26 Shame and reproach. A son who brings shame and disgrace is the one who does violence to (mistreats, robs) his father and chases away his mother. See 20:20. Children should take care of their elderly or sick parents. Children are also to honor their mother and father (Ex 20:12).
v.27 Words of knowledge. Solomon instructs his son that if he ceases to hear instruction he will turn his back on knowledge (see 5:1-2). He of course means “do not cease to hear instruction.”
v.28 Mouth of the wicked. A false witness is a mockery to justice (v.5). The mouth of the wicked devours (gulps down ,NIV) falsehood and iniquity (Jb 15:16).
v.29 Condemnation. Make no mistake about it: fools will be punished. For the rod on the backs of fools see also 10:13. Punishment is made for the scoffer. v.28 and v.29 can be considered together. The false witness identified in v.28 and the appropriate punishment in v.29.

Read Proverbs 19:25-29