Proverbs 29:15 There is a big difference

The rod of correction imparts wisdom, but a child left to himself disgraces his mother.

The big difference I'm referring to in the title is the difference between "punishment" and "discipline."

Let's look at ye old dictionary first:

Punishment: suffering, pain, or loss that serves as penalty or retribution
Discipline: training that corrects, molds, or perfects the mental faculties or moral character 

Every parent knows that we don't have to teach our kids how to do wrong or misbehave. Just like us, they have a natural bent toward getting into trouble! Discipline, however, imparts wisdom, so when we lovingly correct our children, we are teaching them and imparting wisdom on the accepted ways to behave in different situations. Carrying this to its logical conclusion, if we love our children, we will discipline them.
Now, many parents are torn about physical discipline and verbal correction. I believe that the Bible gives parents the authority to dispense physical discipline if they feel it is necessary -- but I also believe that it is not always necessary --- there are many other means to accomplish the same goals. Parents must pray and seek wisdom for the appropriate measure for each child, and for each situation.
I firmly believe that the parent must also explain to the child why they are being disciplined, and how to avoid it in the future!
Many parents, even many Christian parents, become extremely upset when their child "acts up" in public . . . but they turn a blind eye to the same behavior at home. Is it any wonder that the puzzled child can't understand why it's not OK to act that way in public? That may be why some embarrassed moms will swat their kids in the store, and the children are at a loss to know what they did wrong.

I read of a historian's account of the Sioux Indians that I thought was very interesting. Francis Parkham (I have an old edition of one of his books, and it is fascinating) wrote that the Sioux were extremely indulgent of their children. They did not discipline them at home. However, when they acted up in public, all of the adults would turn and look at them, laughing and pointing at them. Humiliating? Yes. Effective? Definitely, according to Parkham. It taught them that to be taken seriously as a member of the tribe, they would need to act more maturely, and the technique worked better and better as the child progressed toward adulthood.

There are scads of verses that address discipline in Proverbs . . .
Proverbs 22:15 Foolishness is bound in the heart of a child; but the rod of correction shall drive it far from him.
Proverbs 23:13 Withhold not correction from the child: for if you beat him with the rod, he shall not die. 14 You shall beat him with the rod, and shall deliver his soul from hell.

This all sounds horrible to us in our day, but the "rod" of correction is an all-encompassing term, according to my commentaries. That rod can be verbal correction, delivered with love and firmness. It can also be a physical correction if a parent believes that is what is necessary. Probably the most important thing is to be consistent!
A child deserves to know the details of what is expected of him/her, and what is the point at which they will have "crossed the line." Things must be laid out as far as right and wrong, and the mom and dad must present a united front, too. Their unity and consistency are key.

It's vital for children to receive positive comments on good behavior, as well as the correction and training on bad behavior. The rod and reproof will not hurt them if done lovingly, consistently, and with their best interest in mind.
Kind of a tall order for us parents, huh?
This is a comfort to us as we seek to discipline wisely:

But if any of you lacks wisdom, let him ask of God, who gives to all men generously and without reproach, and it will be given to him. James 1:5