“On the way they should go” is literally, “according to his way.” It is natural to want to bring up all our children alike or train them the same way. This verse implies that parents should discern the individuality and special strengths that God has given each one. While we should not condone or excuse self-will, each child has natural inclinations that parents can develop. By talking to teachers, other parents, and grandparents, we can better discern and develop the individual capabilities of each child.
Taken from NIV Life Application Study Bible