Sometimes παιδεία is painful because we have done something wrong and our loving heavenly Father would not dream of allowing us to live in our sin. At other times παιδεία is painful because we need to learn and grow, but not because we have done anything wrong.
Please don’t read the negative part of the semantic range of “discipline” into παιδεία as if it is always there. Sometimes it is; sometimes it isn’t. But God is our loving Father who treats us as his true children, and that means he cares enough to use the situations of life to change us.
via koinoniablog.net
Wm. Mounce seems to suggest that the Greek term παιδεία in Hebrews 12 doesn't include the idea of chastening or punishment. What say you?