1) the whole training and education of children (which relates to the cultivation of mind and morals, and employs for this purpose now commands and admonitions, now reproof and punishment) It also includes the training and care of the body
2) whatever in adults also cultivates the soul, especially by correcting mistakes and curbing passions.
2a) instruction which aims at increasing virtue
2b) chastisement, chastening, (of the evils with which God visits men for their amendment)
Part of Speech: noun feminine
Citing in TDNT: 5:596, 753
From G3811; tutorage, that is, education or training; by implication disciplinary correction: - chastening, chastisement, instruction, nurture.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root παιδεία; click on the second column to search for that grammatical form of the root παιδεία; click on the third column to search for that word and grammatical form; click on the total to search for the root παιδεία.