Parents are under command to bring up their children in light and truth (see D&C 93:40). Parents cannot leave decision making about teaching up to school boards school teachers (or Sunday School teachers) alone; these other teachers are here to assist parents in an ultimate responsibility that rests primarily on parents.
It is not enough to educate children academically– reading, math, geography, languages, history, music– we must also make sure they know how to identify light and truth.
The following teachings were suggested by President Hinckley for parents to teach their children: http://www.lds.org/pa/library/0,17905,7461-1,00.html
• Teach them to develop good friendships.
• Teach them the importance of education. Youth will be amply rewarded for their efforts to obtain an education. The Church will also be blessed by their increased capacities and skills.
• Teach them self-respect. The First Presidency and Quorum of the Twelve Apostles encourage modest dress, and discourage tattoos and the piercing of the body other than the minimal piercing of the ears by women for one pair of earrings.
• Teach them to stay away from drugs. Those who use illegal drugs or misuse legal drugs lose self-control.
• Teach them the virtue of honesty.
• Teach them to be virtuous. Sexual urges must be controlled with self-discipline and respect.
• Teach them to look forward to the time when they may be married in the house of the Lord.
• Teach them to pray. It is a miracle that we can approach God in prayer and be heard.