Elder L. Tom Perry
There are two areas I would determine to improve if that privilege were granted to me to have young children in our home again....to spend more time as husband and wife in a family executive committee meeting....(and) to spend more family time.
Conf., April 1994

President Spencer W. Kimball
This mortal life is the time to prepare to meet God, which is our first responsibility.  Having already obtained our bodies, which become the permanent tabernacles for our spirits through the eternities, now we are to train our bodies, our minds, and our spirits. Pre-eminent, then, is our using this life to perfect ourselves....so that one may give leadership to others, and to perform all necessary ordinances.  Secondly comes the preparation for the subduing of the earth and the elements....To subdue self is not only the more important but also the more difficult.  Many men have power over certain natural forces who cannot control their own desires, urges, passions.  We have this life of limited years in which to learn of God, to become the masters of our own destiny and secondly, we have this life plus eternities to learn of the earth and the things thereon, and to accumulate secular knowledge which will help make us gods, which is our destiny....Peter and John had little secular learning, being termed ignorant.  But Peter and John knew the vital things of life; that God lives and that the crucified, resurrected Lord is the Son of God.  They knew the path to eternal life.  This they learned in the few decades of their mortal life.  This exaltation meant godhood for them and creation of worlds with eternal increase for which they would probably need, eventually, a total knowledge of the sciences.  But this fact escapes many:  Peter and John had only decades to learn and do the spiritual but have already about nineteen centuries in which to learn the secular or the geology of the earth, the zoology and physiology and psychology of the creatures of the earth....Can you see why spiritual training through the Church organizations, family life, seminary, and other agencies must be given priority over the secular?  Can you see why a mission should be an unalterable preferred activity to the college work?...Can you see why the Lord emphasized:  "....seek ye first the kingdom of God, and his righteousness, and all these things shall be added unto you." (Matthew 6:33)
"Beloved Youth, Study and Learn" Life's Directions, Deseret Book, 1962, pp. 177-80

President Brigham Young
I am opposed to free education as much as I am opposed to taking property from one man and giving it to another....Would I encourage free schools by taxation?  No!
Journal of Discourses 18:357

President John Taylor
Whatever you do, be choice in your selection of teachers.  We do not want infidels to mold the minds of our children.  They are a precious charge bestowed upon us by the Lord, and we cannot be too careful in rearing and training them.  I would rather have my children taught the simple rudiments of a common education by men of God, and have them under their influence, than have them taught in the most abstruse [or complex] sciences by men who have not the fear of God in their hearts. . .
Teachings of Presidents of the Church, John Taylor, p.90

He, from his earliest recollection, had been taught to reverence the Bible as the word of God, to revere the lives and examples of the ancient worthies . . . . yet all these men, the friends, associates and confidants of the great Creator of heaven and earth, were men with more than one wife, some with many wives, yet they still possessed and rejoiced in the love and honor of the great Judge of all the world . . . And there, in this ignominious position, he stands, [on trial for polygamy] with every person who might possibly be his friend excluded from the jury, without the possibility of a fair trail by his peers, not one of the panel being in the least sympathy with himself; and by such people this unfortunate young gentleman has to be tried, judged, prosecuted, proscribed, and condemned, because of his firm and unswerving faith in the God of Abraham, Isaac and Jacob, of David, Solomon, and numerous other God-fearing and honorable men . . . . no wonder then that our would-be reformers are so anxious to exclude the Bible from our district schools. 
John Taylor, Journal of Discourses, 25:357

And then we want to study also the principles of education, and to get the very best teachers we can to teach our children; see that they are men and women who fear God and keep his commandments.  We do not want men or women to teach the children of the Latter-day Saints who are not Latter-day Saints themselves.  Hear it, you Elders of Israel and you school trustees!  We want none of these things.  Let  others who fear not God take their course; but it is for us to train our children up in the fear of God.  God will hold us responsible for this trust.  Hear it, you Elders of Israel and you fathers and you mothers!
The Mind and Will of the Lord, John Taylor, Address 4:22

Parents . . . do you surround your sons and daughters with every safeguard to shield them from the arts of the vile?  . . Or do you leave them in their ignorance and inexperience to mix with any  society they may choose, at any hour that may be  convenient to them, and to be exposed to the wiles of the seducer and the corrupt?  These are questions you will all have to answer either to your shame and condemnation or to your joy and eternal happiness.
Teachings of Presidents of the Church, John Taylor, p.198

You have elected me Superintendent of Common Schools, and I feel a good deal of interest in the welfare of Common Schools, and also in all of our institutions of learning, where good education can be had, for I feel interested in our youth, and I take this opportunity to speak to the whole country in relation to this matter.  I can perceive quite an interest in educational matters, manifesting itself in our brethren who preside here; and I am much gratified in it.  I hope that this whole county will go at this matter in all good faith, and where you lack good school-houses put them up; and when you have already the school-house, but lack the furniture, get it and try to make the school-house comfortable for the children; and then good teachers who are good Latter-day Saints.  Shall we have them, or shall we employ teachers that will turn the infant minds of our children away from the principles of the Gospel, and perhaps lead them to darkness and death?  Some say, "You ought to be very generous, quite as liberal and generous as others."  I think so.  But if some of these liberal people, who talk so much about liberality, would show a little more of it, we would appreciate it a little better.  I would like to know if a Methodist would send his children to a Roman Catholic School, or vice versa?  I think not.  Do either send their children to "Mormon" schools, or employ "Mormon" teachers?  I think not.  Do we object to it?  No, we do not; we accord to all classes their rights, and we claim rights equal with them.  Well, shall we, after going to the ends of the earth to gather people to Zion, in order that they may learn more perfectly of His ways and walk in His paths, shall we then allow our children to be at the mercy of those who would lead them down to death again?  God forbid!  Let our teachers be men of God, men of honor and integrity, and let us afford our children such learning as will place our community in the front ranks in educational as well as religious matters.  But would we interfere with other religious denominations?  No.  Prevent them from sending their children where and to whom they please?  No.  Or from shipping where they please?  No.  I would not put a hair in their way, nor interfere with them in any possible way; they can take their course, and we want the same privilege.
John Taylor,  Journal of Discourses, .19:.249 - 50, October 21, 1877  

For much more information see "Prophets on Education" on the BYU website at
http://education.byu.edu/edlf/archives/prophets.html