Teaching one's children is part of the primary purpose of marriage. It's not to be delegated without good reason. It's also not the place of the state to impose curricular requirements on what parents teach their children. The Church has the authority to watch over every branch of education, as Pope Pius XI taught us in his encyclical Divini illius magistri, and the state has the duty to protect both the rights of the Church and the family in regard to education of children in its legislation.
'The family therefore holds directly from the Creator the mission and
hence the right to educate the offspring, a right inalienable because
inseparably joined to the strict obligation, a right anterior to any right
whatever of civil society and of the State, and therefore inviolable on the part
of any power on earth.
'That this right is inviolable St. Thomas proves as follows:The child is
naturally something of the father . . . so by natural right the child, before
reaching the use of reason, is under the father's care. Hence it would be
contrary to natural justice if the child, before the use of reason, were removed
from the care of its parents, or if any disposition were made concerning him
against the will of the parents.
'And as this duty on the part of the parents continues up to the time when the
child is in a position to provide for itself, this same inviolable parental
right of education also endures. "Nature intends not merely the generation
of the offspring, but also its development and advance to the perfection of man
considered as man, that is, to the state of virtue" says the same St.
Thomas.' -- Divini illius magistri, nos. 32-33
Every child learns at a different pace and excels at different subjects. It's up to parents to facilitate their children in a well-rounded religious and moral education, as well as see to their physical and civic training insofar as they're able to do so, and provide for the children's temporal well-being.
This being the case, it's not important for every child to learn geometry or even algebra, nor physics, computers, literature, chemistry, nor what passes for biology. These higher pursuits and beyond ought to be left up to the discretion of parents.
It seems to me most reasonable that a child ought to be able to face the world at adolescence with the ability to reason and judge finely, have the habit of good arithmetic, be able to compose and write an expository essay, be able to speak and express himself clearly and certainly, have a good and solid knowledge of the deposit of faith, be well-experienced at the practice of religion, have a firm grasp on and good habit of moral behaviour, be able to sight-read sheet music, have a working knowledge of money management, etc. In general, if the child is female, it seems most reasonable that she has the working ability to make a home for a family, and if the child is male, that he has learned or is in the process of learning a trade.
Obviously if a child (whether male or female) excels greatly at a particular subject which would benefit the common good, it is good for parents to look into particular education in that area from those professionally and classically schooled in that subject, but it's not imperative (nor necessarily advisable) to treat every child that way.
I don't see any real benefit to society to dump 30 children from disparate backgrounds into classroom seats and then try to educate them all at the same level and pace. I know this often happens under the guise of "socialization", but I don't buy it. I personally see it as a propaganda mechanism for the state, though many educators protest this (none actually give good reason, but rather most say they don't "feel" like they're propagandizing for the state).