This common aim would transcend national and cultural boundaries, even while the specific and practical ways in which it is pursued would change from school to school. The Catholic Church and its educational institutions have the unique advantage and challenge of a centralized authority which serves to discern and express the essential elements that make for unity of belief and purpose.
All departments, including the Congregation for Catholic Education, receive direction and communicate reports to the Pope, but the whole reason they exist is so that hundreds of people can do the enormous work of faithfully and helpfully coordinate the efforts of millions of Catholics. Very often, the principal way these departments express the work they do is through documents released to address current developments. The Congregation for Catholic Education has released documents on Intercultural Dialogue, religious education in schools, religious and lay educators, human love (sex education), and several times on the Catholic school itself.
Besides what the Congregation has released with the permission of the Pope, there are also papal documents, including John Paul II’s encyclical Catechesi Tradendae, and numerous addresses to Catholic educators by several popes. Finally, there is a conciliator document, meaning that all the bishops of the world gathered to construct and vote on it at the Second Vatican Council, called Gravissimum Educationis. Church teaching on education of course goes way back before this, but this is far enough back to give us a solid sense of what the Catholic church tries to do with Catholic schools.
You are welcome to read these documents for yourselves, but I believe reading church documents is like flossing: we want to have done it alot more than we want to do it. Luckily, I am a total church nerd, so I have read most of them, and continue to read more. How awesome would it be to have 3 or 5 minute reads that each give you the gist of almost every Vatican document about Catholic education? Joshua and the Israelites flying over Jericho on pterodactyls awesome!
For now, let me try to sum up an actual answer to the question: The first and foremost goal of schools in the Catholic tradition is to participate in the evangelizing mission of the Church. Everything else going on in a school must serve that. Right away, we need to address the common misunderstanding of how the Catholic Church uses the term “evangelization” - it does not mean to ‘proselytize’ (coerce or pressure children into becoming Catholic) and it does not even mean to turn non-Catholics into Catholics primarily. The Catholic idea of evangelization means to spread the good news of Jesus Christ by participating in his mission to all humanity. Just as Jesus taught and healed people who did not end up following him, Catholics see as their Christian duty to serve the authentic needs of humanity, be they physical, intellectual or spiritual. Thus, the Catholic school is not designed primarily to manufacture or maintain Catholic believers (though it does do this) - but rather the Catholic school, like the Catholic Church, serves the whole of humanity. The school does this particularly by recognizing and meeting the learning needs of the individual student as a human person, one which is a composite of body, mind and spirit. It also serves communal needs to strengthen, renew and pass on cultures of knowledge, skill and wisdom. And finally, the fact that religious education is central to the curriculum of the Catholic school means that the spiritual dimension of the human person is attended to in an environment of freedom and love. All of this is evangelization because it leads to the true good of humanity, which we believe God desires to be peaceful, just and flourishing. Every human person is free to inquire and enter the Church, and sometimes that happens because of an encounter with a Catholic school; this is not, however, the modus operendi of the Catholic school, according to Catholic teaching.
There’s much more to be said about the refined and sophisticated Catholic vision of education - look for summaries of Catholic documents coming soon!