New Testament Times:
About one-hundred years before Christ, the Jewish leadership began promoting schools as a counterweight to Grecian influence. The schools were for boys age five to thirteen, teaching rudimentary skills.
"In this period a synagogue presupposed a school, as with us a church implies a Sunday school. Hence the church and Sunday school, not the church and the district school, is a parallel to the Jewish system. The methods in these schools were not unlike those of the modern Sunday school. Questions were freely asked and answered, and opinions stated and discussed: any one entering them might ask or answer questions. Such a Jewish Bible school, no doubt, Jesus entered in the temple when twelve years old...in the apostolic period teachers were a recognized body of workers quite distinct from pastors, prophets, and evangelists (see 1 Cor. xii. 28, 29; Eph. iv. 11; Heb. v. 12, etc.). The best commentators hold that the peculiar work of teachers in the primitive church was to instruct the young and ignorant in religious truth, which is precisely the object of the Sunday school." (Schaff, 2262)
The evidence of this time period is scarce. Some of the church fathers were schooled at home (Gregory of Nyssa), others locally (Basil) and others some combination thereof (Chrysostom). A few of the councils (Constantinople, Toledo and Vaison) ordered the erection of schools or commanded the priests to teach the local children. Some leaders, such as Polycarp, apprenticed local boys at their home. Even though the church fathers cautioned against pagan influence, men such as Chrystostom and Tertullian, allowed and at times encouraged local schooling or tutoring. There were even bible schools for children.
Religious instruction being an important Christian goal, catechetical schools were created.
“These catechetical classes and schools were intended to prepare neophytes, or new converts, for church-membership, and were also used to instruct the young and the ignorant in the knowledge of God and salvation. They were effective, aggressive missionary agencies in the early Christian churches, and have aptly been termed the 'Sunday schools of the first ages of Christianity.' The pupils were divided into two or three (some say four) classes, according to their proficiency. They memorized passages of Scripture, learned the doctrines of God, creation, providence, sacred history, the fall, the incarnation, resurrection, and future awards and punishments..." (Schaff)
Formal schooling existed along side domestic education, even as it was expanding into new venues such as the monastery, cathedral and parish schools.
Summary References & Suggested Reading:
Compendia Rerum Iudaicarum ad Novum Testamentum, Section One. “The Jewish People in the First Century.” Vol. 2.
Catholic Encyclopedia Online
History of Education, Cubberley
A Religious Encyclopedia, Schaff, online.