1 Corinthians 4:15 Galatians 3:24,25, in Greek Paidagogos; a sort of attendant who took the charge of young children, taught them the rudiments of knowledge, and at a suitable age conducted them to and from school. Thus the law was the pedagogue of the nation, and a length conducting them through its types and prophecies to Christ. When a Jew came to a believing knowledge of Christ, this office of the law ceased.
Little is known respecting the schools of the Jews, nor when and how far they took the place of domestic instruction, Deuteronomy 6:7-9 11:18-20. It is probable that elementary education was under the charge of the minister of religion, as well as the instruction of those of riper years. At the time of Christ, it would appear that the Jews in general were able at least to read and write.
Source: ATS Bible Dictionary
Schoolmaster
The law so designated by Paul (Galatians 3:24,25). As so used, the word does not mean teacher, but pedagogue (shortened into the modern page), i.e., one who was intrusted with the supervision of a family, taking them to and from the school, being responsible for their safety and manners. Hence the pedagogue was stern and severe in his discipline. Thus the law was a pedagogue to the Jews, with a view to Christ, i.e., to prepare for faith in Christ by producing convictions of guilt and helplessness. The office of the pedagogue ceased when "faith came", i.e., the object of that faith, the seed, which is Christ.
Source: Easton's Bible Dictionary
Schoolmaster
SCHOOL'MASTER, n. See Master.
1. The man who presides over and teaches a school; a teacher, instructor or preceptor of a school. Applied now only or chiefly to the teachers of primary school.
Adrian VI. was sometime schoolmaster to Charles V.
2. He or that which disciplines, instructs and leads.
The law was our schoolmaster to bring us to Christ. Gal. 3.