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Wherefore [hoste] the law [nomos] was [ginomai] our [hemon] schoolmaster [paidagogos] to bring us unto [eis]
Christ, [Christos] that [hina] we might be justified [dikaioo] by [ek] faith. [pistis] KJV-Interlinear
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Therefore the Law has become our tutor to lead us to Christ, that we may be
justified by faith. NASB
This verse is a bit confusing in that at first look it would imply that the law was the teacher, but such is not the case.
Schoolmaster or tutor, 'paidagogos,' is a sort of guardian but not a school instructor.
Back in Pauls day, wealthy folks, when they had children, would place the infant with a wet nurse who would take charge of the child until it was weaned.
Then the child would be passed along to yet another servant who was the nanny, who would look after the child until they were about five or six years of age and ready for schooling.
Then the child would be placed under the care of yet another servant, often a slave, who was called the 'paidagogos,' or the guardian.
This guardian would look after the child and give them basic instruction, such as manners and hygiene. The primary task of the guardian was to keep the child safe, to keep them from harm, to pull them out of harms way or to redirect their path if the child happened to go off in a wrong direction. One of their duties was to take the child to and from school.
And in this capacity, the Law, was the 'paidagogos,' or guardian, which warned of failure, which taught basic moral law, which taught basic ritual principles, but primarily was to keep the child from temptation and acted in the capacity of a restraint.
The real instructor was doctrine, the written word, Christ.
Thus, the Law was the restrainer, not the justifier. And the restrainer was there in order to contain and direct the focus of the individual toward the real subject, which was faith in the real savior, who is Christ.