The earliest Jewish rabbis are classified as “pre-Tannaitic” because they came before the rabbinic system of teaching that involved “repeating” the oral laws. Twenty-two of these rabbis are named in the Mishnah, though ten of them are only referenced once or twice. Most of these rabbis are paired as contemporary couples (called “Zugot” or sometimes “Zugoth” in being derived from the Hebrew). Five sets of Zugot are named in the period from 142 B.C. to A.D. 10. According to tradition, one of each pair served as president (nasi) of the Great Sanhedrin (the Beit Din HaGadol or Supreme Court), while the second was the “father of the court” (Ab beit din in Hebrew) or, in essence, the vice president. The Sanhedrin gained significant influence after the role of High Priest in the Temple had become politicized.
Hillel and Shammai are the most widely recognized Zugot and were the last of the pre-Tannaitic pairs. Hillel had studied in the school of Shemaiah and Abtalion (the fourth Zugot). Though the exact dates of their deaths are unknown, Hillel and Shammai both might well have been among the teachers that Jesus encountered in Jerusalem when he visited the temple at the age of 12 (Luke 2:41-48). (Note: Jesus’ birth is widely recognized today as having been around 6-4 B.C., and the last Zugot were certainly alive in A.D. 6-8.) Hillel and Shammai founded opposing Tannaitic schools (sometimes designated as “houses”). Hillel was progressive, while Shammai was more conservative in his teachings. Gamaliel, the rabbi under whom Paul studied (Acts 22:3), was a grandson of Hillel and maintained (“repeated” in the Tannaitic tradition) the teachings of the School of Hillel.
One citation from the Mishnah might give you insight into the way the traditions were carried forward in the Tannaitic period. Berakoth 1:3 records: “The School of Shammai say: In the evening all should recline when they recite [the Shema’], but in the morning they should stand up, for it is written, And when thou liest down and when thou risest up. [Deut. 6:7] But the School of Hillel say: They may recite it every one in his own way, for it is written, And when thou walkest by the way. Why then is it written, And when thou liest down and when thou risest up? [It means] the time when men usually lie down and the time when men usually rise up. Rabbi Tarfon said: I was once on a journey and I reclined to recite [the Shema’] in accordance with the words of the School of Shammai, and so put myself in jeopardy by reason of robbers. They said to him: Thou hast deserved aught that befell thee in that thou didst transgress the words of the School of Hillel.”