According to Marvin R. Wilson (pg. 299), there were 480 synagogues in Jerusalem just prior to 70 A.D., each with its own bet sepher and bet talmud.
The bet sepher (house of schooling) was essentially elementary school, starting at age 6 or 7, and focusing on "the book", or the written law.
The bet talmud (house of study) was for the older student, starting around age 10, and focused on the oral law.
The better students, around age 13, went on to bet midrash in their spare time. These "academies" were taught by such distinguished rabbis as Hillel and Shammai.
It's interesting that the Jewish culture considered it inappropriate to use the Torah as a "'spade' for the digging of wealth" (pg. 300), so teachers taught for free, making their living at an occupation, such as woodchopper (Hillel), surveyor (Shammai), blacksmith (Joshua), tanner (Ishmael), water-carrier (Huna), or leather-worker (Paul). I wonder if Jesus was still doing carpentry/masonry(?) during his three years of ministry.
Only males 20 years of age and older were required to pay the Temple tax. When Peter asked Jesus about paying this tax, Jesus told Peter to go fishing, and doing so he caught a fish with a coin in its mouth, just enough to pay the Temple tax for both men, but for none of the other disciples (Matt. 17:24ff). This is suggestive that most of Jesus' disciples were between the ages of 13 and 19 at the time - mere teens.