I'm working on an outline for a short presentation on how new online tools, especially this site, interact with the traditional Jewish learning models of chavruta and teacher-student. What are the main source texts (I suppose mostly in the Talmud, though some may be earlier and later) for the roles and benefits of these two models and the interplay between them? If there's a particular commentary or contemporary source that sums up traditional understandings of any of these primary sources, that would be great to have, too.
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A few raw blobs off the top of my head.
I don't know if this is what you are looking for, but the famous story surrounding the death of Reish Lakish (bottom of Bava Metzia 84a) plays out the benefit of a proper chavrusaship. A translation is here.
R. Yochanan was upset following Reish Lakish's death, and the rabbanan sent R. Elazar b. Pedas to learn in Reish Lakish's stead. R. Yochanan felt the chavrusaship was unproductive, since R. Elazar merely supported (textually) everything R. Yochanan said. With Reish Lakish, R. Yochanan had to defend his position and this allowed a broader understanding of the halacha.
Mishna 5 Perek 5 in Sanhedrin mentions a partnership in learning between dayanim in the case of a death sentence that is unfavourable. In such a case the final judgement is delayed until the following day. Part of the mishna mentioned above reads:
This loosely translates as: "if they find him meritorious he is exempt [from punishment]. If not, his sentence is delayed until tomorrow. [The dayanim then] pair off ['...in order to deepen their understanding' (Kehati)], they diminish in their food intake, don't drink wine all day and critically analyse the case all night ['each and every dayan in his own pair, or alone' (Kehati)]. The next day they arise to the Beth Din".
Although its not possible to learn out a general rule for chavruta study from this mishna, it can certainly be seen as meritorious and something that was done for in-depth understanding.