How to gamify a mentoring activity? I am working on an app where we are aiming to develop peer to peer training. How could we gamify the learning process to make it more fun?
For starters, I think it's a good idea to provide rewards for both students and mentors. As an example: Mentors could receive rewards for answering questions by students, while students receive rewards for solving exercises. Furthermore, the mentor should be able to give rewards for good questions etc.

Actually, it's quite a bit like Stack Exchange, if you think about it. Only, without exercises and without the ability to directly ask one particular teacher who can be rewarded for answering and also reward you for a good question. 

Another idea that pops up immediately, is to have team or group exercises with predefined roles. For example, if the exercises includes writing a calendar program (like Google calendar). One person could be responsible for graphical design, one for coordination etc.
This is maybe not an ideal scenario since a task like that would be quite extensive but I think you get the picture.

In general, I think it's not that difficult to represent the traditional relation between student and mentor. This system is, in a sense, already includes rewards. However, the difference between the traditional system and an app like yours is really the possibility to engage in learning because you feel interest or curiosity about the subject. Having someone who can help and reward you only fuels the intrinsic motivation you already have. In that sense, I believe what really counts is that a system like the one you outline offers a sense of security for the student. The gamification is mostly based on extrinsic motivation and as such only an added bonus. The ability to connect based on interest and the desire to learn is what really makes the difference, I think.

I recommend the documentary 'Alphabet' which recently premiered. In this film, there is also a high emphasis on learning as a game, even though it may not exactly be what you're looking for, it might nevertheless provide some inspiration.