I wouldn't be surprised if this has a lot to do with the latest growth. I've taken one or two Coursera courses (eg. [1]) where Bitbucket was specifically recommended for the private repositories.
It would be a hassle to get counted as a student by Github without an edu email, and it would be too much for them to individually approve tens of thousands of people.
I know Bitbucket maintain a list of student Emails, I imagine Github do the same. They send a confirmation Email, you confirm, you get upgraded - all automatic. No reason to manually approve that. Bitbucket give students unlimited collaborators, but you probably don't need that for Coursera courses anyway.
Bitbucket has a free tier for unlimited private repositories with 5 or fewer collaborators. Though you sign up with an email address, there is nothing about it being with "your school-issued email", because there is no stipulation about the tier being for students.
Github will approve people for using a student email address even if their school doesn't give them an email account, but it happens on a case by case basis, with requirements such as requesting that you forward a scanned copy of your student ID.
The difference is that Bitbucket does not ask you to be a student for the free account, so there is no process to prove that you are a student. Github has many advantages, but hassle-free, free private repositories is not one of them.
What I was saying is that with the increase in students who are encouraged to use remote version control who may not have a student email account, or even a student ID, has likely contributed to the increase in users on Bitbucket. It is worth noting that some of these courses have more than 100,000 people sign up. Even if only a small fraction finish the courses, a small fraction use version control, and many are smaller, there have already been dozens of these courses conducted in the last year on Coursera, Udacity, and EdX.
Sorry, I don't think I was clear. I'm not disputing the Bitbucket free service, I was just pointing out that Bitbucket do have a student account, and it's handled automatically by you just adding your student Email to your account. I assumed (wrongly, perhaps?) that Github would use a similar system, since case by case seemed very odd for that.
I agree with what you're saying, though I hadn't thought about it - and it's also great that these courses are mentioning version control. That really should be a part of a CS curriculum, and it's great they're doing that, my university doesn't which I found quite surprising.
Anyway, sorry for the confusion, I just thought that Github would use the same process as Bitbucket to identify students.
Github will automatically recognize your educational email account if you have an educational email account. The problem for people taking a Coursera class is that they might not be enrolled in any school. I don't think that many of those students need to upgrade to the Bitbucket student account where they get more than 5 users.
It is pretty interesting how people are using version control in these classes. Here's one that distributes the assignments as a repository on Github[1]
It would be a hassle to get counted as a student by Github without an edu email, and it would be too much for them to individually approve tens of thousands of people.
[1] http://www.coursera.org/course/scicomp