I'm not sure about the "best approach" part of the question but you could look at the literature on student engagement for some ideas about the variables that you could look at. I suggest having a look at this paper (http://sasse.ufs.ac.za/dl/userfiles/documents/sasseinpresspaper_1.pdf) for some background. It's a South African study but the concepts are grounded in international work, particularly the National Survey of Student Engagement from the United States. To be clear, I'm not 100% sure if these concepts will translate to the Facebook context, but the "Benchmarks for Effective Educational Practice" (see pg. 4 of the paper I suggested) would seem to help give you some insight into students' engagement.

One approach is to measure the click through rate for varying types of content that are posted online. Another is to determine what percentage of the individuals who like or share the relevant content are from your intended audience and whether this remains stable with time. You can also use Facebook to post links to surveys which can be run from time to time to assess whether the strategy is working and how it can be improved to meet end users needs.

What are the variables that determine engagement with the content? I would suggest some of these would be the demographics of your audience, their preferences for the type of content that is being delivered and their preferences for format of content (graphics versus text).

In some respects if you are hoping to meet educational learning objectives with posting content onto Facebook then you would ideally wish to measure meaningful engagement with the content. I am not sure that is possible with current Facebook analytics.

A bit off-topic perhaps, but in my courses I've decided to leave Facebook for the students. The classes I teach all have Facebook groups where they help each other, the groups use Facebook for their assignments. While I would love to have access to these groups for research purposes, I've found that the students prefer to be left alone in these groups and do their own thing without teacher intervention, so I've chosen to respect that.

Find the attachment.

http://arxiv.org/ftp/arxiv/papers/1501/1501.00528.pdf

Puna:

Perhaps my Facebook conference paper can help in showing how it can be used to enhance students' English writing skills:

https://www.researchgate.net/publication/263767122_Social_Media_in_Education_Bringing_Your_Classroom_to_Life_-_UWI_Research_Expo_2013

Best regards,

Debra

Conference Paper Social Media in Education: Bringing Your Classroom to Life -...