I think all we can really say for now is that “we think there’s something there, but we’re not sure what”.

A cursory glance at the recent PISA figures on student achievement in science seem to show no macro-level relationship between achievement on the one hand, and sense of belonging and participation on the other. For instance, the highest-scoring countries in the domains of literacy, science and math (which include Finland, Canada, Hong-Kong, etc.) are all over the map in terms of sense of belonging and participation.

Both Canada and Finland rank fairly low with regard to sense of belonging and participation, while Hong-Kong has a very high level of participation, but a very low level of belonging (same for Japan, which also tends to score highly on the OECD tests). Luxembourg, which ranks quite low on the science achievement scale, manifests a fairly high level of student participation, combined with low sense of belonging.

Three obvious scenarios (and there are probably more, less obvious ones) present themselves as possible explanations:

  1. There is no relationship between participation/sense of belonging and achievement
  2. There is a direct relationship of some sort between the measures of engagement and achievement, but it only turns up at the meso or micro levels (individual student, or perhaps the classroom)
  3. There is in fact a macro level relationship, but my first-year university Stats 150 course did not provide me with the analytical skills to discern it

Whatever the case, the relationships merit further study. Good luck running a randomized controlled trial on that one.