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:
- There is no relationship between participation/sense of belonging and achievement
- 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)
- 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.