involvement do predict student achievement, others appear to be counterproductive.
During early childhood, both home-based and school-based parental involvement were found to benefit students. The first kind can take such forms as reading or engaging in learning and reinforcing activities at home, while the second involves volunteering, participation in parent-teacher conferences, etc.
In Elementary school, the same was true, but researchers noted the generalization of two new forms of parental involvement: parental expectations, which had a positive effect on student performance; and parental academic pressure, which had the opposite effect. Such pressure can manifest itself, e.g., through the use of commands, punishment, or coercive interactions; and it seems to negatively impact achievement because of its influence on students' self-concept. To the contrary, parental support was found to be positively associated with performance. This would explain why the effects of parental involvement in homework were unclear: because it can take encouraging or discouraging forms.
In Middle school and above, the only new finding was the positive contribution of parent-child educational discussions.
Interestingly, school-based involvement did not seem to make any difference past early childhood.
Finally, the positive relation between supportive involvement and student achievement was mitigated by maternal education: the more educated the mother, the more beneficial the involvement.
However, the most important and encouraging finding of this meta-analysis is probably that the achievement gap between children of more or less wealthy and educated parents seems to diminish and even disappear with very high levels of positive parental involvement.
Source: Boonk et alia (2018)