When James P. Comer at the Yale Child Study Center started to advocate for parental involvement in schools in 1965, he was a voice in the wilderness. Today, the School Development Program (SDP) that he founded has decades of research on this topic. I encourage you to explore comerprocess.org.

Parents interests in their children's academic achievement help to motivate them to do well and all identify areas of doubt and deficiencies that need to be addressed. Sometimes in the latter, the parent can catch the concern before the results at the end of the school term and bring it to the attention of teacher, especially in large classes. I have also included a link to what's available in RG on the topic that I hope would be helpful for you.

Best regards,

Debra

https://www.researchgate.net/search.Search.html?type=publication&query=parental%20involvement%20in%20the%20academic%20achievement%20of%20students%20%20at%20elementary%20school%20level&tabViewId=593c5fcced99e1136723f0b0&previous=researcher

Parents need to motivate students at early level for academics. Along with teachers parents need to monitor the studies and overall attitude of students. Attitude building is important. In overall development attitude plays 85 % role whereas knowledge contribute 15%.

It is important to note that parents influence the education of children from birth. Bourdieu called this influence Cultural Capital, children learn their traditions and habits but also acquire other habits of their community and environment. The education of the parents also influences like contributions in the matter of books that possess, artistic abilities, etc. Everything at the time will help you to develop as a student and as a person in today's society.

I think this is a very complicated question. Parents can be involved in a variety of ways. Whether they can help their child understand the homework assignment surely depends on whether the parents can answer the question, augment on the topic of the question, and get their child to work through the homework together. 

There is a key issue that is seldom discussed: many children have one parent who is working at least one job. If they are exhausted, then what does it mean for them to be involved.

Another variable that is seldom discussed: some parents have an enormous amount of knowledge that they can use to find a way to explain the nature of the homework. 

I note that both of my parents were immigrants who fled Hitler's armies. They never had a change to get a decent education. I was lucky to have others, including peers to work with me. I also got tremendous support from my schools. 

Bottom line: not all parents are able to get involved in a child's school work. They can encourage their children to do well in school and tell them about how important it is to do well in order to advance. In many cases parents are not aware of all the opportunities that are ahead. Therefore, important to have parent groups who are informed about potential options for their childen, the need to have books in the house, etc. 

Lots more, but this will do.

Parent involvement appears to have large effects on school learning outcomes, judging by the research I've read. I would track down:

Grolnick, W. S. (2009). The role of parents in facilitating autonomous self-regulation for education. Theory and Research in Education, 7(2), 164-173. (see p. 166-170)

Grolnick, W. S. (2012). The psychology of parental control: How well-meant parenting backfires. New York, NY: Psychology Press. (see p. 5-8)

Hattie, J. A. C. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London, U.K.: Routledge. (see p. 68-72)

I have had Hispanic students as undergrads and gradeutgerss, who were first of their family to go to either UCLA or Rutgers.. Their parent(s) want them to do well. However, there can be culture clashes. When there was a special event in the family, the student had school work to do or an exam, and did not want to go -- even when they were expected to do so.

I helped  the students think about how to explain the clash with the family. This helped re involving the parents in their children' education.  

Bottom line, the standard idea of parental involvement has to take into account the possibility of culture clashes and therefore different ideas about what it means for adults in a family to involved in their children's education. Things that all parents can do:

Get them and their children cards to the local library. Take English lessons with their children and then study together. Ask the librarian for articles or books re negotiating the Unities States and the differences in the govt of their birth country and the USA. 

See

Article Notebooks as windows on learning: The case of a science-into...