Family involvement in home-centered child education refers to non-formaL ways of learning and school-based teaching practices that take place at home. everal aspects are included, such as support and control of homework, family responses to children's academic achievement and communication between parents and children in school-related issues (Hoover-Dempsey & Sandler, 1995, 1997, 2005; Green, Walker, Hoover-Dempsey, & Sandler, 2007; Santos Rego, 2015).

It is not a matter of measure of parental involvement, just as not all parents can be involved with the expected effectiveness. The main meta-analytic investigations (Fan & Chen, 2001; Jeynes, 2003, 2005, 2007; Hill & Tyson, 2009) clarify us which are the most relevant factors:

- There is a clear relationship between family participation and academic performance in all three levels of education.

- Participation´s modalities more linked to the performance and in the three levels of education are the educational aspirations of the parents, the feelings of belonging to the center and the good atmosphere of study and supervision at home.

- These modalities slightly vary depending on the educational level considered. The perception of accessibility in communication with the center is present only in Early Childhood Education. Being a member or partner of the AMPA only appears in Primary Education.

- On the Elementary and Secondary Compulsory Education levels there are several practices of participation, with positive effects on academic performance, relating to the student who does not need help in school tasks, to participate in the elections to the center and in the activities that it Organizes.

- The socio-cultural status of the families is not associated with the performance in Infant and it is in Primary and Compulsory Secondary. The fact of being an immigrant is not associated to the performance in Infant and Primary and it is in Compulsory High School. The character of the center is not associated with performance in either Infant or Compulsory Secondary, instead it is in Primary for students who are attending to concerted centers.

- The only factor with a negative relationship with the performance in all three levels of education is the attendance at the center´s meetings. The tendency, according to the authors of the paper, is that the more times the student's behavior is dealt with the families, the worse his school performance will be. In general, participation in this modality is considered as an indicator of a problematic students situation with the consequent reaction of the parents (assessment identical to the one made by Hill and Tyson, 2009).

The main objective of the present paper is to verify whether these factors play a significant role in the family involvement with school work at home, based on the empirical contrasts of the model proposed by Hoover-Dempsey & Sandler (1995, 1997). For this, we selected a series of investigations in which this model is contrasted with a multivariate treatment of the data (regression/covariances) (Hoover-Dempsey, Bassler & Brissie, 1992; Hoover-Dempsey & Jones, 1997; Walker, Ice & Hoover-Dempsey, 2011; Ice & Hoover -Dempsey, 2011), followed by an application from a cross-cultural perspective (Yotyodying & Wild, 2014).

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