This additive relationship has been the ruling assumption for the past several decades. The nation has been trying to improve education by dumping billions of dollars into schools, equipment, books and teachers with little to show for it. Another assumption is that educational achievement depends on a multiplicative relationship between the home and school. In that case, if the home environment is worth zero, no matter what resources we put into schools there's going to be disappointing results. That's because zero times anything of any magnitude equals zero.
Considerable evidence suggests a multiplicative relationship.
Children who tend to do well in school generally come from two-parent families. Their parents ensure that homework is done and educational material is in the home. They're lectured about school behavior and punished when necessary. Parents make sure they attend school every day and on time. Parents respond to school notices and grades.