This 186-page document can be found on the internet at http://nces.ed.gov/pubs98/fathers/ (html or pdf format).
Simply put, a father's involvement aids their children's scholastic development. Another finding is that a FULLY INVOLVED noncustodial dad is good for the child, whereas occasional contact isn't. Contact must be regular and continuing for the beneficial effects of father involvement to materialize.
"The involvement of nonresident fathers in their children’s schools appears to be particularly important for children in grades 6 through 12, reducing the likelihood that the children have ever been suspended or expelled from school or repeated a grade. This association remains even after controlling for resident mothers’ involvement in the schools, education, household income, and other potentially confounding factors. Nonresident fathers’ involvement is also associated with a greater likelihood that children in grades 1 through 5 and in grades 6 through 12 participate in extracurricular activities. There is also evidence that the involvement of nonresident fathers increases the likelihood that children in grades 6 through 12 get mostly A’s and that they enjoy school...."
"Because many divorced parents remarry, a large proportion of children also experience step families (Cherlin, 1992). Step families have an economic advantage over single-parent families, but it is not clear that the children in such families enjoy other advantages. Like children in single-parent families, children in step families show elevated risks of maladjustment and school failure compared to children living with both their biological parents (Zill, 1988)....Whatever the combination of reasons, there is no doubt that the relationship between stepparents and their stepchildren is different than the relationship between biological parents and their children." (Note that this is referring primarily to mother-headed households)
"Policymakers have emphasized the provider role of nonresident fathers and have formulated laws and policies to encourage or enforce the payment of child support and, to a lesser extent, visitation. Increasingly, however, observers are arguing that like resident fathers, nonresident fathers have more roles than that of provider in their children's lives."
"Numerous studies have shown that parental involvement in schools promotes school success (Henderson and Berla, 1994; Henderson, 1987). It seems likely that it is not attendance at school activities, per se, that leads directly to improved school outcomes, but rather that such attendance is a marker for other important factors that contribute to children's school success (Zill and Nord, 1994)."
"Fathers...are more likely to be highly involved in their children's schools if the mother in the household is a stepmother. The presence of stepmothers increases the adjusted odds that children's fathers are highly involved in their schools by 194 percent among children in grades 1 through 5 and by 197 percent among children in grades 6 through 12 relative to if the mothers are their biological or adoptive mothers. Thus, in families with stepmothers, fathers appear to assume a greater share of child-related responsibilities than they do when the children's biological or adoptive mothers are present."
"Fathers also are more likely to be highly involved in their 6th through 12th graders' schools...as the number of activities they have participated in with their children in the past week increases."
"Nowadays, with the high rates of non-marriage, separation, and divorce, many children spend part of their childhoods living apart from at least one of their biological parents (Zill, 1996). Extensive research has been conducted on the effects of divorce for children's well-being (Kelly, 1993; Furstenberg and Cherlin, 1991; Wallerstein, 1991; Chase-Lansdale and Hetherington, 1990; Hetherington, 1981, 1979) and the problems experienced by children growing up in single-parent families (McLanahan and Sandefur, 1994). Such research has found that children are better off financially, psychologically, and emotionally when they are raised by two parents."
"...nonresident fathers' involvement in their children's schools is associated with increased odds that children in grades 1 through 12 get mostly A's....nonresident fathers' involvement in their children's schools is associated with increased odds that 6th through 12th graders get mostly A's....Among such children who are living with their mothers (whether in a stepfamily or in a single-parent family), the adjusted odds that they get mostly A's are also greater if their nonresident fathers have participated in school activities compared to if they have not".
"...there is some evidence that children are more likely to enjoy school if their fathers are moderately to highly involved in their schools...".
"Nonresident fathers' involvement in their children's schools reduces the odds that children in grades 1 through 12 have ever repeated a grade, even after controlling for mothers' level of involvement and the other factors in the model. The odds that children in grades 1 through 12 have ever repeated a grade are 39 percent less if their nonresident fathers have participated in one activity at school and 48 percent less if their nonresident fathers have participated in at least two activities at their schools..."
"Nonresident fathers' involvement in schools decreases the adjusted odds that children have ever been suspended or expelled from school even after controlling for mothers' involvement in school. The adjusted odds that children have ever been suspended or expelled among all children in grades 6 through 12 who have nonresident fathers' (model 1) are 50 percent less if the fathers have participated in only one activity and 59 percent less if the fathers have participated in two or more of the school activities."
"Another interesting pattern in the models is that children who have had no contact with their nonresident fathers in the last year are somewhat more likely to enjoy school than children who have had contact, but whose fathers have not participated in any of the school activities. This association is strongest among children in grades 6 through 12 and persists even after controlling for mothers' involvement in the schools. It may be that children with some contact with their fathers, but whose fathers are not as involved as the children might wish, face more ongoing psychological strain that also affects their attitude towards school than children who do not expect that their fathers are going to be involved because they have not seen them at all.
There is some support for this speculation in the literature (Nord and Zill, 1996). There is other evidence that children who have not seen their fathers at all in the past year are somewhat better off than children who have seen their fathers but whose fathers have had no involvement in their schools. Even after controlling for mothers' involvement in their schools, the adjusted odds that children have ever been suspended or expelled are 29 percent less (significant at 0.10 level) if they have not seen their fathers at all in the past year compared to children who have seen their fathers, but whose fathers have not participated in any of the school activities. Moreover, for two of the outcomes, getting mostly A's and having ever repeated a grade, there is no difference in the outcomes among children whose fathers have had contact with them but did not participate in any of the school activities and children who have not had any contact with their fathers in more than a year or who have never had contact with their fathers."
(This shows that a more involved father, as with joint custody, for example, is the best for the child. Standard schedules of every other weekend or less do not provide enough time for the effects and benefits of a father's involvement to become apparent.)
"Taken together, these results may offer a clue as to why existing studies yield mixed results on the importance of nonresident fathers' involvement in children's lives: The measures that are used to assess nonresident fathers' involvement may not be adequate. Often involvement is measured by the simple measure days of contact. The results in these models suggest that it is not contact, per se, that is important, but rather other dimensions of involvement that go along with contact that are beneficial to children's lives. Indeed, contact may be a mixed blessing if the contact is enough to tantalize children but not enough to satisfy."
"Overall, the results in this section provide strong evidence that nonresident fathers' involvement in their children's schools is important to children, particularly to older children."