As men everywhere brace for an onslaught of ties, tools, wallets and novelty socks gifted for Father’s Day, here are two questions fathers of young children should ask themselves: What activities are best for bonding with my child, and when should those activities take place?

New research from the University of Georgia reveals that both the type of involvement—caregiving versus play—and the timing—workday versus non-workday—have an impact on the quality of the early father-child relationship.

The study by Geoffrey Brown, published in the Journal of Family Psychology, reveals that fathers who choose to spend time with their children on non-workdays are developing a stronger relationship with them, and play activities seem particularly important, even after taking into account the quality of fathers’ parenting.

“Fathers who make the choice to devote their time on non-workdays to engaging with their children directly seem to be developing the best relationships,” said Brown, assistant professor in the UGA College of Family and Consumer Sciences. “And on those non-workdays, pursuing activities that are child centered, or fun for the child, seems to be the best predictor of a good father-child relationship.”

However, fathers who spend lots of time helping out with child care-related tasks on workdays are developing the best relationships with their children. And men who engage in high levels of play with their children on workdays actually have a slightly less secure attachment relationship with them.

“It’s a complicated story, but I think this reflects differences in these contexts of family interaction time on workdays versus non-workdays,” Brown said. “The most important thing on a workday, from the perspective of building a good relationship with your children, seems to be helping to take care of them.”

In early childhood, the most common way to conceptualize the parent-child relationship is the attachment relationship, according to Brown. Children form an emotional bond with their caregivers, and it serves a purpose by keeping them safe, providing comfort and security, and modeling how relationships should work.

Decades of research have focused on mother-child attachment security, but there’s much less research on the father-child relationship and how a secure attachment relationship is formed.

For this study, Brown and his colleagues worked with 80 father-child pairs when the children were about 3 years old. The team conducted interviews and observed father-child interaction in the home, shooting video that was evaluated off site and assigned a score indicating attachment security.

“We’re trying to understand the connection between work life and family life and how fathers construct their role. It’s clear that there are different contexts of family time,” Brown said. “Relying too much on play during workdays, when your child/partner needs you to help out with caregiving, could be problematic. But play seems more important when there’s more time and less pressure.

“Ultimately, fathers who engage in a variety of parenting behaviors and adjust their parenting to suit the demands and circumstances of each individual day are probably most likely to develop secure relationships with their children.”