Research has shown that fathers’ involvement has lots of benefits, Dr. Garfield said. “We know that fathers use different words than mothers, and that helps develop the child’s expressive vocabulary, they use different language when out and about in the world.” Fathers are more likely to engage in “rough and tumble” play, he said, and they often keep changing the rules, which can be very exciting for children and helps them learn.

In the poll, 32 percent of the fathers had been criticized for being too rough, and 32 percent for not paying attention to their children. “Some things are unique to dads,” Ms. Clark said. “Being too rough and not paying attention play into some of the gender stereotypes still present in our society.”

Fathers tend to engage with their children in more physically active ways, Dr. Brown said, and tend to take more risks and encourage exploration. “They might be engaging with their kids in a way, not just not harmful but actually helpful, but different from mothers.”