Barbies are for girls and construction sets are for boys. Or are they?

For the first time in Barbie’s more than 50-year history, Mattel is introducing a Barbie construction set that underscores a huge shift in the marketplace. Fathers are doing more of the family shopping just as girls are being encouraged more than ever by hypervigilant parents to play with toys (as boys already do) that develop math and science skills early on.

It’s a combination that not only has Barbie building luxury mansions — they are pink, of course — but Lego promoting a line of pastel construction toys called Friends that is an early Christmas season hit. The Mega Bloks Barbie Build ’n Style line, available next week, has both girls — and their fathers — in mind.

“Once it’s in the home, dads would very much be able to join in this play that otherwise they might feel is not their territory,” said Dr. Maureen O’Brien, a psychologist who consulted on the new Barbie set.

Consumer surveys show that men are increasingly making the buying decisions for families, reflecting the growth in two-income households and those in which the women work and the men stay home. One-fifth of fathers with preschool-age children and working wives said they were the primary caretaker in 2010, according to the latest Census Bureau data. And 37.6 percent of working wives earned more than their husbands in 2011, up from 30.7 percent 10 years earlier.