Researching one’s family tree has become a popular pastime, partly because parents want to pass on family stories to their kids, to give them a deeper sense of identity and history.

Many old family legends, however, are at least partly false.

Megan Smolenyak, a genealogist and author of “Hey, America, Your Roots Are Showing,” says the stories passed down by families are often rooted in one of several common misperceptions. She summarizes them this way:

“Three brothers came to America; one went north, one went south and one went west.” Many people assume they have family ties to large numbers of widely dispersed people with the same surname, but DNA testing and other genealogical tools often disprove it....