Megan and Michael have a deaf child. After his birth, they met opposition. At one point, a Deaf activist told them, "The best thing would be to give your child to a Deaf family and let them raise him."

Their story, retold by Nathan Heller in a recent New Yorker piece, was immediately familiar to me. As the Caucasian mother of two black children I hear sentiments along these lines frequently.

On the day that we took our second son to court to finalize his adoption in our state, the judge solemnly read through the scripted questions about adoption, signed the legal paperwork, then turned to us and said, "But what will you do about their hair?"

Hair? Really?

The subtext seemed to be that our adoption was legally in order but culturally in question.

For trans-racial families, both dirty looks and sincere reservations are familiar. But Heller's article, reviewing and expanding on a new book by journalist Andrew Solomon, Far From the Tree: Parents, Children and the Search for Identity, opened my eyes to other kinds of families who face the same challenge.

In his book, Solomon examines a variety of families where the child is distinctly different from his or her parents. Solomon tells the stories of children with dwarfism; children with autism; children who are criminals; children who are transgender. These children's characteristics diverge from the family pattern and, often, that of the surrounding community.

(Of course, not all of these situations are created equal. Autism is a different kind of challenge than race. Nor is criminal behavior the same as being deaf. But each circumstance creates a unique family relationship.)

There is application here for all parents. Many of us have children who are, in some way, different from us. My friend who is a linguist whose child is dyslexic, for example. Or my left-brained, uber-organized friend and her creative, scattered musician son.

Where do such children find their identity?

According to Solomon, they actually have two kinds of identity. First, a vertical identity—their identification with the characteristics they share with their parents; and second, a horizontal identity—their identification with peers who share the same challenges. So Megan and Michael's son will base his vertical identity on shared appearance and interests with his parents, but his horizontal identity on shared experiences with other deaf people.

The New Yorker article ultimately suggests that parents create a shared identity with their child as they enter into their child's unique culture. Megan and Michael, for example, connected with their son by learning sign language and befriending other deaf people.

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The situation is not unlike cross-cultural missions, and the model for parenting in Heller's article parallels what Christians often call "incarnational ministry."

In incarnational ministry, Christians claim the example of Jesus, who became a man in a certain time and place, in order to redeem his people. This philosophy places a high value on relationships forged by the means of entering into another's culture.

Though they might not call it "incarnational," this is the thinking of people who tell hearing parents to give their deaf child to a deaf family. It's also the philosophy of the well-meaning people who have encouraged our family to join a black church, move to a black neighborhood, and find a black man to mentor our sons.

The philosophy: a child can only be fully served by someone who can entirely relate to his situation.

The incarnational model, says theologian J. Todd Billings, has admirable aims. But, as he cautions in his book, Union with Christ, and in a related Christianity Today article, incarnational ministry can fall short.

For one thing, it's impossible for a person to completely abandon her original culture in order to enter a new one. (Nor is it theologically consistent with the work of Christ, who didn't abandon his deity in order to become man.) As much as parents would like to identify with our children, we can't change everything about who we are.

Another problem with an incarnational model is that it can fail to acknowledge that Christ himself is someone unique, fully God, and that he brings his children into a new identity through union with himself.

Galatians 3 tells us we have "put on Christ," in whom there is "neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are one in Christ Jesus."

In his book, Billings says, "Paul does not seem to be suggesting that … differences no longer matter but rather that they are made penultimate because of the eschatological identity of Jew and Greek—indeed of all tribes and nations—being part of one new humanity in Christ."

Our ultimate goal is not that our children would be highly functioning adults, or be fluent in their racial heritage, or would feel affirmed in their unique abilities. Our goal is that they would be united to Christ and would find their primary identity in him. When this happens, our relationship with them is strengthened. If we are in Christ, and they are in Christ, we are one.

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Parents do emulate Christ the servant (Phil. 2:5-11), whose entire earthly life was dedicated not to his own comfort, but to the good of his children. So, I find myself, perhaps the only white woman ever to sit in this chair, watching the local barber expertly clip my son's hair.

But, we parents don't rest in our ability to forge a relationship with our children through entering into their experiences. We rest on Christ's ability to reconcile all of us—parent and child alike—to a new identity in him. From an earthly perspective, my children will always be different from me. But one day those differences will be subsumed in our common identity in Christ.

Megan Hill lives in Mississippi with her husband and three children. She writes Sunday Women, a weekly blog about ministry life.