"Is it a boy or a girl?" Why is this usually our first question when we see a baby?
It's because it helps us make a quick judgment about the child's behavior and physical features, even though the latter seem to be unambiguous and impervious to bias. If its a girl, then we say she is "pretty" and if its a boy, we say he is "handsome." 
The following excerpts have been taken from Virginia Valian's superbly researched book, "Why so slow? The advancement of women." The research studies show how deeply rooted these gender schemas (intuitive conceptions) are, and how early they take begin to take shape.
Pink or blue
Judith Bridges did a comparative study of 61 girl greeting and 61 boy cards that were sent to congratulate parents on their new arrival . Images depicting physical activity, such as action toys and active babies, were more prominent on boy than girl cards. Thus girl babies are pictured as sleeping or immobile more often than boys are. Verbal messages of expressiveness, including sweetness and sharing, appeared on more girl than boy cards. The most striking difference is that expressions of happiness or joy are found on 64% of the boys' cards in comparison to only 49% of the girls' cards. Greeting cards thus welcome two classes of human infants - one that is pink, decorative, sweet, and passive -- like birds or rabbits -- and the other is sports oriented and physically active -- like bears or puppies -- and brings happiness and joy.
In the eye of the beholder -- gender stereotyping within the first day of being born
In this research study 30 pairs of first-time parents, fifteen with sons and fifteen with daughters, were interviewed within the first 24 hours of birth . "Although male and female infants did not differ in birth length, weight, or Apgar scores, daughters were significantly more likely than sons to be described as little, beautiful, pretty, and cute, and as resembling their mothers. Fathers made more extreme and stereotyped rating judgments of their newborns than did mothers."
Fathers of sons also judged them as better coordinated, more alert, stronger, and hardier than did fathers of daughters. They even said that their sons were firmer and their daughters more soft!
Girls and boys play differently as early as age one. A study of parents of 3-5 year olds indicates that parents have something to do with this gender differentiation . During this study, researchers observed that mothers reacted favorably when either boys or girls chose feminine toys but were especially likely to praise or show affection to girls. Mothers tended to reward their children's choices by praising, helping, or showing affection. Mothers were relatively permissive, but reacted encouragingly when their daughters made gender-compatible choices.
Fathers rewarded boys for masculine choices and punished them by interfering with their play or ridiculing them for non-traditional or feminine choices. Similarly, they rewarded girls for feminine choices and punished them for masculine ones. Fathers were particularly likely to reward boys for masculine choices and clearly indicated to their children what toys they would like their children to prefer.
Child's play turning into work
When little girls play with dolls, their actions directly serve as practice for the child care, kitchen work and home decoration they will likely take charge of as adults . If boys were to spend as much time playing with dolls, they would develop the same nurturing skills; but boys spend very little time playing with dolls.
Although play is inherently enjoyable, adults do shape children's preferences and proclivities for enjoyment. Adults encourage little girls to play at "pretend" housework and child care -- and most girls seem to find it fun. Boys would most likely feel the same, if encouraged in the same way.
But adults prepare boys differently. Fathers in particular, encourage play that rarely involves taking care of someone else and is hardly ever direct practice for adult work. For instance, boys do not play at taking out the garbage or washing the car. If their play does involve someone's welfare like pretending to be a firefighter, the role is one for which adults are paid. However, most of boys' play remains play.
"At present our culture divides the nourishing along gender lines. It is as if we took half the children and encouraged in interest in writing, and took the other half and supported only an interest in drawing.
What would happen if children were not given years of practice in either nurturant or physical play? We don't know. As things stand, children learn to enjoy only half of what is potentially open to them, the half adults give them access to. Girls learn to take pleasure in being nurturant, and boys learn to take pleasure in physical skills. Girls' increasing interest in sports shows how quickly some of them acquire a taste for physical activity. We have yet to provide boys with a parallel opportunity for nurturance." 
The benefits of androgynous parenting and egalitarian values. Why should you treat boys and girls the same?
"Families with one or more androgynous parent (i.e., a mom who repairs the family car or a dad who bakes cookies for the PTA meeting) have been found to be highest on scores of parental warmth and support . These androgynous parents are found to be highly encouraging regarding achievement and developing a sense of self worth in sons and daughters [6-7] Androgynous individuals have been found to have higher self esteem [8-10], higher levels of identity achievement , and more flexibility in dating and love relationships .
Children who have parents with strong egalitarian values tend to be more knowledgeable about nonsex-typed objects and occupations than other children . Children whose mothers work outside the home are not as traditional in sex role orientation as children whose mothers stay home . In fact, preschool children whose mothers work outside the home experience the world with a sense that everyone in the family gets to become a member of the outside world, and their sense of self includes the knowledge that they have the ability to make choices which are not hindered by gender ."
What can you do?
- Dress your daughter in gender neutral colors and clothes.
- Expose her to toys that allow her to experience forces and motion so that she develops an intuition for how things move, work, roll, fly, fall. This may not directly lead to her becoming a physicist or a mechanical engineer, but it will definitely lower the barrier to entry as she will have her own intuition for how the world works.
- Don't provide feedback to girls that you wouldn't provide to boys. For instance, don't say, "oh you are such a good mother" or "you are taking such good care of your babies" when you see a girl playing with her dolls. You wouldn't say similar things to a boy.
- Read her books about machines, vehicles, exploration and discovery
- Encourage her to be independent, to be an explorer
- Put the computer in your daughter's room (usually it's in the boy's room)
- Engage in conversations that focus more on problem solving and critical thinking with your daughter. Ask her questions such as "How did you do that? Why are you doing that? What's going on here? Tell me more about it. What are you thinking about?"
- Encourage your daughter to take risks and step outside her comfort zone.
- Be authentic -- and model confidence, risk-taking and life-long learning
Finally, let her know that "if" was written for her!
"If you can fill the unforgiving minute
With sixty seconds' worth of distance run,
Yours is the Earth and everything that's in it,
And---which is more---you'll be a Man, my son!" -Rudyard Kipling
 Valian, V. (1998). Why so slow? The advancement of women. Cambridge, MA: M.I.T. Press.
 Bridges, J.S. 1993. Pink or Blue: Gender Stereotypic Perceptions of Infants as Conveyed by Birth Congratulations Cards. Psychology of Women Quarterly 17:193-205
 Rubin, J., Provenzano, F., & Luria, Z. 1974. The eye of the beholder: Parents' views on sex of newborns. American Journal of Orthopsychiatry 44:52-19
 Langlois,J.H., & Downs, A.C. 1980. Mothers, fathers, and peers as socialization agents of sex-typed play behaviors in young children. Child Development 51: 1217-47
 Witt., S.D. 1997. Parental Influence on Children's Socialization to Gender Roles. Adolescence
 Sedney, M. A. (1987). Development of androgyny: Parental influences. Psychology of Women Quarterly, 11, 311-326.
 Spence, J. T. & Helmreich, R. L. (1980). Masculine instrumentality and feminine expressiveness: Their relationship with sex role attitudes and behaviors. Psychology of Women Quarterly, 5, 147-163.
 Lundy, A. & Rosenberg, J. A. (1987). Androgyny, masculinity and self-esteem. Social Behavior and Personality, 15, 91-95.
 Shaw, J. S. (1983). Psychological androgyny and stressful life events. Journal of Personality and Social Psychology, 43, 145-153.
 Heilbrun, A. B. (1981). Gender differences in the functional linkage between androgyny, social cognition, and competence. Journal of Personality and Social Psychology, 41, 1106-1114.
 Orlofsky, J. L. (1977). Sex role orientation, identity formation, and self-esteem in college men and women. Sex Roles, 3, 561-574.
 DeLucia, J. L. (1987). Gender role identity and dating behavior: What is the relationship? Sex Roles, 17, 153-161.
 Weisner, T. S. & Wilson-Mitchell, J. E. (1990). Nonconventional family lifestyles and sex typing in six-year-olds. Child Development, 61, 1915-1933.
 Weinraub, M., Jaeger, E., & Hoffman, L. W. (1988). Predicting infant outcomes in families of employed and non-employed mothers. Early Childhood Research Quarterly, 3, 361-378.
 Davies, B. & Banks, C. (1992). The gender trap: A feminist poststructuralist analysis of primary school children's talk about gender. Journal of Curriculum Studies, 24, 1-25.