Gender Development and Cognition

This week in class we read about cognitive approaches to gender development. One major theory we read about discussed how gender development can occur as a process by which children take in information and fit it into preexisting schemas of gender understanding. This got me thinking about how much of an effect individual differences in understanding can impact our gender development. Can one child's views of gender roles be so different from another that they develop their sense of gender differently? I think this is a valid position in all forms of development. We already know that individual differences account for a large portion of how people learn to adapt, so its not too outlandish to think that gender development may be on the same plane as this.
Could individual differences account for differences in schematic categorization of gender typed behaviors? If so, I wonder if this explains why some children are more apt to play with any toy they want, rather than discarding specific toys because they are "for girls" or "for boys." If this is the case, I think that these differences could not only teach us something about development as a whole and its progression, but also about how disparities among individuals can be something we all can observe and learn from to be more tolerant of someone else's ideas.