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Segregation can be described along both horizontal and vertical dimensions. The horizontal dimension describes how women and men are distributed across some set of occupational fields or, in the case of educational programs, different fields of study. Figure E-4-1, for example, shows the subfields of women and men who earned doctoral degrees awarded by mathematics departments in the United States in 2008. The largest number of degrees was awarded in statistics and biostatistics, in which women accounted for 51 percent of the Ph.D. recipients. Women also accounted for just more than half (54 percent) of the doctoral degrees in mathematics education. Among the other nine fields shown in the chart, women accounted for between 12 percent (probability) and 31 percent (differential, integral, and difference equations) of the doctoral degree recipients.

The vertical dimension, then, provides an understanding of segregation within a system that involves ranking. Vertical segregation looks at a particular occupation, or set of occupations, to see how people from different social groups occupy different levels within that occupation. Figure E-4-2, using data from the U.S. National Science Foundation, shows the distribution of women and men across the ranks of U.S. doctoral-degree mathematics faculty. Typically, faculty in the full and associate professor ranks also hold tenure, while those in the assistant and instructor/lecturer ranks are not tenured. Each rank represents a level of additional advancement over the previous one. While women are split nearly equally in the two senior ranks and the two junior ranks, more than half of male doctoral-degreed mathematics faculty were full professors. Altogether, about 80 percent of men faculty in mathematics held relatively secure and powerful positions, while women were more likely to be in lower-level positions. Further, one-in-ten women mathematics faculty holding doctoral degrees were in what are often considered the least secure and least powerful positions as instructors/lecturers.

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