Abstract
velop increasingly large gaps in their success rates for familiar and unfamiliar types of problems, relative to the gaps shown by less cautious problem solvers. When faced with the repeated and varied challenges of a test such as the SAT, they may avoid approaches such as working with unfamiliar modes of representation that seem risky but that offer the best chance of success. The influence of this sort of developmental process on mathematical reasoning needs to be understood before sex differences in performance are attributed by default to biological factors. When sex differences in mathematics performance are understood in terms of both problem-solving and developmental processes, it may be possible to provide the remedial instruction for girls that Benbow suggests. However, a process model of mathematical reasoning may provide evidence that girls' reasoning processes are different from, but not necessarily inferior to, those of boys. The current higher mathematics has been constructed almost entirely by men who were doing the best thinking of which their male minds were capable (Keller 1985). This mathematics is beautiful and useful, but it is not the only mathematics that could exist. Perhaps, as more women go far enough within the male system to do creative work of their own, they will produce new conceptualizations and operations that take advantage of characteristically female modes of reasoning that have yet to be identified.
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