Research on sex differences in children's achievement orientations has suggested that girls have less confidence in their ability than boys, especially among bright children. To examine how sex differences in achievement orientation vary across achievement levels, 250 fifth grade children completed a questionnaire which assessed their preference for intellectual challenge. Several weeks later, each child was individually administered a discrimination-learning task to determine whether the child maintained, improved, or showed a deterioration in problem-solving strategies when confronted with insoluble problems. Children were divided into four achievement levels, according to their grade point average. Results showed that for the "A" students, significant sex differences emerged in the predicted direction. Girls were significantly less likely than boys to prefer challenging tasks; and significantly more likely than boys to show a deterioration in their performance when they confronted insoluable problems. In contrast, there were no significant sex differences within any of the other achievement levels. These findings have implications for understanding why sex differences in achievement orientations emerge in some studies, but not in others. (Author/JAC)