Mathematics self-schemas are students' cognitive generalisations of their selves in learning mathematics (Ng in "Educational Psychology," 34(6), 730-762, 2014). These salient subject-based self-conceptions are conceptualised as a cognitive frame guiding students' coping responses when dealing with challenging mathematics tasks. In study 1, 271 Year 9 Australian students were classified into positive, average, and negative schematics based on their responses to a survey questionnaire. It was found that compared to the other two schematic groups, positive schematics were more motivated, used adaptive coping strategies to deal with difficult mathematical tasks, and were less likely to avoid challenging tasks. In study 2, positive and negative schematics' performance in a difficult mathematics test was compared. These two groups of schematic participants (n = 74) were drawn from study 1. Prior to taking the test, compared to negative schematics, positive schematics had higher performance targets and held stronger intention to complete the test with goals focusing on learning and performance. During the free-choice session, more positive schematics than their negative counterparts attempted an additional set of test questions. On receiving negative feedback about their test performance, significantly more positive schematics considered the test inaccurate and were willing to retake the test. Positive schematics, as expected, performed significantly better than did their negative counterparts in the test. Convergent findings derived from these two studies showed that positive and negative schematic students coped with challenging mathematics in a self-congruent manner.