This survey research which is grounded on the objectivist epistemology and informed by postivism was conducted in the City of Iloilo, Philippines, during school year 2011-2012. Path analysis was used to examine the predictive and mediational role that creativity,self-efficiacy, and anxiety play in the mathematical problem-solving performance of potential mathematically gifted Grade Six pupils from purposively selected private and public schools in the City and Province of Iloilo. The investigation also attempted to explore whether differences on pupils' calibration, in terms of mean bias and mean accuracy, are varied by cognitive ability, sex, or parental support. Eighty-three pupils participated in the study. The participants were given the Kuhlmann-Anderson Tests (Non-verbal component) to determine their cognitive ability which served as the basis for their classification into high potential mathematically gifted (HPMG) and low potential mathematically gifted (LPMG) groups. Based on the results, 40 (49%) pupils were classified HPMG while 43 (51%) as LPMG. The instruments used to gather data were the Mathematics Anxiety Rating Scale (MARS) Mathematical Creativity Test (MCT),Mathematics Self-Efficacy Rating Scale (MSRS), Mathematical Problem-Solving Test, and Parental Support Rating Scale (PIRS). Means, standard deviations, and percentages were used for descriptive data analyses and the Pearson's Product-Moment Correlation, Multivariate Analysis of Variance (MANOVA), Multiple Linear Regression, and Path Analysis (PA) for inferential data analyses, all set at .05 level of significance. Results showed that as a whole group, the potential mathematically gifted pupils reported a moderately high cognitive ability and self-efficacy, low anxiety, average creativity and problem-solving performance, moderately low means bias, and high mean accuracy. When classified as to cognitive ability, HPMG pupils outscored LPMG pupils in all test, had lower mathematics anxiety, were more accurate in the judgement of their problem-solving performance, and were less biased toward overconfidence. When classified as to sex, boys outperformed girls in all tests, were less anxious, were more accurate of their self-perceptions, and were less biased toward overconfidence. Pupils who received high parental support registered higher means scores than those who received high parental support in cognitive ability, self-efficacy, and problem-solving performance. However, in terms of creativity and mean accuracy, the group which received average parental support had lower mean scores than those of high parental support group. There were significant differences in the mean scores of participants in anxiety, self-efficacy, creativity, problem-solving performance, mean accuracy, and mean bias when they were classified as to cognitive ability. No significant differences were observed when participants were grouped as to sex and parental support. In the path model for the whole group, cognitive ability significantly influenced all endogenous variable--self-efficacy, anxiety,creativity, and problem-solving performance; parental support predicted self-efficacy and anxiety; self-efficacy predicted anxiety and creativity; and creativity predicted problem-solving performance. On the other hand, sex was not a significant predictor of any endogenous variable when participants were taken as a whole group and when classified as to cognitive ability. In the oath model for the LPMG group, cognitive ability and parent support significantly predicted self-efficacy, parent support predicted anxiety, cognitive ability predicted creativity, and creativity and cognitive ability predicted problem-solving performance. Among the HPMG pupils, elf-efficacy significantly influenced anxiety, self-efficacy influenced creativity, and cognitive ability influenced problem-solving performance. The total effect of cognitive ability,sex,and parental support on problem-solving performance suggests that part of their influence was mediated by pupils' self-efficacy perceptions, anxiety, and creativity. The three path models reflect that in terms of total effect, the three variables with the strongest influence on problem-solving performance were cognitve ability, craetivity, and self-efficacy. Self-efficacy, anxiety, and creativity, and self-efficacy. Self-efficacy, anxiety and creativity, on the other hand, mediated the effect of cognitive ability and parental support as their respective total effects on problem-solving performance were much stronger than their direct effects. The direct influence of self-efficacy on both anxiety and problem solving performance, especially in the LPMG sample, was very weak. However, its total effect--when all other variables are part of the path analysis model--was strong. Generally, potential mathematically gifted pupils overestimated their mathematical problem-solving performance. The LPMG pupils overestimated their performance by a greater average number of problems than did the HPMG group. Girls in both ability groups were more overconfident than the boys although differences were not statistically significant.All girls belonging to the LMPG group were overconfident about their capacity to solve mathematics problems. Pupils who belong to the high parental support group were overconfident on more number of items than were those in the average parental support group. One very pronounced conclusion that can be drawn from the results of the study is that a potential mathematically gifted pupils' innate ability, if coupled with high sense of mathematics efficacy, and ability to produce many ideas, to generate varied approaches observed in a solution, and to come up with novel an unique ideas would make him a succesful problem solver. One recommendation that is advanced is that this study be replicated at secondary or tertiary levels and should include longitudinal,in-depth secondary analysis of similar study through qualitative research methodology or quantitative efforts should be complemented by qualitative studies aimed to exploring hoe efficacy beliefs, problem-solving skils, and creative potentials are developed and how mathematics anxiety can be avoided or reduced.