This study was designed to investigate the cognitive level of development and mathematical fluency of first grade children. A total of (N = 100) 6- and 7-year-olds from two low socioeconomic level elementary schools participated in this study. Piaget's conservation-of-liquid task was administered to children to determine their cognitive level of development. The fixed factor was the between-subjects variable group, which included (n = 50) conserving and (n = 50) non-conserving children in the first grade. The research hypotheses were addressed by using a MANOVA with the two dependent variables addition fluency and subtraction fluency. A counterbalanced method was employed to administer two separate single-skill math fact probes for two minutes to measure addition and subtraction fluency. The results indicated a highly significant effect on addition fluency and subtraction fluency (P-values less than 0.001) as a factor of conservation ability with neither addition nor subtraction having a substantial advantage over the other. The covariate of age had a separate effect on mathematical fluency above and beyond cognitive level of development. The covariates race and gender had no effect on fluency. As indicated in this study, cognitive level of development was not a grade- level-based designation; levels of cognitive development were characterized by different abilities in mathematical fluency. Implications of this study point out that instruction and curriculum are not the sole factors in mathematics achievement. A teacher's use of curriculum through instruction should be considered subject to the cognitive abilities children. Developmentally appropriate teaching practices should be considered in the context of learning elementary school mathematics. Nine appendices present: (1) Consent Form: English; (2) Consent Form: Spanish; (3) Institutional Review Board Approval; (4) Conservation-of-Liquid Task: Standard Directions; (5) Math Fact Probe: Addition; (6) Math Fact Probe: Subtraction; (7) Single-Skill Math Fact Probe: Standard Deviations; (8) Nonconserving Subjects; and (9) Conserving Subjects. (Contains 2 tables and 2 figures.)