Although science and engineering (S&E) fields continue to grow, certain groups including first-generation students and women remain underrepresented among S&E degree recipients. Mathematics, specifically calculus, is often the gatekeeper to entering STEM majors that open the pathway to financially lucrative careers in S&E. Although incoming college students typically take math placement exams to determine their first college mathematics course, the use of noncognitive measures, such as math self-beliefs, in addition to cognitive skill assessments has been recommended due to high rates (25%-33%) of misplacement using solely skill assessments. A self-beliefs survey about math performance was collected for the 2022 cohort (N = 333) and 2023 cohort (N = 373) from incoming first-year college students at a small liberal arts institution. The first study compared a hypothesized four-factor model (self-efficacy, expectancy, value, and cost) and a three-factor model (ability beliefs, value, and cost) for the math self-beliefs data. The theoretical framework for the three-factor model was Eccles's & Wigfield's situated expectancy-value-cost theory (SEVT) while the four-factor model was a composite of SEVT theory and Bandura's social cognitive theory. Confirmatory factor analysis indicated the four-factor model was a better fit of the data for the 2022 cohort, which was independently validated with the 2023 cohort. Factorial invariance was also tested across first-generation status and gender to ensure measurement equivalence for both cohorts. The analysis indicated that the four-factor model for self-beliefs achieved strict invariance indicating that the measure's structure, factor loadings, item intercepts, and measurement errors were invariant across first-generation status and gender for the 2022 cohort and subsequently confirmed with the 2023 cohort. The second study utilized structural equation modeling (SEM) analysis with full information maximum likelihood estimation to compare two models representing the relationships between the self-belief latent factors (four-factor model from the first study), high school preparation, STEM interest, gender, first generation status, and performance on a math placement exam. Model 1 represented math performance by a total placement score (Part I algebra score combined with Part II emergent Calculus skills) while Model 2 represented math performance by an endogenous latent variable with three indicator variables (Part I Score, Part II Score, and Math Experience). SEM analysis indicated that Model 1 was a better fit for the data for the 2022 cohort and validated with the 2023 cohort. Model 1 was subsequently used to test for a moderation effect by first-generation status on the measurement weights and structural weights. No moderation effect for first generation status was discovered for Model 1 with either the 2022 cohort or the 2023 cohort. A follow up partial moderation analysis was run that supported the findings of the full moderation analysis for the 2022 cohort and the 2023 cohort. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]