We report the results of a five year evaluation of the reform of introductory calculus-based physics by implementation of Modeling Instruction (MI) at Florida International University (FIU). Our analysis of MI from a "participationist" perspective on learning identifies aspects of MI including conceptually based instruction, culturally sensitive instruction, and cooperative group learning, which are consistent with research on supporting equitable learning and participation by students historically under-represented in physics. This study uses markers of conceptual understanding as measured by the Force Concept Inventory (FCI) and odds of success as measured by the ratio of students completing introductory physics and earning a passing grade by students historically under-represented in physics. FCI pre and post scores for students in MI are compared with lecture-format taught students. Modeling Instruction students outperform students taught in lecture-format classes on post instruction FCI (61.9% vs 47.9%, p<0.001), where these benefits are seen across both ethnic and gender comparisons. In addition, we report that the odds of success in MI are 6.73 times greater than in lecture instruction. Both odds of success and FCI scores within Modeling Instruction are further disaggregated by ethnicity and by gender to address the question of equity within the treatment. Results of this disaggregation indicate that although ethnically under-represented students enter with lower overall conceptual understanding scores, the gap is maintained, but not widened, during introductory physics, and the odds of success for under-represented students is not different from majority students. Women, similarly enter with scores indicating lower conceptual understanding, and over the course of MI this understanding gap increases, yet we do not find differences in the odds of success between men and women.