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), a Hispanic-serving institution. MI is described in the context of FIU's overall effort to enhance student participation in physics and science broadly. 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 (i.e., Black, Hispanic, women). 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 (i.e., C- or better) by students historically under-represented in physics to reflect equity and participation in introductory 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 less than 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. The results of this disaggregation indicate that although ethnically under-represented students enter with lower overall conceptual understanding scores, the gap is not widened during introductory physics but instead is maintained, 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. Contrasting these results with the participationist view on learning indicates a movement toward greater equity in introductory physics but also indicates that the instructional environment can be improved. (Contains 5 figures and 3 tables.) [A 59-item list of references and notes is provided.]