The opportunity to learn for African American and Latino children is extremely limited in a large number of US classrooms. Many societal issues are to blame, but high-stakes testing has exacerbated this problem. The pressure to increase test scores has caused a narrowing of the curriculum, particularly in low-performing schools, most of which are attended by poor children and children of color. For mathematics, in particular, this curriculum is characterized by a narrow set of knowledge and skills. Seven teachers, all of whom had previously participated in professional development focused on supporting teachers' efforts to engage with elementary students in algebraic thinking, were videotaped and audiotaped as they taught lessons on the equal sign and relational thinking. This study analyzed the performance of the students in order to assess their mathematical proficiency using the five strands of mathematical proficiency defined by the National Research Council (2001) and also analyzed the teachers' lesson structures and classroom norms. The results of the analyses were used to detail how teachers afforded or constrained students opportunities to develop mathematical proficiency. Classes in which the majority of students were found proficient had several norms in common, including sociomathematical norms around what counts as an adequate explanation. Additional, the classes in the majority proficiency group had norms that encouraged students to share multiple solutions and facilitated productive group work. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]