Well-prepared beginning teachers of mathematics structure learning opportunities and use teaching practices that provide access, support, and challenge in learning rigorous mathematics to advance the learning of every student. |

Teaching for access and equity is evidenced as well-prepared beginning teachers view their roles as developing robust and powerful mathematical identities in their students, demonstrating commitment to view each and every student as a capable and unique learner of mathematics. Well-prepared beginning teachers embrace and build on students’ current mathematical ideas and on students’ ways of knowing and learning, including attending to each student’s culture, race/ethnicity, language, gender, socioeconomic status, cognitive and physical abilities, and personal interests. They also attend to developing students’ identities and agency so that students can see mathematics as components of their cultures and see themselves in the mathematics. For instance, well-prepared beginners often connect mathematics to students’ everyday experiences or ask students to tell stories because they know that making mathematics relevant to students’ lives can make the learning experience more meaningful and raise achievement (Turner, Celedón-Pattichis, Marshall, & Tennison, 2009). Ensuring equitable mathematics learning outcomes for each student is an essential goal and a significant challenge. Achieving this goal requires (a) clear and coherent mathematical goals for students’ learning, (b) expectations for the collective work of students in the classroom, (c) effective methods of supporting the learning of mathematics by each student, and (d) provision of appropriate tools and resources targeted to students' specific needs.

Teaching with a commitment to access and equity entails striving to reach each student whose life is affected by what occurs in the mathematics classroom. Well-prepared beginning teachers plan for and use an *equity-based pedagogy* (AMTE, 2015) by structuring learning opportunities to provide access, support, and challenge in learning mathematics. This practice includes considering students’ individual needs, cultural experiences, and interests as well as prior mathematical knowledge when selecting tasks and planning for mathematics instruction (Leonard, Brooks, Barnes-Johnson, & Berry, 2010). For example, what everyday, informal language might support or hinder the specialized use of language in mathematics? What are students’ prior experiences with specific mathematical representations or strategies? What scaffolds are needed to support students with special needs? What assessments can help identify the strengths and weaknesses of students who are in need of interventions? What topics, activities, places, books, movies, television shows, and video games are currently popular with students and could be incorporated into tasks or problem-solving opportunities?

Well-prepared beginning teachers of mathematics strongly believe that each and every student can learn mathematics with understanding, and they take conscious and intentional actions to build students’ agency as mathematical learners (AMTE, 2015; Gutiérrez, 2009). That is, the teachers believe in each student’s ability to make sense of mathematical tasks and situations, to engage in mathematical discourse, and to judge the validity of solutions. For example, the beginning teacher envisions a classroom community in which students present ideas, challenge one another, and construct meaning together; varied mathematical strengths are valued and celebrated. Well-prepared beginners understand the importance of communicating the relevance of mathematics—specifically, that students can use mathematics to address problems and issues in their homes and communities.

Additionally, well-prepared beginners intentionally foster growth mindsets among students about learning mathematics and persistently counter manifestations of fixed mindsets (e.g., that some people are good at mathematics and others are not). This practice includes public praise for contributions, use of applicable strategies, and perseverance (Boaler, 2016; Dweck, 2008). For example, well-prepared beginners acknowledge mistakes as critical for learning and help students view mistakes as important in the learning process and for engaging in mathematics.