## How we think about mathematics education

In our vision of mathematics education, teachers support and mentor students as they engage deeply with mathematical concepts and ideas through investigations, collaborative learning, and mathematical thinking and discourse. This vision is supported by current research on children’s mathematics learning and teaching practices linked with student growth. Teachers must understand content deeply in ways that support them in making content and practices learnable by children and be skillful in a set of high-leverage teaching practices.

Teachers must also work to broaden conceptions of what it means to do mathematics and what it looks like to be proficient in mathematics. This involves noticing and naming student strengths that are not only related to correctness and fluency. It means integrating reading, writing, discourse, and critical thinking into the daily mathematics routines that children engage in.

## How we think about teaching mathematics

When teachers support students to deeply engage with concepts and practices, students make sense of mathematical ideas, engage in mathematical practices, and make connections across ideas. This requires teachers to treat students as people capable of developing and sharing their own ideas and understandings, evaluating and adjusting their ideas and understandings, and engaging with challenging content. This means that teacher educators must support teacher candidates to be curious about children’s mathematical ideas and methods and to seek to understand those ideas. Additionally, they must support teacher candidates to develop mathematical knowledge for teaching (Ball, Thames, & Phelps, 2008), the ways in which teachers need to know mathematics in order to support student learning; skill with teaching mathematical practices; and schema for matching content with appropriate teaching practices.

## Advancing justice through mathematics teaching

To advance justice through mathematics teaching, teachers must have deep knowledge of learners and create opportunities for all children to engage in deep mathematical work. Teachers must also carefully consider the contextual aspects of their curricular materials, in particular, how they and their materials portray the work of mathematics and what it means to be successful in mathematics class. Novice teachers need opportunities to interrogate curricular materials and structures in order to adapt them to broaden ideas of mathematics engagement and success.

Teachers must have a broad view of mathematics and a deep understanding of mathematical knowledge for teaching in order to be able to notice and name the strengths of each of their students in ways that position children as capable in mathematics classrooms. Novice teachers should have ample opportunities to practice examining student work and talk in order to become facile with identifying student strengths carefully and quickly.

## How we think about high-leverage content for teaching mathematics

Mathematics teachers must have a deep understanding of mathematics—both the mathematics they teach and the broader k-12 curriculum. In addition to what is traditionally thought of as mathematics content, the mathematical topics, teachers must understand mathematical practices and key strategies that students may use to solve problems. Because the mathematics curriculum is quite broad, we focus in teacher preparation on a set of content that meets some of the following criteria:

- It is foundational to other k-12 concepts
- It occupies a lot of space in the curriculum
- It is difficult for novice teachers
- It requires significant unpacking

Examples of such topics are fractions in the elementary curriculum and ratio and proportional reasoning at the middle school level. In addition to these topics, teacher preparation should focus on core mathematical practices including building and critiquing arguments and using mathematical structure.