Standard C.2: Pedagogical Knowledge and Practices for Teaching Mathematics

### Standard C.2. Pedagogical Knowledge and Practices for Teaching Mathematics

Well-prepared beginning teachers of mathematics have foundations of pedagogical knowledge, effective and equitable mathematics teaching practices, and positive and productive dispositions toward teaching mathematics to support students’ sense making, understanding, and reasoning.

Teaching mathematics effectively involves significant knowledge, skills, and dispositions. Well-prepared beginning teachers of mathematics draw upon their knowledge of mathematics content, processes, and curriculum and blend it with effective and equitable mathematics teaching practices. They begin teaching with a solid foundation of pedagogical content knowledge. That is, they have studied teaching approaches unique to the subject matter of mathematics, such as knowledge of how to structure and represent mathematics content (e.g., fractions, ratios, algebra) in ways that make it accessible to students; knowledge of the common conceptions, misconceptions, and difficulties that students encounter when learning mathematics; and knowledge of specific teaching strategies to assess and address students’ learning needs in mathematics (Shulman, 1986). Well-prepared beginners realize that the teaching of mathematics has its own nuances and complexities specific to the discipline and are ready to start using and expanding their established foundations of pedagogical content knowledge to guide their instructional actions in planning for and interacting with each and every student in mathematics classrooms.

Well-prepared beginners take seriously their responsibilities as new teachers to develop each student’s ability to engage in mathematical sense making, understanding, and reasoning. Toward that end, they present positive attitudes toward the subject of mathematics as a discipline when interacting with students, families, colleagues, and community members. They also demonstrate productive dispositions toward teaching mathematics, including engagement in collaborative communities of practice and ongoing learning as professional educators. Well-prepared beginners know that they will continue to develop and refine their pedagogies and practices, and, as with all complex endeavors, their skills and effectiveness in teaching mathematics will improve with time, experience, and deliberate reflection.