C.1. Mathematics Concepts, Practices, and Curriculum
Well-prepared beginning teachers of mathematics possess robust knowledge of mathematical and statistical concepts that underlie what they encounter in teaching. They engage in appropriate mathematical and statistical practices and support their students in doing the same. They can read, analyze, and discuss curriculum, assessment, and standards documents as well as students’ mathematical productions.
Knowledge of Mathematics for Teaching extends beyond general subject matter knowledge. It includes the knowledge of mathematics that teachers need to design and adapt lesson plans, anticipate student questions and misconceptions, evaluate student work, use proper notation and vocabulary, and the knowledge of how mathematics content is connected across grade levels in order to convey mathematical ideas accurately, anticipating how these ideas develop over time. This knowledge is part of what Shulman (1986) described as Pedagogical Content Knowledge: “the ways of representing and formulating the subject that make it comprehensible to others… an understanding of what makes the learning of specific topics easy or difficult; the conceptions and preconceptions that students of different ages and backgrounds bring with them to the learning of those most frequently taught topics and lessons” (p. 9).