Indicator P.3.2. Provide Foundations of Knowledge About Students as Mathematics Learners

A main learning outcome for a mathematics methods course is to develop candidates’ understanding of how students think and learn about mathematics (see Standard C.3). Effective mathematics teacher preparation programs provide multiple experiences (e.g., reading, analyzing videos, conducting teaching experiments) that develop deep understanding of at least one (or two) learning trajectories (e.g., sequences of patterns of thinking for a topic). For example, a methods course would provide extensive, complementary experiences focusing on how students think and learn about a key topic such as whole number and operations for early childhood, fractions for elementary mathematics education, proportional reasoning or algebra for middle school mathematics teachers, and functions for high school mathematics teachers. These experiences also develop competencies in connecting these progressions to specific implications for instruction—that is, candidates learn a complete learning trajectory—and connecting content to mathematical practices.

In effective programs, mathematics methods courses simultaneously provide candidates with experiences to develop strategies for understanding and build students’ (a) productive dispositions and positive mathematics identities and (b) meaningful mathematical sense making and use of mathematical practices.