Indicator P.3.1. Address Deep and Meaningful Mathematics Content Knowledge

Because many candidates enter mathematics methods courses (or equivalent professional learning experiences) without having deeply conceptualized all the mathematics they will be responsible to teach, mathematics methods courses in effective mathematics teacher preparation programs present multiple opportunities for candidates to reconsider and deepen their mathematical understandings as both learners of mathematics and as mathematics teachers. If the approach taken to mathematics is solely or primarily procedural, the other worthy goals of the methods course will be subservient to propagating a widely held practice that mathematics, instead of fundamentally being about engaging in ways of reasoning about quantitative and spatial concepts and principles, is fundamentally about learning to memorize mathematical facts and carry out procedures (Hiebert et al., 2005).

In effective programs, candidates not only learn mathematics concepts and procedures but also develop productive mathematical dispositions. Teacher candidates come with years of experience as mathematical learners and some may hold unproductive beliefs about mathematics and mathematics teaching and learning. Therefore productive mathematical disposition is the oft-missing strand of mathematical proficiency, and mathematics methods courses in effective programs support candidates in developing richer and more positive mathematical dispositions.

Mathematical tasks are central to mathematical reasoning, and rich mathematical tasks emphasizing high cognitive demand (Stein, Smith, Henningsen, & Silver, 2000) must be an integral component of mathematics methods courses. However, even rich mathematical tasks are often rendered devoid of most of their mathematical richness when teachers over-scaffold, thereby leading students through the task without focusing on the underlying thinking and reasoning that the tasks were intended to evoke. In effective programs, candidates in mathematics methods courses not only engage in rich mathematical tasks that are implemented in ways designed to sustain the cognitive demand but also learn to successfully implement high-level tasks in Pre-K–12 settings (Smith, Bill, & Hughes, 2008).