Standard P.2. Opportunities to Learn Mathematics
An effective mathematics teacher preparation program provides candidates with opportunities to learn mathematics and statistics that are purposefully focused on essential big ideas across content and processes that foster a coherent understanding of mathematics for teaching.
In this section, we comment on how high school mathematics teacher preparation programs can support their candidates’ opportunities to learn mathematics, particularly the specific content preparation they need.
Effective programs preparing teachers of mathematics at the high school level are focused on the relevant content knowledge needed for teaching high school mathematics, including connections to material that comes before and after high school mathematics. Coursework consists of the equivalent of an undergraduate major in mathematics (including statistics) with at least three content courses particularly relevant to teaching high school mathematics and incorporating sufficient attention to a data-driven, simulation-based modeling approach to statistics. [Elaboration of P.2]
Table 3.2 summarizes the requirements for the content preparation of teachers of high school mathematics as follows:
- The equivalent of an undergraduate major in mathematics (including statistics) that includes three courses with a primary focus on high school mathematics from an advanced viewpoint.
- Three courses in statistics that include a data-analytic and simulation-based approach with a focus on statistical models and inference (to be incorporated in the undergraduate major).
These requirements build on the recommendations in Chapter 6 of MET II (CBMS, 2012), on the recommendations for high school programs in the CUPM guide (Tucker et al., 2015), and on SET (Franklin et al., 2015). We reiterate Tucker et al.’s point of view that a “traditional liberal arts major in mathematics is neither necessary nor sufficient preparation for teaching high school mathematics” (p. 1). Departments of mathematical sciences in effective programs preparing high school mathematics teachers commit the necessary resources to ensure that the mathematics and statistics courses in teacher preparation programs for high school mathematics address content that enables teacher candidates to focus on essential ideas of high school mathematics in an environment that engages them fully in the robust practice of mathematics.
In a mathematics-degree program that is tailored for prospective teachers, candidates need opportunities to examine the essential ideas of high school mathematics. Authors of the CUPM guide recommend lower division content in calculus, linear algebra, mathematical proof, and data-based statistics with a focus on statistical inference and upper division coursework in mathematics organized around a variety of topics. We reiterate the CUPM’s and MET II’s main recommendation that the mathematics major for teachers include the equivalent of 9 semester-hours of coursework focused on “high school mathematics from an advanced standpoint” (CBMS, 2012, p. 55). The CUPM guide provides examples of organizing this coursework around geometry, algebra, analysis, modeling, number theory, discrete mathematics, or the history of mathematics; we recommend that programs include some attention to all these content areas, within courses designed specifically for teachers if possible. In these courses, the essential ideas of high school mathematics and their connections to middle grades and university mathematics are central. Chapter 6 of MET II provides a comprehensive analysis of such connections.
In addition to mathematics content, mathematical practices and processes form the foundation of mathematics coursework in effective programs. Program personnel attend to the increasing importance of statistics and ensure that prospective teachers engage with statistical ideas through three courses that follow the design principles articulated in SET (Franklin et al., 2015).
As a philosophy underlying the mathematical education of high school teachers, all mathematics courses that include prospective teachers (not just those specifically targeting prospective teachers) need to provide examples and opportunities for students to examine how related mathematical ideas exist within high school curricula. These examples and opportunities can be provided as naturally and automatically as examples are provided for prospective engineers, or nurses, or business executives, within most mathematics courses. In recognition that fitting appropriate experiences into existing programs can be challenging, many researchers are focusing on providing such examples. For instance, the MTE-Partnership’s MODULE(S)2 Research Action Cluster is developing modules related to key areas of mathematics content for teachers (e.g., geometry, statistics, and modeling). These unit-long modules can either be bundled into a domain-specific course (e.g., three modules on geometry) or into a capstone course including modules from across domains. Alternatively, they can be inserted into an existing mathematics course for students from a variety of majors, such as including one geometry module into a Euclidean geometry course. Some instructors have included one of these modules into a mathematics methods course. Collaborative efforts like this are helping to create resources to address the ongoing challenges of creating programs that provide high school mathematics teacher candidates with experiences in mathematics relevant to their chosen profession.
The varied states’ requirements for teacher certification present ongoing challenges. Some states’ requirements are coursework-based, others are content-exam-based (e.g., based on a minimum score on the Praxis II), and some are both. Some programs prepare teachers within a 120-credit 4-year degree that includes mathematics content, education coursework, and student teaching; others are fifth-year post-baccalaureate programs; and still others include a master’s degree including initial teacher preparation. These differences preclude our recommending a one-size-fits-all program. In the examples at the end of this chapter, we describe sample high school teacher preparation programs from a variety of perspectives, fully recognizing that these illustrations do not completely capture the variation of the possibilities that exist. A particular challenge for graduate preparation programs is that prospective teachers may come to the program with undergraduate mathematics degrees designed to prepare them for graduate school in mathematics. Providing them with both additional mathematics content from the perspective of content knowledge relevant for teaching and education coursework within the confines of one year can prove challenging. However, programs need to include this essential background knowledge for well-prepared beginning high school mathematics teachers.
Finally, we reiterate our previous point that high school teacher certification or licensure programs that include some or all of the middle grades need to attend to the content needed for middle grades mathematics as described in Chapter 6.