High school mathematics teachers must have strong content knowledge, knowledge of mathematicsspecific pedagogy, and much more—including knowledge about their individual students and their cultural contexts, school policies, and how to collaborate with other teachers. Only with this knowledge, will mathematics teachers be able to meaningfully support the learning of each and every student.
In this chapter, particular attention is given to ensuring that each and every high school student has opportunities to learn meaningful mathematics well in equitable and empowering learning environments. In Part 1 of this chapter, we put forth elaborations and examples of the standards in Chapter 2, describing the knowledge, skills, and dispositions that wellprepared beginning high school mathematics teachers need to develop, highlighting actions they need to take. Part 2 provides elaborations and examples of the standards in Chapter 3, describing what is needed in high school level preservice programs to ensure the effective preparation of their candidates. The chapter concludes with example approaches that programs might take in achieving the standards. A summary of the high school elaborations is given in Table 7.1. The elaborations in this chapter focus on those standards for which there are specific highschoollevel considerations; therefore, although all the standards in Chapters 2 and 3 apply to highschoollevel mathematics teacher candidates, not all require elaboration.
Table 7.1. Elaborations of Candidate and Program Standards for High School Teachers of Mathematics 

Part 1. Candidate Knowledge, Skills, and Dispositions 

HS.1. Essential Understandings of Mathematics Concepts and Practices in High School Mathematics 
Wellprepared beginning teachers of mathematics at the high school level have solid and flexible knowledge of relevant mathematical concepts and procedures from the high school curriculum, including connections to material that comes before and after high school mathematics and the mathematical processes and practices in which their students will engage. Relevant mathematical concepts include algebra as generalized arithmetic, functions in mathematics, diagrams and definitions in geometry, and statistical models and statistical inference. [Elaboration of C.1.1 and C.1.2] 
HS.2. Use of Tools and Technology to Teach High School Mathematics 
Wellprepared beginning teachers of mathematics at the high school level are proficient with tools and technology designed to support mathematical reasoning and sense making, both in doing mathematics themselves and in supporting student learning of mathematics. In particular, they develop expertise with spreadsheets, computer algebra systems, dynamic geometry software, statistical simulation and analysis software, and other mathematical action technologies as well as other tools, such as physical manipulatives. [Elaboration of C.1.6] 
HS.3. Supporting Each and Every Student’s Opportunity to Learn Mathematics 
Wellprepared beginning teachers of mathematics at the high school level understand the importance of providing each and every high school student with opportunities to learn mathematics that will enable him or her to think analytically and creatively in preparation for the workforce, college, citizenship, and life. [Elaboration of C.2.1] 
HS.4. Cultivating Positive Mathematical Identities in Each and Every Student 
Wellprepared beginning teachers of mathematics at the high school level draw on students’ strengths to cultivate positive mathematical identities. [Elaboration of C.4.2 and C.4.3] 
Part 2. Program Characteristics 

HS.5. Effective Programs to Support Preparation of Teachers of Mathematics at the High School Level 
Effective programs preparing teachers of mathematics at the high school level are specifically focused on preparing high school teachers of mathematics. 
HS.6. Partnerships to Support Preparation of Teachers of Mathematics at the High School Level 
Effective programs preparing teachers of mathematics at the high school level engage mathematicians and statisticians, school partners, and other stakeholders in supporting the growth of their candidates to become wellprepared beginning teachers. [Elaboration of P.1.1] 
HS.7. Mathematical Content Preparation of Teachers of Mathematics at the High School Level

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 datadriven, simulationbased modeling approach to statistics. [Elaboration of P.2] 
HS.8. Ethics and Values for Teaching Mathematics at the High School Level 
Effective programs preparing teachers of mathematics at the high school level include multiple opportunities for candidates to develop political clarity on the profession and their advocacy roles in teaching. [Elaboration of P.3.3] 
HS.9. Mathematics Methods Experiences for Teachers of Mathematics at the High School Level 
Effective programs preparing teachers of mathematics at the high school level provide multiple opportunities for candidates to learn to teach mathematics effectively through the equivalent of three mathematicsspecific methods courses. [Elaboration of P.3.4] 
HS.10. Clinical Experiences for Teachers of Mathematics at the High School Level 
Effective programs preparing teachers of mathematics at the high school level provide clinical experiences in which candidates develop teaching practices that support the learning of conceptual knowledge and mathematical practices and processes for each and every student. [Elaboration of P.3.5] 
Programs preparing candidates to teach a broader range of grades than Grades 9–12 (e.g., 6–12 or 7–12) must also attend to the recommendations in this document for middlelevel preparation. Preparation to teach high school does not automatically prepare a candidate to teach middle school. Such candidates need to have content courses focused on middle level mathematics content, methods courses particularly focused on teaching middle school mathematics, understanding middle school students, and significant clinical experiences at middle school. See Chapter 6 for details as well as additional commentary about preparing candidates to teach a broader range of grades embedded throughout this chapter.
This chapter includes a number of vignettes meant to bring to life the recommendations put forward. The vignettes serve a number of purposes, including proposing tasks that may be used with candidates for particular purposes, providing example interactions from mathematics or mathematics methods courses to exemplify effective instruction, and describing the experiences of teacher candidates. Each vignette was chosen to highlight a particular point, but use of an isolated vignette may require surrounding context to preserve the spirit intended by the use of the vignette.
The vignettes show the importance of wellprepared beginning teachers’ possessing strong pedagogical content knowledge and knowledge of their students. Even though some of the vignettes appear to focus more on issues of access and empowerment, mathematical content is a central component of what is discussed. Teacher candidates need opportunities to think about scenarios in which each and every student is involved in reasoning and sense making of mathematics and those in which some students are not. Providing high school mathematics teacher candidates with such opportunities helps them to examine their own beliefs and to think about how their beliefs influence what instructional practices they value and use to support or unintentionally marginalize particular students. For secondarylevel mathematics teacher preparation to be focused not only on mathematics content, which tends to be in the forefront, but also on affective factors that may affect students’ mathematics engagement and achievement is imperative.
Part 1. Elaborations of the Knowledge, Skills, and Dispositions Needed by Wellprepared Beginning High School Mathematics Teachers
This section provides additional detail, commentary, and examples of the knowledge, skills, and dispositions wellprepared high school mathematics teachers have, organized by the general standards described in Chapter 2.
Part 2. Elaborations of the Characteristics Needed by Effective Programs Preparing High School Mathematics Teachers
This section provides additional detail, commentary, and examples of what preservice programs need to do to effectively prepare their students to teach high school mathematics. We begin with general discussion of the nature of high school mathematics teacher preparation programs. Further elaboration is provided, organized by the Standards in Chapter 3.
HS.5. Effective Programs to Support Preparation of Teachers of Mathematics at the High School Level
Effective programs preparing teachers of mathematics at the high school level are specifically focused on preparing high school teachers of mathematics.
An effective program for preparing teachers of mathematics at the high school level provides coursework and experiences focused on the teaching of secondary mathematics. All too often, the prevailing attitude is that secondary mathematics teachers need only a degree in mathematics to be prepared to teach. Although having a strong content background is important, it is not sufficient (CBMS, 2012). Others may emphasize the need for general courses on pedagogy or education with related field experiences. Such a background has value, but it is also insufficient. A wellprepared beginning secondary teacher of mathematics needs coursework and experiences that build their understanding of both the content of, and teaching methods particular to, high school mathematics, given the social context in which mathematics teaching occurs.
An analysis of various degrees at a major state university revealed results about the preparation of teachers that were startling to us (Strutchens, 2012). Most degree programs required a significant number of hours specific to the major. For example, a degree in electrical engineering required 49 credit hours in coursework specific to electrical engineering, 31 credit hours of supporting content courses (mathematics and physics), and 15 credit hours in general principles of engineering. In contrast, a degree in secondary mathematics education at this university could include as few as 22 credit hours specific to mathematics education (which also includes a studentteaching experience), with 42 credit hours in mathematics courses taken by all mathematics majors and 15 credit hours in education courses taken by candidates from all teaching fields. Clearly, the balance of coursework in mathematics teacher preparation is out of alignment with other professional preparation programs. Students in secondary mathematics education programs need and deserve coursework to specifically prepare them for success in their field of study, including mathematicsspecific methods courses and mathematics content courses specific to teaching as well as meaningful clinical experiences in secondary mathematics classrooms overseen by supervisors who have expertise in secondary mathematics across the grades they will be certified to teach; these courses are described in depth in the following sections. The example pathways in the final section of this chapter provide illustrations of how these requirements may be met in various types of programs preparing teachers of mathematics at the high school level.
High school teacher certification or licensure programs may include some or all of the middle grades; for example, a license may be valid for Grades 7–12, or 6–12, or even 5–12. Such programs must also meet the recommendations in this document for middle level preparation. A candidate prepared to teach high school is not automatically prepared to teach in the middle grades. Preparation for teaching mathematics at the middle level as addressed in Chapter 6 requires that wellprepared beginners have knowledge and skills about learners at this stage of their cognitive and affective development and about the intended curriculum at the middle grades that calls for integrative approaches and experience in teaching within interdisciplinary teams. Certainly, effective preparation for teaching high school mathematics provides many of the attributes needed to be effective with middle level learners, but the significant differences among learners at these different levels as well as the differences in how middle and high school curricula and schools are organized require that programs that prepare future teachers for broader grade ranges address standards in both this chapter and the previous one. One theme of this chapter, also reflected in MET II is “that the mathematical topics in courses for prospective high school teachers and in professional development for practicing teachers should be tailored to the work of teaching, examining connections between middle grades and high school mathematics as well as those between high school and college” (CBMS, 2012, p. 54).
This recommendation may present challenges for programs with small numbers of secondary mathematics education teacher candidates. Enrollment in such programs may be inadequate for them to offer coursework specific to mathematics education or to support clinical supervisors with mathematicsspecific expertise to assist candidates at the high school level; offering such support for a broader range of grades is even more problematic. In the Mathematical Association of America’s (MAA’s) Committee on the Undergraduate Program in Mathematics Guide to Majors in the Mathematical Sciences (CUPM guide), Tucker, Burroughs, and Hodge (2015) provided options for such programs at the high school level, including “regional consortia, distance learning, or coconvening courses with inservice teachers seeking graduate credit or professional development” (p. 1). Alternatively, they might focus on providing outstanding preparation in mathematics, with the intent that students intending to pursue careers in teaching mathematics enroll in graduate programs to prepare to teach. Just as not every college or university has the capacity and resources needed to offer a degree in electrical engineering or other specialized majors, so it must be acknowledged that not every college or university has the capacity and resources needed to offer a degree in secondary mathematics education. Institutions that cannot offer the necessary experiences should strive to develop the necessary partnerships or other approaches to meet both the standards in Chapters 2 and 3 and the elaborations in this chapter. This recommendation may require some institutions to make difficult decisions about whether to offer a mathematics teacher preparation program at the high school level.
Closing Remarks
Wellprepared beginning teachers of mathematics at the high school level need knowledge, skills, and dispositions related to mathematics and statistics content relevant for teaching, along with processes and practices, mathematicsspecific pedagogy, the needs of individual students and their cultural contexts, and the political context for teaching. Wellprepared beginners must understand the critical importance of providing each and every high school student with opportunities to learn mathematics that will effectively prepare them for their futures. Wellprepared beginners draw on students’ strengths to cultivate positive mathematical identities that will contribute to their students’ successful participation in mathematics.
To ensure candidates to teach mathematics at the high school level are indeed well prepared, effective programs need to specifically focus on preparing high school teachers of mathematics. Simply providing a mathematics degree without attending to the specific needs of candidates preparing to teach high school mathematics will not suffice. Effective programs include the equivalent of three content courses specifically designed for teachers of high school mathematics, three mathematicsspecific methods courses (or equivalent experiences), and clinical experiences where candidates are mentored by high school mathematics teachers who themselves have the necessary knowledge, skills, and dispositions. Throughout these experiences, candidates should develop political clarity on the profession and their role as an advocate for their students and the profession. Partnerships with mathematicians and statisticians, school partners, and others involved in teacher preparation are essential in achieving the vision of this chapter.