Programs to prepare high school mathematics teachers can be organized in many ways, depending on state policies, college or university guidelines, the intended audience (e.g., career changers), and so forth. However they are organized, effective programs must meet the requirements of the standards and their elaborations for high school in this document. Following are several examples of how differently organized programs can meet these recommendations.

### Program 1. Four-year Bachelor of Science Degree

One approach to establishing a program that leads to the well-prepared beginning teacher of mathematics could be in the form of a four-year Bachelor of Science degree. This program has a major in mathematics with a teaching option. Consistent with *MET II *(CBMS, 2012), mathematics and statistics coursework consists of single and multivariable calculus, differential equations, two courses in data-based statistics and statistical inference, transition to proof, and linear algebra, each at the lower division. Upper division coursework includes three courses designed specifically for teachers, each of which allows the focus on essential ideas of high school mathematics: one course situates high school algebra and precalculus in the context of number theory, algebra, and analysis; a second course focuses on Euclidean and non-Euclidean geometry; and a third course focuses on modeling using the tools of mathematics without calculus and using simulation-based statistics. Each of these courses embeds the use of technology as a tool for learning mathematics. Mathematics coursework also includes three upper division elective courses in mathematics or statistics, and students choose from among courses including algebraic or geometric reasoning in the middle grades, history of mathematics, and others.

The program includes designated mathematics methods courses with field experiences, and embeds selected opportunities for working with students within mathematics content courses. Although the ideal program would include three methods courses, this program cannot currently do so, given the constraints of the program requirements as a whole. The program designers recognized this need for attention to teaching methods, and have addressed it by integrating pedagogy assignments and field experiences within mathematics content courses. The program includes education coursework completed by all high school teaching majors in the state, and includes student teaching.

### Program 2. Integrated Fifth-Year Graduate Program

A second program achieves the recommendations of this chapter via a fifth-year graduate program that follows a strong undergraduate major in mathematics teaching. The undergraduate coursework includes three content courses addressing mathematical content for teaching. In addition to generic education coursework taken by all high school teaching majors, two content-specific high school mathematics methods courses, both of which include explicit attention to the teaching and learning of high school mathematics topics, are required, along with a course addressing using technology to teach mathematics taken by all middle and high school mathematics candidates. Furthermore, although equity issues are addressed in generic education courses, equity issues are also explicitly addressed within the mathematics methods courses, because only then will candidates understand that equity is not separate from, but fundamentally a part of, effectively teaching mathematics to high school students. Student teaching takes place concurrently during the methods courses, with the students assuming increased classroom-teaching responsibility over the course of each semester and from the first to the second semester. Because candidates student teach while taking courses, issues that arise in student teachers’ practice are incorporated into the mathematics-methods-course discussions. Note that students coming from a general mathematics major that does not focus on mathematics teaching may have to complete pre- or co-requisite coursework.

### Program 3. Graduate Program for Career Changers

An alternative version of the second program does not require prerequisite courses for mathematics teaching to be included in the undergraduate program, because the candidates may be career changers. Instead, this coursework is included in the program, embedded within courses addressing mathematical content relevant for teaching and mathematics-specific methods courses. Efforts are made to ensure that the program fully meets the standards and elaborations for high school mathematics preparation, noting that most candidates will require more than one year to complete the program. Depending on state requirements, candidates may be granted licensure or certification at the end of the first year and may then complete any remaining degree requirements the second year while employed as a full-time teacher.

### Program 4. Liberal Arts Program

In a final program, the recommended standards are achieved in a liberal arts mathematics program that is a part of a coalition of universities and colleges offering high school mathematics teacher preparation. Specialized mathematics content courses for teachers as well as mathematics-specific methods courses are offered collaboratively with a nearby state university that leads a local partnership of higher education institutions and school districts. Some of these jointly offered courses are delivered online. In other cases, students meet on one of the campuses or at a central location. In this model, students in the smaller program can complete the requirements for becoming high school mathematics teachers that meets the recommendations in this document, and students at the state university can interact with colleagues from another context, thus broadening their awareness of issues related to mathematics education, particularly if the liberal arts college reflects demographics different from those of the state university.