There is no shortage of recommendations on the preparation of mathematics teachers (e.g., Association of Mathematics Teacher Educators, 2017; Conference Board of Mathematical Sciences [CBMS], 2012). Scholars agree that mathematics teachers need both content knowledge and pedagogical content knowledge. Specifically, CBMS (2012) proposed that the preparation of mathematics teachers should develop an understanding of secondary mathematics from an advanced perspective and knowledge of the content and practice standards in Common Core State Standards in Mathematics (CCSSM). In this paper, we report the results of a national survey of secondary mathematics teacher education (SMTE) programs in the U.S., focusing on program characteristics and opportunities to learn (OTL), in an effort to provide a snapshot of current SMTE programs. Given both the algebra-for-all movement (e.g., Teuscher, Dingman, Nevels, & Reys, 2008) and algebra’s role as a gatekeeper to post-secondary opportunities (e.g., Kilpatrick & Izsák, 2008) and therefore a civil right (e.g., Moses, 1995), the preparation of future algebra teachers was a particular focus of the study.

Methods

The web-based survey includes 13 multiple-choice and seven open-ended items related to SMTE programs; this article focuses on several of the items. We received 128 responses (representing 44 states) from individuals at different institutions of higher education whom indicated their program led to initial teacher certification in mathematics education. Respondents identified themselves as instructors (34%), program coordinators (33%), advisors (11%), or others (23%), such as department or division chairs or people who served multiple roles. We report results by grouping them into the two most common program types, that is four- and five-year Baccalaureate programs and Postbaccalaureate programs.

Results

Both program types most commonly offered “combined middle school and high school preparation,” as reported by 76% of the institutions. The number of graduates of the institution’s largest SMTE program for each of the three academic years preceding the survey ranged from 0 to 55; the overall median and mean were five and nine graduates per year, respectively.          

Opportunities to learn in the SMTE programs were investigated through questions about reported perceptions of opportunities and factual information about required courses and credits. One question asked, “To what extent does the secondary mathematics teacher education program provide opportunities to learn in the following areas: Algebra, Algebra teaching, Issues in achieving equity in algebra learning, and Algebra as described in the Common Core State Standards in Mathematics (CCSSM)?” Table 1 summarizes responses to this question.

Table 1. Frequency of Opportunities to Learn Algebra, to Teach Algebra, about Equity Issues in Algebra, and Algebra in CCSSM Provided by Baccalaureate and Postbaccalaureate Programs

Respondents from Baccalaureate programs generally reported their SMTE program provided opportunities to learn algebra to a great extent (60%), with fewer reported opportunities to learn (to a great extent) about teaching algebra (34%), equity issues (8%), and algebra in CCSSM (33%). Very few respondents from Baccalaureate programs indicated a significant emphasis on equity issues related to algebra, and even more reported  they lacked knowledge of the extent of provided opportunities related to equity issues. In contrast, representatives of Postbaccalaureate programs reported less emphasis on learning algebra and more opportunities to learn about equity issues in algebra than those from Baccalaureate programs.

Table 2 presents descriptive statistics for course type requirements of the two categories of programs: Mathematics (e.g., Linear Algebra), Mathematics for Teachers (e.g., Algebra for Teachers), Mathematics Education (e.g., Teaching Secondary Mathematics), and General Education (e.g., Teaching Diverse Learners).

Table 2. Required Number of Courses for Each Course Type in Baccalaureate and Postbaccalaureate Programs

Respondents in both categories of programs reported more emphasis on mathematics and general education courses than mathematics courses designed for teachers and mathematics education courses. Those from Postbaccalaureate programs indicated fewer mathematics and general education courses and one more mathematics education course than those from Baccalaureate programs. 

Figure 1 presents the frequency with which the two types of programs required particular courses.

Figure 1. Percentage of Baccalaureate and Postbaccalaureate SMTE programs requiring particular courses (only courses required by at least 50% of one type of program are included).

Of the courses required by at least half of the SMTE programs, nine were mathematics courses. The most common mathematics courses in both types of programs were Calculus and Linear Algebra. Only one mathematics education course was required in at least half of the programs. No Mathematics for Teachers courses were required in at least half of the programs; in fact, the most commonly required course, Geometry for Teachers, was required in only 13% of the Baccalaureate programs and 25% of the Postbaccalaureate programs.

Discussion

This study provided empirical data about composition and variation in SMTE program requirements and emphases; in general, programs included a large number of mathematics courses and general education courses. In contrast, they required far fewer mathematics for teachers and mathematics education courses. Baccalaureate programs also reportedly emphasized learning algebra content more than learning: to teach algebra, about the algebra described in CCSSM, and about equity issues related to algebra. In contrast, Postbaccalaureate programs offered a more balanced emphasis in these areas, perhaps due in part to the mathematics courses often required for admission into these programs. These findings beg the question whether more courses that include attention to both mathematics and education (e.g., Mathematics for Teachers courses, Mathematics Education courses) would better serve M-PSTs in their future teaching than the current focus on courses which address either mathematics or education. Studies of SMTE programs with varied approaches to course offerings and requirements are needed to better understand the impact of these program structures. At this point, we are largely depending on conjectures, suppositions, and anectdotal evidence to make these important decisions.

The results provided information about both general program characteristics and specific course-taking requirements. The most common type of program reported was a Baccalaureate combined middle school and high school program. As noted earlier, professional groups have emphasized that both teachers’ content knowledge and pedagogical content knowledge are important for mathematics teacher preparation. In fact, CBMS (2012) called for “coursework that allows time to engage in reasoning, explaining, and mak­ing sense of the mathematics that prospective teachers will teach is needed to produce well-positioned beginning teachers” (p. 17). More specifically, they recommended 15 semester-hours of such coursework for those preparing to teach middle school mathematics and three such courses for those preparing to teach high school mathematics. Our study found that, in spite of more than a decade of calls from the professional community, SMTE programs are not offering many courses in which mathematics pre-service teachers M-PSTs have opportunities to develop mathematics-specific pedagogical knowledge. The programmatic changes necessary to meet the professional recommendations may require potentially challenging conversations across departments at many institutions in order to reconceive courses and collaboration, potentially innovating in ways new to either department. At this point, it seems moving toward these recommendations is essential in order to give both M-PSTs and their future students the best chances for success.

Although our study found that most programs reported offering at least adequate opportunities to learn algebra, the teaching of algebra, and the algebra described in CCSSM, they typically do not address equity issues in learning algebra adequately. This result suggests the need for both further research and professional development related to better understanding what programs that report addressing equity issues in algebra are doing in order to provide other programs with recommended activities, readings, and experiences to increase M-PSTs opportunities to learn in this area, see Mintos, Hoffman, Kersey, Newton, & Smith, (2018) for a detailed analysis of Equity OTLs in five case study SMTEs. This is particularly critical as the diversity of students, including their race, ethnicity, culture, and socio-economic status, in algebra courses has never been greater. Without opportunities to understand how algebra may serve to excaberate differences in educational and career opportunities and also ways to promote equity in algebra learning , M-PSTs will not be prepared to serve their most underserved students.

In summary, our study found a wide range of program content of SMTE programs, as well as some areas in need of reform in order to align with current recommendations for program experiences. Despite variation in SMTE licensure paths, most M-PSTs are having opportunities to develop mathematical content knowledge, but many fewer opportunities to develop pedagogical content knowledge and to learn about equity issues in their programs.

References

Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Retrieved from https://amte.net/sites/default/files/SPTM.pdf

Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. Providence, RI, and Washington, DC: American Mathematical Society and Mathematical Association of America.

Kilpatrick, J, & Izsák, A. (2008). A history of algebra in the school curriculum. In C.E. Greenes and R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics. (pp. 1-18). Reston, VA: National Council of Teachers of Mathematics.

Mintos, A., Hoffman, A., Kersey, A, Newton, J., & Smith, D. (2018). Learning about issues of equity in secondary mathematics teacher education programs. Journal of Mathematics Teacher Education. Retrieved from https://doi.org/10.1007/s10857-018-9398-2.

Moses, R. (1995). Algebra, the new civil right. In C. Lacampagne (Ed.), The Algebra Initiative Colloquium Volume 2 (pp. 53-67). Washington, DC: U. S. Department of Education, Office of Educational Research and Improvement.

Teuscher, D., Dingman, S. W., Nevels, N. N., & Reys, B. J. (2008). Curriculum standards, course requirements, and mandated assessments for high school mathematics: A status report of state policies. NCSM Leadership Journal, 10(2), 49-54.