Elementary education programs seek to provide a variety of experiences for teacher candidates (TCs) within a limited timeframe. Given that elementary TCs require preparation to teach several subjects, mathematics-specific learning experiences may be limited. Therefore, mathematics teacher educators (MTEs) must prioritize and craft impactful experiences (i.e., courses, assignments, practica, field, etc.) within these time constraints. One important lever for determining which mathematics-related experiences get priority in teacher education programs is recommendations from professional and accreditation organizations (e.g., Association of Mathematics Teacher Educators, 2017; Council for Accreditation of Educator Preparation, 2022).

However, to complement these recommendations, it is important to understand which experiences graduates found most impactful in preparing for the classroom so MTEs can improve the experiences to maximize learning and impact. Attending to these perspectives can help bridge the gap between life in the classroom and teacher education (Feiman-Nemser & Buchmann, 1985). Given the challenges of teaching, particularly for novice teachers (Sydnor et al., 2024), and the challenges the profession faces regarding teacher retention (Ingersoll et al., 2018), responding to practicing teachers’ feedback regarding teacher education programs may support better outcomes for teachers and students.

For better understanding of what mathematics-specific experiences were most impactful, we sent a survey to recent graduates (between one and five years) of elementary education initial licensure programs around the United States using convenience sampling. This survey included questions about preparation experiences, the challenges graduates have faced as early career teachers, and how their program could have better prepared them to navigate those challenges. Eighteen teachers who graduated from seven universities completed the survey entirely. Through qualitative analysis, we identified three themes that emerged across graduates from multiple programs. We propose these themes as recommendations for MTEs.

Recommendations

Based on responses from the practicing teachers, MTEs could better support TCs to teach mathematics by: 

1) incorporating elementary textbooks and curricula in coursework (more), particularly those connected with field placements and local schools; 

2) being (more) explicit about why TCs are learning and focusing on mathematical content, including how this knowledge is important to their future teaching; and 

3) providing (more) emphasis on “how to” teach math. 

Incorporating Elementary Textbooks and Curricula

Many teachers indicated that increased use of relevant K-5 textbooks and curricula in their mathematics courses would have been helpful. One teacher identified that they felt prepared because they “had a good understanding of how to adjust math curriculum to [their] students’ needs.” While this teacher felt prepared because of their experience adjusting curriculum, other teachers commented this was a necessary area of growth for their program. For example, one teacher commented that their biggest challenge related to teaching mathematics was “working with and around required workbooks and curriculum.” In addition to identifying challenges, teachers suggested solutions: “have [TCs] teach a lesson from three different curriculums” and “utilize the learning materials from the textbooks that schools are actually using.” The solutions that best fit a particular program may vary, but MTEs should attempt to incorporate K-5 math textbooks and curricula into coursework (more), with particular attention to materials that are connected to TCs’ field placements and local schools.

Being Explicit about the Purpose of Learning Mathematical Content 

Multiple teachers discussed learning mathematical content as they reflected on their teacher preparation experience. One teacher explained that “learning math through the [Cognitively Guided Instruction] model was impactful for me because it made me fall in love with teaching math. I realized that the way I learned math only taught me how to solve, not why it works.” While this teacher felt the focus on mathematical content through CGI was beneficial, another teacher lamented that “many of the courses also focused too much on our personal understanding of math, not how to effectively transfer our knowledge of the subject.” Given the documented importance of mathematical knowledge for teaching (e.g., Hill et al., 2005; Hill et al., 2008) and the recommendations for teacher education programs (e.g., AMTE 2017), MTEs must continue to cover the mathematical content. However, this feedback suggests that MTEs should work to be more explicit about the importance of content understanding and provide connections between content understanding and teaching. For example, MTEs may see connections between content knowledge and pedagogical ideas that are opaque to TCs (e.g., how content understanding supports anticipating and responding to student thinking or differentiating instruction). Highlighting these connections may help TCs see the importance of learning mathematical content in their coursework.

“How to Teach” Math

Perhaps no idea was more salient across the survey responses than TCs’ desire for greater emphasis on how to teach math. One teacher identified that “while I understood the materials and subject, I did not feel that my ability to present those materials to students was adequate.” Similarly, another teacher commented that “I have an understanding of how to solve math concepts, but I struggle finding ways, either through verbal or kinesthetic learning, to educate my students.” These teachers attributed this difficulty to an imbalance between content and pedagogy relative to their needs in the classroom, explaining, “I needed more opportunities to learn how to teach, not learn more math.” Balancing the importance of MKT and this feedback, MTEs should consider learning opportunities that integrate mathematics content and pedagogy. A teacher highlighted one possible learning opportunity: “prepping and teaching a number talk routine to our teacher peers helped me learn to think through questioning and gain confidence in choosing appropriate materials to help students discover different mathematical concepts.” As opportunities to teach in field placements are often limited, leading number talks and microteaching in (content and methods) coursework may provide valuable teaching approximations. These opportunities, coupled with increased connections between content and pedagogy, might provide TCs with the “how to teach math” emphasis they are seeking.

Note About Other Pathways to Elementary Education

Several respondents completed initial licensure programs other than an undergraduate degree in elementary education, including a transition to teaching program, master’s degree in special education or applied behavior analysis, or a bachelor’s degree in early childhood or special education. These graduates lamented taking few or no courses focused on teaching mathematics. As other required courses dominate these programs, it is important that MTEs also advocate for math-specific experiences in non-traditional and graduate programs to ensure that TCs are prepared for teaching mathematics.

Conclusion

As MTEs, we consistently work to build impactful experiences that support TCs’ development of teaching skills and practices. This study sought feedback from graduates of elementary education programs regarding what experiences they found most impactful for their teaching and how to improve these experiences to maximize learning. In being responsive to this feedback, here are three main calls to action for mathematical teacher preparation: 1) incorporate textbooks and curricula in coursework (more), particularly those connected with field placements and local schools; 2) be (more) explicit about why TCs are learning and focusing on mathematical content, including how this knowledge is important to their future teaching; and 3) provide (more) emphasis on how to teach math. We recognize that MTEs are often limited in their time with TCs and that considering new recommendations may seem burdensome; however, the voices of our graduates—teachers in the field—should be prioritized as we design learning opportunities to better prepare TCs as they begin the demanding work of teaching.

References

Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. https://amte.net/standards

Council for Accreditation of Educator Preparation. (2022). CAEP revised 2022 standards workbook. https://caepnet.org/wp-content/uploads/2024/10/caep-2022-standards-workbook-final.pdf

Feiman-Nemser, S., & Buchmann, M. (1985). Pitfalls of experience in teacher preparation. Teachers College Record, 87(1), 53–65. https://doi.org/10.1177/016146818508700107

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371

Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235

Ingersoll, R., Merrill, E., Stuckey, D., & Collins, G. (2018). Seven trends: The transformation of the teaching force—updated October 2018. Consortium for policy research in education. Philadelphia, PA: University of Pennsylvania. https://repository.upenn.edu/cgi/viewcontent.cgi?article=1109&context=cpre_researchreports

Sydnor, J., Davis, T. R., & Daley, S. (2024). Learning from the unexpected journeys of novice teachers’ professional identity development. Education Sciences, 14(8), 895. https://doi.org/10.3390/educsci14080895