On June 23, 2024, in Park City, UT, the 2024 Association of Mathematics Teacher Educators (AMTE) Service, Teaching, and Research (STaR) cohort created Teaching Interest Groups (TIGs). Six hours into our STaR experience, yet feeling an overwhelmingly positive connection to one another, we apprehensively shared teaching practice topics of interest. Five of the 18 STaR members united over a shared passion for the 5 Practices for Successfully Orchestrating Mathematics Discussions (Smith & Stein, 2018) and we formed a TIG to explore the use of the five practices model in our methods courses. The five practices are a model that consists of six sequential teaching routines: 0) setting goals and selecting tasks, 1) anticipating, 2) monitoring, 3) selecting, 4) sequencing, and 5) connecting (Smith & Stein, 2018) – supporting ambitious, dynamic mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2014). During our time together we created reflection documents on our experiences with the five practices and read our document aloud to one another. We further captured our subsequent discussions stemming from the reflection documents through audio transcription.

Each of us encountered this model across various settings and valued its instructional power. A few of us learned about the five practices during our graduate studies while simultaneously teaching in K-12 mathematics. Karie shared, “I can remember the first time I used the five practices as a high school teacher during a graduate course. I was blown away by the amazing connections my students made during their exploration of angle relationships and the rich discussion we had afterwards.” Ashley reflected, “Getting students talking about math and working through high quality tasks was the key to engagement that my classroom had been missing.” Others learned about this approach during our doctoral programs. Sean noted that learning about the five practices as part of teaching a methods course provoked him to rethink what it meant for students to do math. While assisting a middle school math educator during the fifth year of his doctoral program, Deependra learned about the five practices and appreciated how it provided “the tools to conduct purposeful, effective discussion in mathematics teaching.”

As we journeyed into our mathematics teacher educator (MTE) positions, each of us knew that the five practices would have a place in our instruction. Laura reflected, “In my previous positions I encountered components of the five practices and then connected them to The 5 Practices in Practice (Smith et al., 2019) to form a complete picture of how I wanted to prepare future mathematics teachers.” Ashley shared, “After years of success implementing the five practices with K-8 students, I knew it was a non-negotiable for my instruction within higher-ed courses.” And so, as MTEs, we each incorporated explicit instruction about the five practices into our courses with preservice teachers (PSTs).

Collectively, our experiences as early career faculty include teaching mathematics methods courses to a variety of grade bands in K-12, including in-person, online, and hybrid formats. Each of us has introduced the five practices to our methods courses in distinct ways, which has led to both common and unique challenges. Table 1 details our course structures, along with the various coursework expectations for our PSTs to use the five practices.

Table 1

Five practices Incorporation by MTE

Despite our varied contexts, we experienced common challenges in implementing the five practices within our MTE courses. After our collaborative narrative sharing, which we audio recorded and created transcripts from, we applied color-coding and inductive coding (Mayring, 2021) to determine two predominant themes of shared challenges: PSTs’ implementation of the five practices and programmatic logistics.

The challenges of PSTs’ implementation included many factors. One factor being PSTs’ comfort and ability implementing one or more components of the five practices. For example, Deependra noted, “Often the PSTs struggle to distinguish a learning goal from a performance goal.” Our TIG noticed similar struggles and discussed PSTs’ difficulties selecting a cognitively demanding mathematical task that aligns with their learning goals. Additionally, the group shared narratives of PSTs’ difficulties in developing and using a monitoring chart. Ashley noted, “My PSTs described feeling overwhelmed with documenting student thinking during the monitoring practice.” Another factor included PSTs’ self-awareness of effective implementation of a five practices lesson. For example, PSTs’ post-lesson reflections often focused on student behavior rather than the depth of mathematical connections. Thirdly, the PSTs experienced pedagogical discomfort discerning when and how to implement the five practices in their field placements. When planning, some PSTs interpreted the five practices framework as either a review for assessment or as an activity before “a real math lesson” began. Often what PSTs referred to as “a real math lesson” was instruction focused on the low levels of cognitive demand (NCTM, 2014), memorization and/or procedures without connections.

The second shared challenge our TIG’s narratives illuminated was programmatic logistics. These challenges included (a) connecting the five practices to the specific lesson plan templates and (b) constraints associated with the timing of our courses and/or fieldwork. Notably, we all questioned and wondered about the appropriate timing of the introduction of the five practices within our courses and reflected on the amount of time devoted to the practices before PSTs were expected to plan and implement a lesson. Adapting our MTE instruction on the five practices to the various modalities of our courses also surfaced in narratives. Karie noted, “It is challenging to model some elements of the five practices (like monitoring) realistically in a hybrid setting, though the use of shared documents and slides have helped.”

Since the five practices serve as a model for high-quality mathematics instruction (NCTM, 2014), we dedicated time, while we were together at the STaR summer institute, to brainstorm strategies to overcome our common challenges. We wondered if exploring the five practices is of interest to other novice and/or experienced MTEs. Additionally, we wondered if other MTEs experience implementation challenges similar to ours. Because of the importance of MTE collaborative learning, we offer this preliminary reflection in hopes of continuing conversations about how to improve MTE instruction of the five practices model. In particular, we would like to highlight to the AMTE community the limited literaure discussing PST learning experiences with the five practices. We are encouraged by the publication of Coaching the 5 Practices (Smith et al., 2024) to support instructional coaches working with in-service teachers on the five practices model. However, much of the current literature focuses on analysis of veteran teacher and teacher educators’ use of the five practices (i.e. Groth, 2015; Nabb et al., 2018; Smucker et al., 2024).

We are incredibly grateful that the STaR program provided the opportunity for us to connect and discuss our novice instructional practices surrounding the five practices model. We plan to continue our work as a TIG to further unpack and research our teaching practices of the five practices to PSTs. We encourage our fellow MTEs who are also interested in this topic to continue your work, as you are not alone in this interest. We hope the preliminary reflections of our experiences stimulate continued interest in this necessary endeavor of developing PSTs’ mathematical pedagogical and content knowledge.

References

Groth, R. E. (2015). Using the five practices model to promote statistical discourse. Teaching Statistics, 37(1), 13–17. https://doi.org/10.1111/test.12052

Mayring, P. (2021). Qualitative content analysis: A step-by-step guide. Sage.

Nabb, K., Hofacker, E. B., Ernie, K. T., & Ahrendt, S. (2018). Using the 5 practices in mathematics teaching. The Mathematics Teacher, 111(5), 366–373. https://doi.org/10.5951/mathteacher.111.5.0366

National Council of Teachers of Mathematics. (2014). Principles to action: Ensuring mathematical success for all.

Smith, M., Bill, V., & Sherin, M. (2019). The 5 practices in practice: Successfully orchestrating mathematics discussions in your elementary classroom. Corwin Press.

Smith, M., & Sherin, M. (2019). The 5 practices in practice: Successfully orchestrating mathematics discussions in your middle school classroom. Corwin Press.

Smith, M., Steele, M., & Sherin, M. (2020). The 5 practices in practice: Successfully orchestrating mathematics discussions in your high school classroom. Corwin Press.

Smith, M., & Stein, M. (2018). 5 practices for orchestrating productive mathematics discussions (2nd ed.). National Council of Teachers of Mathematics.

Smith, M., Yurekli, B., & Stein, M. (2024). Coaching the 5 practices: Supporting teachers in orchestrating productive discussions. Corwin Press.

Smucker, K., Sepúlveda, F., Weiland, T., Cannon, S., Casey, S., & Byun, S. (2024). Considering the 5 practices through a statistical lens. Mathematics Teacher: Learning and Teaching PK-12, 117(2), 86–97. https://doi.org/10.5951/MTLT.2023.0233