Problem of Practice

Supporting teachers in enacting ambitious and responsive mathematics teaching that builds on students’ mathematical strengths is a persistent challenge in mathematics education. High-quality professional learning (PL), such as Cognitively Guided Instruction (Carpenter et al, 2015), can introduce teachers to core principles of responsive teaching. However, pull-out PL alone is rarely sufficient to transform classroom practice; rather, teachers need ongoing, collaborative opportunities embedded in practice and focused on students’ learning (Borko et al., 2010). Within CGI PL, teachers learn frameworks for interpreting students’ strategies and develop skills in attending to, interpreting, and responding to students’ ideas (Jacobs et al., 2010). They begin to anticipate strategies, interpret partial understandings, and consider how to build on emerging thinking. Yet enacting these practices in real time—within the work of teaching—is complex.

As Cobb et al. (2018) argue, transforming instruction requires ongoing learning experiences coordinated across settings. Teachers must have structured opportunities to move between learning about teaching and learning from teaching (Santagata & Guarino, 2011). This movement enables professional learning to be operationalized: translated into concrete instructional decisions when planning lessons and in the moment of teaching and refined over time through careful analysis of student thinking.

In our context, teachers participated in two years of CGI-focused pull-out PL in which they developed a strengths-based lens for noticing student thinking, explored how the CGI framework intersects with mathematics standards, and learned to make responsive instructional decisions that build on students’ emerging thinking, such as by asking intentional questions during lessons (Jacobs & Empson, 2016) and tailoring mathematical tasks based on students’ existing strategies (Empson et al., 2021; Land et al., 2019). To translate these learnings into practice, we implemented the Looking at Student Work Protocol (LASW) (adapted from Bray et al., 2019). Through the LASW, during weekly grade-level team meetings supported by a facilitator, teachers noticed strengths in students’ mathematical thinking and decided future mathematics learning goals, tasks, and instructional routines based on that thinking.

The LASW

The protocol (see Table 1) is intended to be brief (no more than 30 minutes), routine, and embedded in teachers’ regularly scheduled meetings and supported by a facilitator who elicits teachers’ thinking and contextualizes their conversations within the tenets of CGI and broader principles of ambitious and responsive mathematics instruction.

Table 1 

Looking at Student Work (LASW) Protocol 

Affordances for Teacher Learning

We have implemented this protocol across multiple districts. Through these experiences, we have come to see how participating in LASW meetings supports teachers’ learning and enactment of responsive teaching. During the LASW, teachers are afforded opportunities to routinely notice strengths in students’ mathematical thinking. As they attend to specific details of students’ written work, they recognize students’ emerging ideas as resources for future learning and celebrate students’ growth over time (Kimmerling, 2026). Further, teachers learn to plan responsively, drawing on their knowledge of students’ emerging understandings and research on children’s mathematical thinking introduced during CGI PL. Teachers come to recognize that not all tasks provide the same opportunities for students to make their thinking visible. They learn to select tasks and numbers that will promote particular mathematical strategies. Teachers intentionally open up tasks and discuss instructional routines to elicit student thinking and support individual students’ progress.

To illustrate these opportunities for teacher learning, we present examples from a single meeting of a first-grade team. Teachers Jessica^[1], Nadia, and Megan analyzed students’ work on 64+23.  These numbers were carefully selected the week before so that students could add two 2-digit numbers with a sum less than 100 as they continued to work on strategies using place value and properties of operations to solve addition problems. In addition to the mathematical goal, teachers were working with students to communicate their thinking in writing. During the meeting, teachers noticed strengths in students’ work. For example, Jessica shared:

Students showed tens in different ways. Letty drew tens first, she had her six tens and two tens.  Then she drew the ones. I feel like she's essentially combining like units with direct modeling, and using drawings to help her navigate it. That was exciting, a good way for her to show her work. 

In describing Letty’s strategy, Jessica highlighted a nuance in Letty’s work, relating it to a more abstract strategy, combining like units, while simultaneously recognizing the strengths in her thinking.

After all the teachers shared their work, Jody, the facilitator, supported them in selecting a goal for future mathematics learning:

Jody: What feels like a next step, considering where all of your students are?

Megan: Labeling. Writing equations.  Juan decomposed, then drew all the circles. When I asked him, what did you do here? He said, 60 plus 20 is 80, 4 plus three is 7, 80 plus seven is 87. He could verbally tell me. Putting it down on paper is where there's a disconnect. How do I bridge that gap?

Jessica: Yeah, that's something I want to continue working on, labeling papers and

adding more numbers...especially for students that are direct modeling, for them to be more comfortable thinking about it, not only conceptually what a ten is, but also, these two 10s make 20. And here's my six 10s, 60. I want to work my students towards combining like units if they aren't already there. That would be a good stepping stone. Similar to what Megan said, trying to get them confident in using equations when that's exactly what they're saying and how to show it.

Jody: That might be interesting for the students writing 6+2=8 and 4+3=7.  They’re saying it's really 60+20=80 and writing something different. That would support them too.

In this exchange, the goal emerged from teachers' knowledge of their students, their understanding of how children think about mathematics, and relevant mathematics standards. The conversation continued regarding which numbers teachers might select for the next task.

As teachers participate in LASW meetings over each school year, we see evidence that they learn from their teaching (Santagata & Guarino, 2011) by leveraging their students' thinking. They viewed themselves as playing a key role in student learning and took direct responsibility for supporting and advancing each student's learning. They took pride in getting to know their students, including their understandings and dispositions, and engaged with them as partners in learning. Further, discussions served as resources for teachers to center mathematics goals, leverage students’ thinking toward those goals, and make principled instructional moves as they taught lessons planned during LASW meetings (Kimmerling, 2026).

Three Essential Design Features

We highlight three design features of the LASW that are central to advancing ambitious and responsive mathematics teaching. First, the tool deliberately centers student thinking. Each segment of the protocol begins with soliciting concrete evidence of students’ mathematical thinking, positioning teachers to ground decisions in strengths rather than deficits. A shared CGI framework offers common language for interpreting strategies, identifying next steps in a progression, and conjecturing tasks and instructional moves to advance learning. Professional learning content is situated in teachers’ daily work and in their students’ thinking.

Second, the LASW is organized around team and time. The same grade-level team meets routinely, briefly, and within the workday, creating a sustainable, job-embedded inquiry cycle. Consistency builds trust, shared instructional reasoning, and collective responsibility for student learning. This structure situates learning in practice, redefining meetings as a space for learning and improvement alongside colleagues.

Finally, a skilled facilitator—an instructional coach or mathematics teacher educator with strong content knowledge and experience in ambitious teaching—is essential. This facilitator presses teachers to attend to key mathematical nuances, connect strategies to broader frameworks, and anticipate how number choice and instructional moves might shape thinking. Together, these features operationalize and sustain professional learning through continuous engagement with students’ mathematical thinking.

Conclusion

In our context, the LASW became a routine, job-embedded support that sustained teachers’ learning from pull-out PL, creating opportunities for teachers to operationalize that learning in their teaching. During meetings, teachers learned to notice strengths in students’ written work, select future learning goals based on that noticing, and then discuss tasks and instructional moves that support students’ progress. Ongoing supports, such as the LASW, allow teachers to contextualize learning in their practice with their students and have implications for their in-the-moment decision-making during teaching (Kimmerling, 2026), thus serving as a bridge from pull-out PL to practice.

References

Borko, H., Jacobs, J., & Koellner, K. (2010). Contemporary approaches to teacher professional development. International Encyclopedia of Education, 7(2), 548-556.

Bray, W. S., Johnson, J. D., Rivera, N., Fink, L. A., Bauduin, C., & Schoen, R. C. (2019). Unlocking mathematical understanding together through FACT meetings. Teaching Children Mathematics, 25(6), 370-377.

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children's mathematics: Cognitively guided instruction (2nd ed.). Heinemann.

Cobb, P., Jackson, K., Henrick, E., & Smith, T. M. (2018). Systems for instructional improvement: Creating coherence from the classroom to the district office. Harvard Education Press.

Empson, S. B., Krause, G. H., & Jacobs, V. R. (2021). “I stewed over that number set for like an hour last night”: Purposeful selection of numbers for fraction story problems. The Journal of Mathematical Behavior, 64, 100909.

Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. Zdm, 48(1), 185-197.

Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.

Jilk, L. M. (2016). Supporting teacher noticing of students' mathematical strengths. Mathematics Teacher Educator, 4(2), 188-199.

Kimmerling, C. (2026). Teacher collaboration in service of ambitious and asset-based mathematics instruction: Investigating facilitation practice and teacher learning [Doctoral dissertation, University of California, Irvine]

Santagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. Zdm, 43(1), 133-145.