From Wall to Bridge: Supporting Mathematics Learning Through Collaboration and Guided Facilitation

By Yang Jiang, Edith Aurora Graf, and Jessica Andrews-Todd

Mathematical concepts, especially those in algebra, are central to mathematics education and often serve as gateways to advanced mathematical thinking. But for many students, algebra concepts feel less like a gateway and more like a wall. The Nation’s Report Card highlighted a decline in math performance across the United States compared to pre-pandemic levels and a significant drop in algebra enrollment among 13-year-olds. So, how do we support math learning in a way that helps students not only scale that wall but also turn it into a bridge to further study?

At the ETS Research Institute, one promising approach we’re exploring is small-team collaboration. Imagine three or four students sitting at a computer, chatting with each other as they solve math problems. Engaging students in small teams allows them to actively construct knowledge rather than passively absorb it through lectures. Collaboration also supports social and emotional learning, from boosting engagement and motivation to improving peer relationships.

But, collaboration alone may not be enough. Students whose knowledge has not fully developed may benefit from facilitators who guide group interactions and keep them engaged, focused, and productively participating in collaboration.

Building on a learning progression and scaffolded tasks developed as part of a previous project led by Edith Aurora Graf, we, along with collaborators from the Algebra Project, Southern Illinois University Edwardsville, the Young People’s Project (YPP), and the University of Nebraska-Lincoln, are focusing on how small-team collaboration can advance students’ mathematical thinking with respect to that learning progression. 

In our current project, we explored the question: Can human facilitation improve how students work together to solve math problems and support mathematical thinking?

In this study, high school students worked in small teams to solve problems focused on functions, a core but challenging algebra concept. Working with Catherine O’Connor, our YPP colleagues trained human facilitators in the use of Michaels and O’Connor’s “talk moves,” strategies to guide student dialogue by eliciting reasoning and encouraging students to build on each other’s ideas rather than giving answers. For example, facilitators might ask, “Can you explain your thought process on that?”, “Who can build on what was just said?”, or “Do you agree or disagree, and why?” These prompts help students articulate their thinking, listen to their peers, and engage in collaborative sense-making. Importantly, these facilitators weren’t teachers or math experts. Most were near-peer mentors—college students with slightly more experience than the high schoolers they supported, but not so much more that they seemed out of reach. Why near-peer mentors? Research suggests they may be uniquely positioned to support learners due to shared identities, closer social proximity, and similar recent experiences.

We zoomed in on the chat conversations happening within teams by using advanced data analytics methods like epistemic network analysis and sequential pattern mining to unpack how dialogue unfolded. Why chat logs? Because hidden in those lines of text are rich clues about how students reason, negotiate, and build understanding together.

Key findings:

• Facilitated teams may show greater advancement with respect to a mathematics learning progression than unfacilitated teams.
• Near-peer mentors successfully triggered productive collaborative behaviors such as reasoning, explaining, and negotiating ideas.
• Different facilitation strategies led to targeted collaborative interactions:
  • Asking students to respond to each other often sparked negotiation, as students took turns to express agreement or disagreement with other team members.
  • Prompting for explanations led to richer information sharing.
• Facilitation also reduced off-task or inappropriate chats, helping students stay focused.

These findings highlight the power of human support to guide student collaboration and mathematical thinking. By looking beyond task performance and into the collaborative processes through advanced data analytics methods, we gained deeper insights into how learning happens and how facilitation shapes collaboration.

Looking ahead, we are excited about the potential of combining human facilitation strategies with generative AI. Could a large language model simulate near-peer mentors and support student discourse through avatars? This study lays the groundwork for innovation.

Algebra doesn’t have to be a wall. With the right support, it can become a bridge.

Yang Jiang is a research scientist at ETS. Her work focuses on how technology-based curriculum and assessments can help students learn and the use of AI in education. Jessica Andrews-Todd is a managing senior research scientist at ETS. Her work explores the assessment and development of interpersonal skills and the use of digital environments to support student learning and assessment.

Edith Aurora Graf is a senior research scientist at ETS. Her work focuses on automatic item generation, cognitive modeling for mathematics assessment and instruction, and learning progressions.

This work was funded by the National Science Foundation, Grant No. 2101393. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.