Building on Bob Moses’ collaboration with ETS that began in 2011 when he was a Visiting Scholar at nearby Princeton University, the Algebra Project is finishing up the second U.S. National Science Foundation* (NSF) funded research project with ETS and partners about how high school students come to understand the mathematical concept of function. In 2011, Dr. Michael Nettles, then Director of ETS’s Policy & Evaluation Research Center, expressed interest in the Algebra Project and began discussions with Bob. Since ETS is a leading organization for research and development on assessment, it was natural for the conversation to continue. ETS became a key partner for discussions on Question 3 of the Algebra Project’s three fundamental questions: what should we teach, how should we teach it, and how should we assess learning, so that students can attain the mathematics literacy needed for 21st century citizenship?
Beginning in 2013, the Algebra Project and ETS collaborated on several meetings with researchers and practitioners from around the country and began developing research proposals. These discussions were initiated by Nettles with support from Jon Rochkind of ETS’s Policy Evaluation & Research Center, and involved ETS researchers, the Algebra Project, the Young People’s Project (YPP), and colleagues from around the country. Soon a project led by ETS cognitive scientist E. Aurora Graf was funded by the NSF (Development and Empirical Recovery for a Learning Progression-Based Assessment of the Function Concept (#1621117) and was completed in 2021. PI Graf then came together with an ETS expert on collaboration, Jessica Andrews-Todd, for another project with the Algebra Project, YPP, Southern Illinois University Edwardsville (SIUE), and University of Nebraska-Lincoln (UNL): Investigating the Role of Collaboration on the Development of Student Ideas Using a Learning Progression for the Function Concept (#2101393). This project is wrapping up and will conclude this summer.
Collaboration is now considered an important skill for 21st century work, and educators need to know how to engage students in productive collaboration for learning. This project brought together a range of important perspectives, all relevant to seeking a better understanding of how to improve the teaching and learning of mathematics. The ETS team included E. Aurora Graf, cognitive science, learning and assessment; Jessica Andrews-Todd, collaboration, learning science, and development of digital environments for learning and assessment; Peter van Rijn, psychometrics and educational measurement; and Yang Jiang, data science, cognition and learning with educational technology systems. Two university-based researchers brought expertise in mathematics education: Yvonne Lai, (UNL) and Cheryl Lizano (SIUE). The YPP served to involve and ensure the voices and perspectives of students, through Maisha Moses, Executive Director, and Charlene Deleon Cuevas, Director of Operations. Staff and consultants who have all worked with the Algebra Project since the 1990s contributed the Algebra Project’s perspective on teaching and learning. Bill Crombie participated as Director of Professional Development, and Ben Moynihan as Executive Director. Frank Davis and Mary West, who have studied implementations at many sites, provided their research perspectives; Davis also served as the Project Evaluator. Lynne Godfrey, one of the first Algebra Project teachers and an experienced teacher developer and mentor, assisted in training teachers, and Mary Catherine O’Connor, a linguist from Boston University who specializes in productive classroom discourse, consulted on the analysis of “talk moves”.
While effective collaboration is now recognized as an essential 21st century work skill, the Algebra Project has been using collaboration in its classroom routines since it was founded. YPP, founded in the mid-1990s by Algebra Project “graduates” and middle school students in Jackson, MS, and led by Maisha Moses, adopted collaboration as a key feature of its after-school, near-peer math teaching and learning. As presented in our Fall 2024 Newsletter, small-group collaboration is one phase in the Algebra Project’s classroom “work cycle”. Students work on math problems collaboratively in small groups, then each group presents their work to the whole class, and the teacher facilitates a whole class discussion. Davis and West have observed how this phase of the “work cycle” engages students and develops their participation more effectively than if the teacher simply leads from the front of the class and calls on individual students. After some months, Algebra Project students also reported the sense of being in a “learning community” — a powerful support for students who may in the past have hung back. The National Council of Teachers of Mathematics recommends small group work as a part of instruction as well.
Both the Algebra Project and YPP follow a model of effective facilitation of small groups based on work with Harvard University psychologists during the 1990s and used in international consulting by the HayGroup/Boston. The Algebra Project has used the model in its teacher professional development program since the 1990s, and YPP uses it today in the training of near-peer ‘math literacy workers’ who facilitate learning of younger students in after-school programs. This NSF-supported project was an important opportunity to learn more about collaboration and how to facilitate meaningful mathematical discussions in today’s classrooms and out-of-school activities, as well as supporting technologies.
Both this project and the previous one were unusual in employing youth from the target population in key roles. In the first project, a team of YPP-trained youth vetted the wording of the math problems for the research on learning progressions, to ensure fair assessment of learning. In the second project, YPP-trained facilitators guided the small group collaboration. Both projects met high standards to be culturally and socially responsive to the language and cultures of the students.
The current project, which began in 2021, used a computer-based platform to present problems to small groups of 9th and 10th graders as they collaborated via an online chat. A total of 81 small groups from 9th– and 10th– grade classrooms in the United States participated. The degree of experience that teachers and students had with Algebra Project curricula and pedagogy varied from classroom to classroom. Before and after their small group session, students were assessed individually on their understanding of the function concept. The scoring of students’ understanding of functions was based on a learning progression, the development and validation of which was the focus of the previous project.
The research study included two conditions: in one, the students’ group conversations were facilitated by a young person or early-career professional trained in certain group facilitation skills based on “talk moves” as conceptualized by Sarah Michaels and O’Connor; in the other, students worked without input from a facilitator. Student collaboration was coded using three different schemes, reflecting three different perspectives on the data: 1) the Low-Inference Discussion Observation (LIDO) tool developed by O’Connor and colleagues, which captured “talk moves” used by facilitators; 2) the CPS ontology developed by Andrews-Todd, which identifies social and cognitive collaboration behaviors; and 3) the learning progression developed in the previous project, which describes the level of mathematical reasoning. The researchers asked whether the group work enhanced students’ knowledge as measured by the learning progression, and whether having a facilitator was helpful in supporting mathematical reasoning. Yang Jiang of ETS used advanced data analytics methods like Epistemic Network Analysis and Sequential Pattern Mining to unpack how the dialogue unfolded. The key findings are described below.
Key Findings
- Facilitated teams may show greater advancement with respect to the mathematics learning progression than unfacilitated teams, indicating the potential effect of facilitation on learning of the function concept.
- The facilitators 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.
Researchers’ Reflections and Next Steps
In recent interviews about their experiences in the project, researchers appreciated not only the findings but the collaboration with team members and the diverse expertise they brought. One said: “One of the powerful pieces is that we looked at this data from a lot of different perspectives, and the way we gathered it was also informed by different perspectives.” Another appreciated having the young people involved: “this is a different take on what research IS…not as rigid as we think of research. And how [the analyses] presented it, seeing how collaboration takes place in the chats…has been really interesting for me.” A third appreciated the implications for improved classroom teaching: “Talk Moves helps [teachers] to state the right questions in class to get [certain] kinds of responses. Look for the response needed to know what question to ASK — that’s fascinating.” A fourth noted: “We found significant differences in students’ behavioral patterns…that show the effectiveness of the facilitation. These results do have practical implications in terms of how to apply these facilitation strategies in classrooms to better shape the conversation among students as they work on math problems…Very exciting, I look forward to getting involved in the next steps.”
Team members also pointed to questions for further research:
1. How will students do in a longer experiment with longer periods of collaboration?
2. How can these results help with teacher preparation and ongoing professional learning?
3. What more can we learn about technologies that can benefit students’ collaborative learning in community or home activities — especially now that so many schools are under-resourced and lack learning materials that engage students effectively?
The final question is crucial to the Algebra Project’s new effort to develop a Digital Learning Lab that engages students, teachers and others in effective math learning activities online, including collaborative activities. The Algebra Project has embraced learning technologies all along, beginning with graphing calculators, and later a website for community engagement. Ben Moynihan, Executive Director, asks: “How can we ensure that teachers are empowered and safe, can find their voice, their agency and identities as learners and teachers of mathematics, and participate in a professional learning community of value to them as individuals and collectively, one that others can learn from? How can educational technologies help support that effort while maintaining the authentic values of human interaction that are the hallmark of Algebra Project work?” The Algebra Project looks forward to exciting next steps.
*Disclaimer Note: This research was supported by grants from the U.S. National Science Foundation (NSF). The opinions, findings and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the NSF.