At its simplest, the Algebra Project Work Cycle that moves from Individual Activity, to Team Collaboration, to Class Discussion, is the backbone of how an Algebra Project classroom functions. But in practice, it’s more than a sequence of steps. It is, in fact, not a sequence of steps at all since it can be taken forward, backwards, or in any order. Rather, it supports a classroom culture shift away from mathematics as a silent, isolating exercise and toward mathematics as a public, collaborative act of reasoning.
“Mathematics doesn’t just come out of your head without the support of a community,” says Director of Professional Development Bill Crombie. “[And so] the desiderata is discourse-rich classrooms.”
This emphasis on discourse is structurally embedded in our pedagogy across the board. Bob Moses’ Five-Step Curricular Process, the Algebra Project’s engine for mathematizing lived experience, depends on the Work Cycle to turn that experience into shared reasoning. Together, the two processes reflect something true about mathematics throughout history: Math has always been a product of people talking to each other.
“The Work Cycle is a fundamental expression of how we conceive of the doing of mathematics within the Algebra Project,” Bill explains. “We are making our thinking public. Unless the culture of the classroom is built to support the public sharing of ideas, the public sharing of ideas will not happen.”
Before either process begins, the class builds shared expectations. This is non-negotiable: A collaborative space cannot be imposed or assumed; it must be co-designed and cultivated.
“You come out with agreements on how we’re going to talk to each other and treat each other. Rather than give them to students, they develop them.”
These agreements become the soil the rest of the work grows out of.
Individual Work
Both the Five-Step Curricular Process and the Work Cycle start from the same place: a shared physical event and individual meaning-making.
This is an unusual beginning for math class. Students are not told what matters. They’re deciding it on their own.
By encountering a concrete event, our classic example being a trip around the school or neighborhood, and then privately deciding what about that event seems important, students generate the first raw material for mathematical thinking. They draw, write, model, or narrate what they noticed, experienced, or cared about.
Bill puts it plainly: “Individual work begins with the shared concrete event… it’s not mathematically right or wrong. It’s the fertile ground we want to establish with all students.”
That “fertile ground” is psychological as much as mathematical. It tells students that math is not a secret code hidden behind a teacher’s explanations or a higher-level of consciousness unattainable to all except a few chosen ones. It’s something they can build. Something they can explore. Something they can be creative with.
And for many students, especially those who have been conditioned to believe math is about speed, correctness, or innate ability, this reframes the entire subject. It lowers anxiety and increases ownership, thus creating a pump where there once was a filter.
Even though the work is independent, in many ways individual work is about voice: each student has the floor without interruption or comparison. Their instinct and perspective is the only thing that matters.
Team Collaboration
Once students have articulated their own thinking, they move into small groups. This is the first moment of exposure. A transition point where we put private thought into shared space.
Bill captures this shift, “Team collaboration is the first moment when thinking is no longer private, but shared.”
This is where ideas get tested, not by a teacher, but by peers who are trying to understand one another.
Students ask each other questions, clarify what their teammates meant, refine their representations, and discover differences that matter.
Team Work adds cognitive pressure, but a healthy kind. To explain something to peers, students must articulate it clearly. To defend an idea, they must understand it more deeply. And to revise an idea, they must be willing to reconsider their own thinking.
Crucially, this phase keeps the stakes low. Students are not yet speaking to the entire room; they’re speaking to a small circle where trust has been intentionally built. The conversation becomes a microcosm of mathematical discourse: listen, interpret, critique, elaborate.
When groups “publish” their findings, through chart paper, diagrams, or models, they prepare for the final step.
Class Discussion
The final stage of the Work Cycle is whole-class discussion, where teams bring their thinking forward to the room. Bill likes to frame the three stages in academic publishing terms:
“There’s individual production, team publication, and finally class peer review.” But he’s quick to clarify, “Peer review is not cut-throat. We are establishing a very different culture of mathematics in the Algebra Project.”
This whole-class discussion is where mathematical reasoning becomes fully public. Students compare how each team interpreted the same event which involves examining differences in representation and pushing toward shared definitions or shared understanding.
This is also where the class practices empathy before critique, something Bill terms putting “empathy before advocacy.” Students are trained to understand each team’s thinking before offering a different or more refined perspective.
That cultural norm is protective, but it’s also generative. Students learn that critique, like math in general, is about clarity. They learn that their ideas can be examined without insecurity and that through rigorous review, they aren’t winning or losing but collaboratively building a mathematical understanding.
And they learn something deeper still.
“If we can build this discourse in a class, it gives us a model for the discourse we build in our civic life, because we’ve done it before and we know what it feels like.”
Mathematical discussion becomes rehearsal for democratic participation.
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Teachers often ask: What should students get out of the Work Cycle? Better math scores? Deeper understanding? More engagement? All true, but incomplete.
The Work Cycle, in concert with the Five-Step Curricular Process, is designed to cultivate voice, agency, and identity at the level of the individual, the team, and the class.
“A product of this process is rigorous mathematics—not because it’s given by the teacher, but because the students build the reasoning and logic themselves,” Bill explains.
In traditional classrooms, rigor is often equated with difficulty, speed, or abstraction. In the Algebra Project, rigor emerges from ownership. When students produce and share the logic behind a concept rather than memorize someone else’s, they understand it at a deeper level.
This doesn’t mean teachers step back. Their job is to facilitate student discourse rather than control it.
And that requires the two processes, the Work Cycle and the Five-Step Process, working in tandem.
“We capture this picture not just in the Work Cycle but in how the Work Cycle interacts with the Five-Step Curricular Process. Both the Five-Step Curricular Process and the Work Cycle in unison support student voice,” Bill explains.
The Five-Step Process offers the structure for mathematizing experience. The Work Cycle provides the social engine that turns experience into collective reasoning.
One provides the “what.” The other drives the “how.”
Thus, the Work Cycle reflects something true not just pedagogically, but historically. Math has always been collaborative: letters exchanged across continents, proofs debated, ideas refined through discourse.
Yet in most classrooms, math is treated as solitary work.
The Algebra Project incorporates that solitary work but ultimately returns math to being a public activity to increase clarity and understanding.
“This is not an algorithm that can be mechanically established. It is an artistic process embedded in the humanities.”
We aim teach math like we teach writing, argument, and interpretation, or in other words, through a literacy approach. We see math literacy as the ability to read, write, and reason with the principal algebraic and geometric symbol systems of mathematics. And that shift to a literacy approach in the teaching and learning of mathematics matters most for the students who have historically been left out or left behind.
“For communities where math proficiency has been the greatest issue, students do better when mathematics is framed in this collaborative fashion.”
As Bill puts it, “Mathematics can be generated in different fashions. But for the mission of the Algebra Project, the collaborative culture is what works.”
For those who wonder why the Algebra Project invests so much in culture-building, discourse norms, and community agreements, why we insist on humanizing mathematical work, the answer is simple. You cannot build a mathematical community without empathy. You cannot expect students to make their thinking public unless they trust their peers. And you cannot expect students to take intellectual risks without cultural safety.
The Work Cycle is the architecture that makes that possible.
Individual work gives students voice. Team work gives them agency. Class work and discussion cultivates students’ identity as practitioners of mathematics both in the mathematical community and beyond it.
Together with the Five-Step Curricular Process, the Work Cycle transforms the doing of mathematics from a private act into a shared human experience.
And, most importantly, it lets students build the mathematics they deserve to understand.