The Algebra Project’s ethos is that, while mastery of computations and algorithms is useful, true math literacy extends far beyond that. An intuitive, logical, creative, and exploratory mindset transforms mathematics from a memorization game to an active practice. Fostering each student’s voice, agency, and identity is critical to developing their engagement and understanding of mathematics. It lays the foundation for establishing a classroom culture in which every learner sees themselves as a mathematician.
We rely on Bob Moses’ Five-Step Curricular Process as a pedagogical framework that allows students to intuitively hone their own mathematical sensemaking. We utilize a collaborative Work Cycle alongside the Curricular Process, and the first component is Individual Work which enables students to leverage their own thoughts in the development of their conceptual understanding of math.
“In the Algebra Project, the focus is on what the students are thinking, giving them tasks to figure out on their own and struggle productively. As a facilitator, I didn’t just guide them step by step – I let them work through the problem independently. It’s about allowing students to realize they can hold knowledge, not just mimic the teacher. (Traditional mathematics instruction) doesn’t emphasize this ownership of thinking; it’s more about following a set path to a predetermined answer. The shift is in giving students the space to engage in the process and make connections on their own,” Paola Caicedo explains. Paola is an Instructional Specialist for Broward County Public School District in Florida, where she taught high school mathematics before shifting to her current role supporting other teachers.
“My teaching career kind of started with the Algebra Project. I think it was a huge part of my journey, really shaping who I am as a teacher. Even after they got rid of the program at my first school, I stayed connected through conferences and continued to support it in a new district. It shaped everything I did, and I ended up piloting it in Broward for four more years. It was really the core of my teaching experience.”
Paola embraced the Algebra Project’s cohort model in her teaching in Miami-Dade Schools and in Broward Schools. The cohort model is a novel strategy in which teachers stayed with the same students for all four years of high school. “What I appreciated most about the Algebra Project was the ability to loop with the kids. Time wasn’t a constraint – it gave me the opportunity to see growth over the years. Some kids opened up in the first year, while others took four years, but having that time allowed me to build real relationships. Consistency and care were key. The kids knew I was always there, and I was their math teacher for four years. That stability helped them feel safe to share mistakes and truly learn.”
That stability, and the security it offered students, was instrumental. Mathematics is about exploration. Traditional math instruction often prioritizes rote memorization and mechanical execution of algorithms. While these skills are necessary, they can inadvertently present mathematics as rigid and prescriptive, stripping it of its inherent dynamism. A hallmark of Algebra Project classrooms is moving from individual work, to small group work, and on to whole class collaboration. Teachers step into a role of facilitator rather than lecturer. When students are given the opportunity to work independently, it not only helps create self-reliance, but also allows them to reflect on how they view themselves as learners. When a teacher can witness how students work through problems, and how students describe shared events, without the teacher passing any judgment on the correctness of their students’ observations, it allows students to bring their own perspectives to the table, emphasizing the exploratory nature of math.
“The traditional gradual release model starts with the teacher doing most of the thinking, showing how to solve a problem, and then having students mimic it. But with the Work Cycle, it’s different. It begins with the student thinking for themselves, focusing on problem-solving and productive struggle. Instead of just being handed math problems to solve, they’re asked, ‘What are you thinking?’ and how they would tackle the task on their own,” she said of the more prevalent ‘I Do, We Do, You Do’ model of math teaching where a teacher demonstrates how to solve a problem, does it with the students, then has the students do it on their own.
In the Five-Step Curricular Process students are encouraged to grapple with uncertainty and ambiguity, and to veer away from the application of predetermined formulas, as they mathematize features they observe in shared physical events. For example, they might spend time articulating the features of an event, like a bus ride to school or the difference in height between their friends, using their own words, pictures, and models. Students engagement in individual work gives them the opportunity to formulate their own perspective on the event, what strikes them as being notable, and thereby indicate their ownership and understanding of the event.
“The resistance in learning comes from confidence and comfort – it’s about being okay with the holes in your thinking. It doesn’t happen overnight, but by starting with accessible tasks that everyone can engage with, students can build confidence over time. Using shared, concrete events like a Trip Line activity lets everyone contribute without fear of getting something wrong. As they get more comfortable with mistakes, their thinking deepens, and they begin to trust themselves and their classmates to help fill in those gaps.”
She recalls the shift in how this learning process helped one student approach mathematics, “In my last cohort, one student, initially quiet and lacking confidence in math, struggled to articulate his thoughts verbally. However, when he was given the opportunity to think and work independently, he would visualize math concepts, like drawing out factors and primes. Although he couldn’t always explain his ideas verbally, he found that showing his understanding visually allowed him to communicate more effectively. This approach gave him the space to grow. By the end of the year, he was sharing his ideas with others and even helped his peers articulate their own thoughts.”
This practice encourages students and teachers to view mathematics as a field where their unique perspectives and lived experiences are valuable contributions to the process of learning. By engaging independently, students develop their internal mathematical voice, recognizing that they have the capacity to navigate and contribute to the world of numbers and equations.
“Building the right classroom culture was key, with relationships at the center. I worked to convince the students that their thoughts and voices mattered. Whether it was through math games or group discussion, the focus was on sharing ideas and building confidence. I wanted them to shift their mindset about math – not about speed or perfection, but about the process and being comfortable making mistakes. Through team games and activities, they also developed soft skills like communication and public speaking, which contributed to a stronger learning environment.”
Agency in mathematics begins with the realization that one’s thoughts and strategies matter. And that’s not just a slogan. The Five Step Curricular Process and the Work Cycle enable young people to lead their own mathematical development. During Individual Work, students are given the space to approach problems in their own way, fostering a sense of ownership over their learning. This autonomy contrasts sharply with the passive reception of knowledge that dominates many traditional classrooms. Instead of waiting for the ‘right’ answer to be revealed, students actively construct their own understanding, strengthening their problem-solving abilities.
Drawing on Vygotsky’s Zone of Proximal Development, Individual Work allows students to operate within their current capabilities while stretching toward new insights. Mistakes are embraced as natural and essential steps in the learning process, reinforcing the idea that growth arises from effort and persistence. This shift not only boosts students’ confidence in their mathematical abilities but also cultivates resilience and hampers anxiety, since many students arrive at the math classroom believing they’re ‘not a math person.’
During Individual Work, students aren’t critiqued for using their own natural, spoken language, nor do Algebra Project teacher’s attempt to mold how young people speak or reason. As they independently navigate problems, students begin to see their thought processes as valid contributions to the mathematical discourse. Over time, this builds a positive self-concept, where students identify as capable and creative mathematical thinkers.
The emphasis on voice, agency, and identity in Individual Work also sets the stage for a broader cultural shift within the classroom. When students recognize their own capacity to engage with mathematics, they naturally begin to place higher expectations on themselves. When they place higher expectations on themselves, they place higher expectations on their peers. This redefines the classroom dynamic, transforming it into a community of learners who collaborate, challenge, and support one another, which will become necessary for the following Work Cycle component, Team Collaboration.
“Individual time allows students to fully explore and articulate their own thoughts without influence. This raw thinking provides a foundation for meaningful group collaboration. When students come together, they can refine their ideas, fill in gaps, and learn from each other’s perspectives. Without the individual reflection first, group work becomes more about choosing the ‘best’ idea rather than engaging in deep collaboration that leads to richer understanding,” Paola says.
In this reimagined classroom, the teacher’s role evolves from that of an authority figure dispensing knowledge to a facilitator guiding exploration of knowledge. Teachers invite open-ended investigation, encouraging students to think critically and creatively. They provide support and feedback that reinforces students’ efforts while allowing them the freedom to arrive at their own conclusions.
In Paola’s words, “The teacher’s focus moves from driving the discussion to guiding it. Instead of dictating what students should think or say, the facilitator’s role is to center the conversation around the learning objective while allowing students to explore and express their own ideas. This approach fosters more student-centered thinking, where the teacher listens intently to student contributions and asks questions to encourage deeper connections between students’ thoughts. While the gradual release model focuses more on teacher-led procedures, the Work Cycle emphasizes student discourse, making it a more challenging and cognitively demanding process for the teacher, as they embrace silence, avoid direct corrections, and think flexibly to guide the group towards understanding without giving away the answers.”
Moreover, teachers model the values of the Work Cycle by demonstrating curiosity, patience, and a willingness to embrace uncertainty. By embodying these qualities, they help students see mathematics as a collaborative and dynamic endeavor, rather than a static set of rules to master.
Reflection is a cornerstone of the Algebra Project’s methodology, and it is particularly vital during Individual Work. Students are encouraged to think deeply about their approaches, strategies, and outcomes. This process not only enhances their understanding of mathematical concepts but also strengthens their metacognitive skills, enabling them to become more effective learners.
By reflecting on their Individual Work, students gain insights into their own thought processes, identifying strengths to build upon and areas for growth. This self-awareness is a key component of agency, as it empowers students to take control of their learning journey. It also reinforces their identity as mathematicians, as they recognize their ability to contribute to the mathematical community.
When students engage in a Shared, Physical Experience, and then work independently to form their own perceptions of the event, the concepts of ‘right’ or ‘wrong’ do not apply. Such judgments can only arise when a group arrives at a shared understanding. The purpose of the Five-Step Curricular Process and the Work Cycle is not merely to cultivate individual thinking, but to guide students toward a collective and shared understanding over time, as they progress through all five steps. By the time they reach Symbolic Representation, the concepts of right and wrong become meaningful. Individual Work plays a crucial role here, allowing educators to assess students’ conceptual understanding and identify the approaches students are developing.
Therefore, Individual Work is not only an introductory phase. It is a transformative process that redefines how students engage with mathematics, emphasizing exploration, creativity, and personal agency. By cultivating students’ voices, identities, and sense of ownership, it lays the groundwork for a classroom culture where mathematics is not merely a subject to be studied but a field to be experienced and lived.
In this culture, mathematics becomes intuitive, logical, and deeply personal. It is no longer a series of computations to memorize but a dynamic and evolving practice that invites curiosity and collaboration. Through the Individual Work phase, students discover their potential as mathematicians, building the confidence and skills needed to navigate the complexities of both mathematics and life. This is the power of this experientially-based pedagogy: to transform not only how students learn but also how they see themselves and their place in the world of mathematics.
When asked if this method of teaching is harder than more traditional approaches, Paola laughs, “Yes. It’s much harder. Teachers always need to think about things like time constraints, and this takes longer. But there’s a beauty in letting students figure it out on their own. When you see that ‘light bulb’ turn on without you telling them what to do, all you did was ask questions – that’s where the beauty is. That’s worth it.”