For the past three years, the Algebra Project, in collaboration with Kennesaw State University and the National Society for Black Engineers, has been pursuing an NSF-funded research agenda around calculus accessibility for high schoolers, aptly named the Accessible Calculus Project (ACP). The ACP began with a simple reframing: what if Algebra and Geometry aren’t prerequisites to calculus, but are, in the ways students actually encounter them, already calculus-adjacent? The traditional high school sequence — Algebra I, Geometry, Algebra II, Precalculus, and then Calculus — treats each course as a gate students must pass through before reaching the next, with calculus held out as the distant goal. The ACP’s research took a different reading of that same sequence: The state Algebra and Geometry standards students already study contain the conceptual seeds of the calculus. Rather than adding pre-calculus content to those courses, the research explored teaching for the intersections among Algebra, Geometry, and the central ideas of calculus, so that learning builds vertically through those connections instead of marching horizontally through a chain of prerequisites.
That research undergirds the design of our Advanced Study Academy (ASA): a six-week, paid summer program where rising 10th and 11th graders take on calculus-adjacent work through Algebra and Geometry contexts. The Academy is a program featured under our national math literacy campaign, Math Makes Movement, which has seen support from organizations like the Cisco Foundation who are interested in empowering underserved communities through novel technology.
The first weeks utilize the Algebra Project’s Five-Step Curricular Process, working through a set of knowledge games we developed such Let’s Take a Trip!, the Winding Game, and Road Coloring, and overall grounds students’ numeracy in shared experiences which they learn to mathematize, while compensating them as entry-level knowledge workers gives them a stake in the work. On that foundation, students then develop the central concepts and techniques of both the differential and the integral calculus across three summers. The way the Academy work is structured is doing double duty: It’s also designed to build students’ Voice, Agency, and Identity (VAI). The bet is that math fluency and VAI rise together, and that together they’re what actually set students up to succeed once they hit a calculus sequence.
That’s the theory. What does it look like in practice? We had the opportunity to test-drive our ASAs in three different communities over the summer: Cambridge Public Schools, the Michigan Hispanic Collaborative in Detroit, and Simmons College of Kentucky in Louisville.
Each took a different shape, co-designed by its own community and context, with the Cambridge Advanced Study Academy (CASA) most closely resembling how we originally envisioned the program to fit into a public school environment; Michigan and Kentucky each adapted the model to fit an existing partner infrastructure.
In Cambridge, rising 10th, and 11th graders were paid through the City of Cambridge’s Mayor’s Summer Youth Employment Program to participate in CASA. A Cambridge Public Schools math teacher co-facilitated all six weeks, and students organized two open houses throughout the summer to share their work with the wider community.
“I got to see students who only had Algebra I experience working through problems that would typically be in a Calculus course,” Stasia Nedoroscik, the math teacher at Cambridge Rindge and Latin School who co-facilitated CASA, said.
One student, Stasia explained, started off feeling pretty insecure about his math knowledge and reserved about sharing his ideas. By the end, though, that same student was volunteering to be the MC for their open houses, offering to make PSAs, and asking to stay involved with the CASA Club the coming school year. Stasia’s read was that the student’s math identity had grown so much over the six weeks that he could finally say to himself, ‘I’m capable of doing calculus work.’
Vertically aligning algebraic and geometric concepts with calculus didn’t just produce Aha moments for the students, however.
The Michigan Hispanic Collaborative (MiHC) is a nonprofit that builds the navigational and decision-making infrastructure connecting students’ talent to opportunity. MiHC had never before offered a math-focused experience; MiHC educators completed four days of professional development with the Algebra Project before facilitating the 6-week summer experience for rising sophomores.
One teacher with the MiHC, reflected on how the program shaped how they think about student voice.
Feeling discomfort around verbalizing their ideas during the professional development portion, they realized that understanding something and being able to communicate it clearly to someone else are two different skills entirely. That reframed how they thought about their own students. Specifically, that students may know more than they can easily put into words, and part of the work is helping them find their voice.
That word, voice, stuck with the MiHC teacher, “I used to feel like I didn’t have a voice, and as an adult I’m learning how to use it. Even though it still feels scary, I have had to intentionally push myself to speak up, ask questions, and share my thinking. This training reminded me how important it is to create spaces where students feel safe using their voices, even when they are unsure or confused.”
The partnerships in Michigan and Kentucky were particularly unique. ASAs were conceptualized as a way for communities to raise the floor of math literacy during a period when Algebra I increasingly filters out underserved students from advanced math sequences. Research shows that students who perform best in math consistently have more support, whether through paid after-school tutoring or schools providing longer math periods. The ASA was designed to give students who didn’t have the resources for after-school tutoring a level playing field. The Michigan Hispanic Collaborative and Simmons College of Kentucky showed what happens when a community-based partner develops the model with a synergistic agenda.
At Simmons College of Kentucky, the institution took the lead on much of its own organizing, building its own online course infrastructure to support the ASA. The Algebra Project provided a single day of PD, and Simmons and the Algebra Project facilitated the work with students from the surrounding community.
Myra Rock, Chief of Staff to the President at Simmons College of Kentucky said the partnership represented a natural extension of Simmons’ historic mission, “Bob Moses challenged us to understand math literacy as a civil right. That is important because this work is ultimately about much more than whether a student can solve an equation. It is about whether young people have access to the knowledge and literacies necessary to participate fully in higher education, in our economy, in our democracy, and in shaping the future of their communities. That vision deeply resonates with the mission of Simmons College of Kentucky.”
Dr. Kevin Fields, Program Curator for the Algebra Project at Simmons initiative, said one of the most important outcomes was seeing students develop their own mathematical voice.
“What was powerful was not simply watching students arrive at an answer. It was watching them reason their way toward understanding and then find the language to explain that reasoning to someone else. The students were thinkers, questioners, collaborators, and problem-solvers. When young people begin to see that their ideas have value and that they have the ability to make sense of mathematics, the learning becomes theirs.”
That notion of Voice consistently came up as one of two of the most improved upon arenas for students.
The second was Identity.
“Last year, I struggled in math and even had to attend summer school. Coming to this program helped me understand algebra better, and I feel like I’m becoming more confident in solving problems.” 12th-grader Kelise, who participated in the Simmons ASA, said about her own math identity growth.
However, after a robust year of piloting our ASAs, the program still has work to do on developing student Agency.
“I feel like identity is where I saw the most growth. Agency, close to none. I feel like for the most part, the students were waiting to be told what to do, waiting to be given direction.” Stasia gave me a common refrain.
Students, in general, struggled when in a room with authority figures to demonstrate agency. The ASAs did anticipate this, and tried to address it with how we structured our open houses, where students invited families, friends, and community members to experience and learn about the work they had been doing.
“For the first one, I was not in the room at all, we just let them run the show, and I truly think that was their best work. In a way, it felt like they were more nervous doing things in front of me. They felt like they were gonna either mess up or that I would be judging them.” Stasia explained of the CASA open houses. “Students have the most agency when a facilitator takes a step back and just lets them run the show. For the second open house, we were in the room, but we weren’t, helping the students facilitate any of the activities. We were just participants. And, again, that’s where I think I saw their best work.”
Some of the students of CASA aim to start a CASA Club this coming school year to continue working together as knowledge workers and as mentors. That continuation points to the ASA’s natural three-year cycle: students enter as rising 10th graders, return as rising 11th graders, and complete the cycle as rising 12th graders. Across those three summers, students develop an understanding of both the differential and the integral calculus commensurate with the college calculus course as the standard. Each returning cohort deepens its own work while mentoring the cohort coming up behind it. Building on the lessons and successes of all of our pilots, the Algebra Project plans to carry the ASAs through that full cycle.
Ultimately, it is our vision for ASAs to be a far-reaching Algebra Project flagship program providing greater access to advanced mathematics for all students in communities across the US.