The Question of Access
There is an important tension in the work of democratizing access to calculus and advanced mathematics. The Algebra Project is presently helping several communities across the country develop Advanced Study Academies: community-based parallel educational institutions that deliver calculus knowledge to high school students outside the traditional school curriculum sequence. Whenever this model is described, it raises understandable concerns about its disruptive implications. What happens when students return to school carrying mathematical knowledge that places them ahead of the grade-level sequence? How will schools respond when students acquire, outside the formal system, forms of knowledge that the school has historically treated as scarce, delayed, and selectively distributed? These are not marginal questions. They go to the heart of how educational institutions organize access to advanced knowledge.
Disruption Is Not Accidental
My own view is that this disruption is not accidental. It is intrinsic to, and one of the most important aspects of, the work. The existing educational structure does not merely sequence knowledge in a neutral way. It regulates access to advanced mathematics through a set of institutional arrangements: age-graded progressions, long prerequisite chains, tracked pathways, selective expectations, and assumptions about who is “ready” for higher-level work. Under these conditions, calculus is not simply taught late; it is socially and institutionally reserved and rationed. It has become a scarce, high-value credential for the few. The issue, for us in the Algebra Project, is not only whether more students can succeed in advanced mathematics. The critical issue is whether the current access structure is educationally necessary or better understood as a historically produced system of privilege.
The Internal Path
That is why I see the two related paths of this work as parts of a single strategy for institutional change. On the one hand, the Algebra Project works within the educational system to introduce accessible calculus. This is the internal path. It seeks to reconstruct the mathematics, the pedagogy, and the curricular sequence so that advanced ideas become broadly teachable and broadly learnable. This path matters because the goal is not simply to criticize schools from the outside. The goal is to transform what schools are able to do. Work inside the system helps create teacher capacity, curricular legitimacy, and institutional uptake. It gives districts and schools a pathway for moving toward a more democratic mathematics education without collapsing into confusion.
The External Path
On the other hand, we are also working on an external path. This path works through organizations outside the school district structure—community organizations, and cultural institutions—to create Advanced Study Academies that offer students direct access to advanced mathematics regardless of where they are in the formal curriculum sequence. This is not an enrichment model. It is the development of community-based parallel institutions as a response to the inertia of our education systems. It is a way of building educational capacity where the formal system has failed to provide it. The academy model says, in effect, that students should not have to wait for institutional permission to encounter powerful mathematics. If the school cannot yet deliver that access, community-based institutions must. In a sense, this is the origin of the Freedom Schools Movement in the Mississippi Civil Rights struggle during the 1960s, and even of the Russian School of Mathematics, a community-based response in the greater Boston area from the late 1990s.
Two Paths, One Strategy
The two paths strengthen one another. The internal path without the external path risks becoming slow, cautious, and endlessly absorbed into institutional delay. Schools can always say that students are not yet ready, that teachers need more time, that standards need adjustment, or that the sequence cannot be disturbed. The external path changes the terms of that conversation. Once students in community-based academies are demonstrably learning advanced mathematics successfully, the institution can no longer hide behind the fiction that such learning is impossible. The burden shifts. The issue becomes not whether students can do the work, but why the system has chosen not to make that work available.
At the same time, the external path by itself is not sufficient. If it remains detached from efforts to transform schools, it may generate islands of excellence without changing the broader structure of exclusion. That is why I believe the most effective strategy here is neither pure reform nor pure disruption. It is best understood as external pressure joined to internal reconstruction. The outside academies generate proof, aspiration, organized demand, and moral challenge. The inside work develops the conceptual and pedagogical means by which schools can eventually respond. One creates leverage; the other creates a viable route for institutional adoption.
Concerns as Design Questions
The concerns this model raises should be taken seriously, but not in a way that blunts the strategy. I see those concerns as pointing to design questions. Students returning to school with advanced knowledge will, in all probability, encounter friction. Teachers may not know how to place them. Schools may interpret their new knowledge as a scheduling problem or a threat to the curricular sequence rather than as evidence of true capacity. There is also the question of legitimacy: will schools recognize what students have learned outside of formal classrooms? And there is the question of scale and equity: how do we ensure that these academies are not available only to a small number of students? These are real issues of design. They are reasons to build the model with enough seriousness that it can cope with both issues of educational power and associated institutional consequences.
Making Disruption Productive
I see the aim of this work as not to avoid disruption, but to make the disruption productive, principled, and strategic. The academies need to do more than accelerate students through content. They need to cultivate greater voice, agency, and identity in the students who move through them. Students should return to school not simply as students who have “seen some extra material,” but as students whose competence challenges the system’s assumptions about who can and should do advanced mathematics. Bob Moses referred to this as an earned insurgency. The academy becomes a social proof that advanced mathematics belongs to everyone, not only to those whom the institution has chosen in advance.
A Historical Tradition
Historically, parallel institutions have often been necessary wherever dominant institutions failed to provide equal access. Freedom schools, citizenship schools, and community-based educational formations did not simply supplement the system. They exposed its failures and created the capacity for broader change to become possible. I believe the Advanced Study Academies should be understood in that tradition. Their role is not to replace schools, but to act as engines of institutional transformation by showing what is possible when access to advanced knowledge is treated as a right rather than a privilege.
Conclusion
This dual approach is the strategy the Algebra Project has adopted: inside schools, reconstructing curriculum, pedagogy, and teacher development around the idea of accessible calculus; outside schools, partnering with organizations to build Advanced Study Academies that directly challenge the gatekeeping structure of conventional mathematics education. The purpose is not disruption for its own sake. The purpose is to disrupt the institutional habits that have made calculus and advanced mathematics into symbols of privilege rather than instruments of literacy. Put plainly, when an institution cannot yet deliver justice, parallel institutions become necessary as engines of change. That, in my thinking, is the proper way to understand the role of Advanced Study Academies in the larger movement for math literacy and greater access to advanced mathematics.