They’re Taking Our Money: Building on the Dialectics of Political and Mathematical Knowledge to Write the World

Abstract

Justice-oriented mathematics aims to support students’ understanding of the relationship between mathematical knowledge and political knowledge to examine how they conspire to shape reality. The notion of the formatting power of mathematics is helpful here in that it calls for an excavation of mathematics that makes explicit the actual use of mathematics hidden in social structures and routines. In this paper, the author examines how a mathematical unit on home mortgages was carried out to support 12th grade students’ understanding of the mathematics of mortgages, revealing the formatting power that mortgage lenders hold in reordering the reality of marginalized communities. Drawing on a qualitative analysis of student journals, student work, post-class student interviews, and teacher/researcher journals, the findings revealed two pedagogical features that contributed to students’ reading and writing the world with mathematics: engaging mathematics from multiple directions and attending to the formatting power of the mathematical and political knowledge dialectic. These findings offer pedagogical guidance for practitioners and teacher educators in curriculum design and implementation of critical mathematics.

1. Introduction

Justice-oriented mathematics scholars have advocated for ways to make mathematics classrooms more just through humanizing pedagogies that include a problem-posing curriculum and dialogic modes of engagement (Frankenstein, 2009; Freire, 1970/1999), centering students’ dignity and humanity (Sengupta-Irving & Vossoughi, 2019) and honoring multiple ways of knowing and being (Warren et al., 2020). Justice-oriented pedagogues position students as knowledgeable, creative, inquisitive, and intellectually capable beings. These commitments and orientations go a long way towards building solidarity with students to imagine and work together towards more equity and justice in our shared world. I use justice-oriented mathematics as an umbrella term that includes Teaching Mathematics for Social Justice (Wager & Stinson, 2012), Critical Mathematics (Skovsmose, 1994), Social Justice Mathematics (Kokka, 2022), and other pedagogical frameworks with a shared purpose and urgency to support our collective agency towards building a peaceful and sustainable future for ourselves and subsequent generations.

Justice-oriented scholarship and practitioner materials for mathematics have expanded greatly in the past 20 years, with the publication of critical and culturally relevant guides (del Rosario Zavala & Aguirre, 2024), curricular task-based resources for PK-20 educators (Bartell et al., 2023; Berry et al., 2020; Conway et al., 2022; Gutstein & Peterson, 2006, 2013; Koestler et al., 2023), edited volumes on Black liberation in mathematics (Martin, 2010; Davis & Jett, 2019), and international handbooks on the ethical role of mathematics in society (Mukhopadhyay & Roth, 2012; Skovsmose & Greer, 2012; Skovsmose, 2023). These resources range from reproducible tasks to philosophical and pragmatic deliberations on the social, racial, cultural, economic, political, and ecological implications of mathematics education at the individual, classroom, and societal levels. Despite this growing interest to interrogate and re-envision the goals and purposes of mathematics education, justice pedagogies continue to remain at the margins (Chen, 2023).

The marginality of justice-oriented mathematics teaching is persistent for many reasons. Scholars have documented the tensions and challenges associated with teaching mathematics about, with, and for social justice (Wager & Stinson, 2012). Challenges include administrative pressure to teach the school-, district-, and state-sanctioned content (Raygoza, 2020); lack of time and guidance on how to create relevant, critical, and conceptually rich tasks (Gregson, 2013; Raygoza, 2020); complexity involved in designing developmentally challenging curriculum generative to students’ particular social realities (Gutstein, 2016; Turner, 2003; Gregson, 2013); and being responsive to students’ expectations of classical mathematical knowledge (Gutiérrez, 2013) and their well-being (Kokka, 2019). Unraveling how mathematics shapes the real world is complex and often requires specialized, technical knowledge, placing a big demand on teachers to do this work, often alone within a field where “abstraction, deduction, and objectification are considered superior to concrete or contextualized forms of reasoning… [and] rote practice and rule-following [overshadow] sensemaking or creativity.” (Chen, 2023, p. 279).

For this analysis, I look to a compelling case of an experienced critical mathematics educator, Eric “Rico” Gutstein, working largely without the pressures of high-stakes testing and with reasonable access to the material and human resources needed to develop a year-long 12th grade mathematics course based on themes reflective of students’ social realities. This class was a full-year instantiation of critical mathematics and differed from a traditional classroom in distinct ways. Most prominent were the topics studied (e.g., voter disenfranchisement) but in other ways it resembled an inquiry-based classroom in that students interrogated topics from a mathematical lens. For my dissertation project (Buenrostro, 2016), I interviewed many of his students 2–4 years after completing the class to understand how this experience of studying generative themes shaped their own worldview and understanding of mathematics as a weapon in the struggle. I found it remarkable but not surprising that the students in the interviews overwhelmingly were able to recall the unit on displacement and, more specifically, their learning about how mortgages and interest-bearing loans disproportionately impact them and their communities. There are powerful reasons why these ideas stuck around for years after taking the class, nothing short of the fact that as one student cogently wrote in one of her class journals, “debt is the magic word in America”. Considering the finding that so many could remember these ideas, more so than other themes studied in the class, my aim is to understand what we can learn from the teacher’s pedagogy and the evolution of their learning during the displacement unit. Gutstein, in previous publications (Gutstein, 2012, 2013, 2016), has written about the displacement unit where he focused on how displacement, as a theme that emerged from the experience of the neighborhood, underscored connected struggles across Black and Latiné communities, theorizing, from the study of his practice, how to “connect and synthesize [Community, Classical, and Critical] knowledge bases…to develop liberatory mathematics education” (Gutstein, 2016, p. 458). While our analyses are related, he does not explore the specific pedagogical features foregrounded in this paper. This analysis builds on his previous work to look a bit more closely into the pedagogical practices he enacted to support students’ learning to read and write the world with mathematics. Specifically, I ask the following questions:

• What trends in focal students’ mathematical and political knowledge emerged from journal entries focused on the mathematics of mortgages?
• What pedagogical features contributed to students’ ability to read and write the world with the mathematics of mortgages?

2. Theoretical Framework

2.1. The Role of Mathematical Knowledge in Society

I situate this analysis from the perspective that mathematics education in classrooms can contribute to our collective ability to interrogate, critique, and transform some of our most urgent socio-political contradictions and problems—from the people’s perspective and those most affected. In their introduction to the edited volume of Applying Critical Mathematics Education, Andersson and Barwell (2021) assert that critical mathematics education (CME) can address pressing, complex issues in society, characterizing it as politically active and engaged. Scholars have long debunked the idea that mathematics is objective and value-free (Frankenstein, 1983). In the real world, mathematics is categorically political in the sense that it “produces new inventions in reality” while simultaneously “colonis[ing] part of reality and reorder[ing] it.” (Skovsmose, 1994, p. 42). With countless examples such as modern computing, economics, military offense, and global markets, just to name a few, mathematics has played a definitive and consequential role in society. The idea that mathematics plays a prominent role in formatting aspects of society is increasing, as can be seen with the popularization of books such as Weapons of Math Destruction: How Big Data Increases Inequality (O’Neill, 2016) and Algorithms of Oppression (Noble, 2018) (Andersson & Barwell, 2021), and a rise in websites and programs dedicated to exploring the relationship between mathematics, democracy, and society (e.g., mathematics-democracy-institute.org, www.citizenmath.com, and www.radicalmath.org). Most recently, the film Count ≠ d Out (Abeles, 2024), a film dedicated to former civil rights and math champion Bob Moses, explores how we might make mathematics more connected to students’ worlds in ways they “can understand the math that undergirds society—and can help shape it?”.

Mathematics is used to describe, predict, and prescribe the world (Borba & Skovsmose, 1997). Numbers can obscure as much as they can describe relationships. Frankenstein (1998) offered the unemployment rate and federal poverty levels as examples that reveal the political struggles embedded within such calculations; who constitutes the labor market, who is considered unemployed (e.g., part-time versus full-time), and what accounts for a living and poverty wage are all politically charged considerations, far from objective. The corresponding assumptions at the heart of these political struggles have material consequences for the allocation of resources, to say the least. Gerrymandering is a powerful example of how mathematical decisions for the delineation of legislative districts are designed to predict and prescribe elections with politics explicitly in mind. Moreover, the current reach of technology in shaping our reality is untenable given the unwieldy and widespread use of algorithmic processes and AI technology in automating much of our social reality. To be clear, mathematics has always played a political role in shaping reality and dictating school-sanctioned mathematics at least as far back as Sputnik. But what is most promising is the notion that we could be at a place in history when the public desire to make mathematics more meaningful and consequential for democracy and critical citizenship could challenge the imperialist goals of mathematics education (Buenrostro et al., 2025). To this end, I highlight below some of the theoretical underpinnings of the relationship between mathematical knowledge and political knowledge to support the pedagogical goals of this shift.

2.2. Dialectical Relationship Between Mathematical and Political Knowledge

The idea of dialectics, an age-old philosophical concept, is a common construct that is central to Freire’s pedagogy (Freire, 1970/1999) and similarly in other critical mathematics scholars’ interpretations of how to support students’ critical consciousness through connecting mathematics and political knowledge (Frankenstein, 2009; Gutstein, 2016). Dialectics is the idea that through exploring and examining opposing viewpoints or ideas and their interactions therein, a more profound truth can be realized (Giroux, 1981). For example, in elaborating a framework for developing a criticalmathematical [sic] numeracy with her students, Frankenstein (1998) distinguished between the mathematics of political knowledge and the politics of mathematical knowledge. Returning to the calculation of the unemployment rate, the mathematics of political knowledge describes how the mathematics (the rate) informs our political knowledge or understanding, in this case, of the state of un/employment in the country. Conversely, the politics of mathematical knowledge can be seen in how political knowledge (the political struggle(s) involved in determining who is counted) informs the mathematics (the rate); depending on who is counted or left out, the rate will represent different phenomena with differential consequences. The fundamental idea here is that by understanding how these two knowledges interact (in potentially complementary and/or contradictory ways), we can apprehend knowledge that “points to the connections between critical knowledge and emancipatory social change” (Frankenstein, 1983, p. 4).

Gutstein (2016) also built on the idea of knowledges in a dialectical relationship, although his conceptualization of reading and writing the world with mathematics (RWWM) laid out “two sets of dialectical relationships associated with RWWM” (p. 457). The first set of relationships points to the relationship between students (or anyone) reading or making sense of the world and how they come to see mathematics as part of reading the world. He theorizes that by using mathematics to study their reality, students learn that mathematics can support their understanding of the world. In turn, reading the world with mathematics can support their critical reading of the world. These two knowledge bases (reading the world and reading the mathematical word) are in a dialectic relationship in that they can support one another, leading to what he coined as reading the world with mathematics. As students become more proficient at using mathematics to read the world in critical ways, they begin to develop sociopolitical awareness which has the potential, then, to support their writing of the world or transform it; this represents the second set of dialectical relationships. Hence, Gutstein asserts “that students develop deeper sociopolitical awareness through learning and using mathematics to study reality, which prepares them to shape society by using mathematics, at the moment and in the future” (p. 457).

In this paper, I draw on the dialectical relationships, as outlined above by Marilyn Frankenstein and Rico Gutstein, to illustrate how Rico’s pedagogy supported students learning to read and write the world with mathematics. Indeed, Gutstein has shared aspects of his pedagogy in several writings and ones specific to this unit but my contribution to this scholarship is examining how students developed a level of consciousness around predatory lending practices from an insider–outsider perspective. I believe the pedagogical insights from this analysis offer specific guidance to practitioners and teacher educators in powerful and specific ways.

3. Methods

3.1. Research Context

In the 2008–2009 academic year, 6 Black (two male; four female) and 15 Latiné (4 male; 11 female) students opted into taking the Math for Social Justice class (herein referred to as the M4SJ class) during their 12th grade year1. The justice-themed high school where the class took place is a small, open enrollment neighborhood high school located in Chicago and drawing from Little Village, the surrounding Mexican/Latiné immigrant community, and the neighboring Black community of North Lawndale—two working-class neighborhoods. The students met with the instructor, Rico Gutstein, the year prior to taking the class to collectively decide on the units of study for this 4th year mathematics (required) elective. The class met four days a week for 50 min each day during which time they examined voter fraud in the 2004 presidential election, neighborhood displacement, the HIV-AIDS pandemic, criminalization of youth, and sexism. The focus of the class was to use mathematics as a disciplinary tool to deepen their understanding of issues plaguing their community. At the conclusion of the class, students put together an 81-page PowerPoint slide deck and presented what they learned in the class to their communities. By foregrounding the orientation to read and write the world with mathematics, this class and students’ work, reflections, and interviews became a formidable source for investigating the development of students’ mathematical and political knowledge.

Also notable about the context are Rico’s and my relationship with the students; the students’ mathematical histories and dispositions, including their prior experiences with studying social justice math; and the political timing of the class. First, Rico and I started working with this group of students during their first year in high school in 2005. Rico and I worked with the mathematics department over the 3 years leading up to the M4SJ class to support their implementation of inquiry-based and justice-focused mathematics lessons and units, at times co-developing justice-based lessons with teachers in response to locally and nationally emergent issues (Gutstein, 2007; Sia & Gutstein, 2007). In addition, beginning two years prior to the start of the M4SJ class, Rico worked with 7 of the students as part of a research crew outside of class where they discussed, analyzed, and reflected on social justice mathematics, presenting at a total of 17 education-focused conferences locally and across the country (Gutstein, 2016). Several of these students became critical peer supports during the M4SJ class. Second, the students’ mathematical identities ranged from enjoying mathematics to experiencing mathematics anxiety, while others could take it or leave it. Several students were interested in both the mathematics and the socio-political focus of the class, while others primarily the latter. All of them knew what the class was going to focus on prior to signing up for the class, given their previous relationship with Rico and experiences with social justice projects; throughout the first 3 years of high school mathematics, students had engaged with upwards of 15 justice-focused units and lessons ranging between one and two weeks. Thirdly, the year was 2008–2009, the year of the U.S. financial crash resulting from an implosion of sub-prime mortgage lending (Agarwal et al., 2014). Other units were timely as well. For example, in the first unit of the year, students investigated whether the 2004 presidential election was stolen precisely during the months (September–November 2008) leading up to the historical election of the nation’s first African American president, Barack Obama. These points are significant because they point to the trustworthy relationships Rico had with a critical mass of the M4SJ students, their familiarity with connecting mathematics and social justice, and the personal and political relevance of voter fraud and interest-bearing lending practices as new voters and future loan consumers, respectively. One last note on engagement is that the students’ personal and family lives at times interfered with the students’ ability to prioritize school and learning. These are real conditions in which our children live and breathe, and we need to take seriously how their lived experiences need to inform our pedagogy and moment-to-moment engagement. This is not to extend pity but rather to double down on the urgency to make school relevant and to support young people in their agency to effect change.

3.2. Researcher Positionality

I was part of the struggle to found the school from which this study is situated. I am a second-generation Mexican cis-gender female who, at the time of the study, had spent 15 years as a community resident (7 years as a young child and 8 years post-college). In 2001, I, alongside community members, fought for the school to be built and was part of the community planning process that brought Black and Latiné community members together, with a complex and protracted history of alliances and tensions. Our efforts were intentional with regard to bridging the two communities as they made up the school demographics (70% Latiné and 30% African American). I began graduate school the year the high school opened its doors (2005) and continued my work there at the high school as a community volunteer, teacher–scholar–activist, and educational consultant. I frequented the high school wearing many different hats, from organizing a student delegation to New Orleans in 2007 in support of local rebuilding efforts, to consulting with one of the schools on alternative, outcome-based assessment practices. I was part of a collective, grassroots effort with many friends, family members, and colleagues committed to seeing the success of the high school campus. More specific to this analysis, I worked with the school’s math department in supporting their efforts to implement the Interactive Mathematics Program (IMP; Fendel et al., 1999) and collaborated with Rico Gutstein to support a critical mathematics agenda interspersing justice-focused mathematics projects across the first four years of the high school (2005–2009). I became a regular in the mathematics classrooms and the school in general across the first 3 years and in the 4th year, I attended the M4SJ class twice per week from September through mid-April as a participant-observer. My work with the administration and teachers across these four years was complex, with disagreements on policies at times, and celebratory at other times. My son attended the school and graduated in 2014. I was a parent on the local school governing council from 2010 to 2012. I was and am deeply committed to seeing the high school and community thrive.

3.3. Data Sources and Analysis

Primary data sources for this analysis were student journals, teacher and researcher journals, a video transcript from one class (6 January 2009), post-class interviews, and classroom activity handouts for the focal unit. I began with the open and focused coding of two student journals specific to the mortgages portion of the Displacement unit (Journals #10 and #12) using MAXQDA qualitative software (version 24.0) to identify major themes that came out of students’ reflections specific to my goals to examine their mathematical and political knowledge as well as other emerging patterns. Of the 21 students, I had in my possession and drew on 12 student journals #10 and 13 student journals #12; within this corpus, there were 10 cases of having both journals #10 and #12 from the same student. These journals were my primary source of data for this analysis and the source for all student quotes unless otherwise indicated. I drew on the remaining data sources to support claims about student dispositions and classroom culture. I engaged in an iterative process of constant comparative analysis (Creswell & Poth, 2016) between the emergent codes and patterns and other data sources to examine how students came to read and write the world with mathematics. In making claims about patterns, I looked across all the data for confirming and disconfirming evidence to ascertain the validity of my claims.

3.4. Focal Unit Description: Displacement

The Displacement unit was designed to have students understand the external political forces that were greatly responsible for displacement in the Black and Latiné communities: gentrification in the Black community, foreclosures in both communities, and immigration and deportation in the Latiné community. The teacher’s overarching goal was for students to understand how land grabs, predatory lending practices, and cheap and disposable transnational labor markets were part of a global and racial capitalist structure that impacted their lives directly (Gutstein, 2013). In the first five weeks of the unit, students engaged with the following main activities and ideas:

• Previewed gentrification through readings and personal testimonies;
• Shared family migration stories;
• Examined neighborhood changes in and inter-relationships between median family incomes (MFI) and median housing values (MHV) over a 30-year period;
• Predicted future values intuitively (student-generated) and mathematically (linear regression) for MFI and MHV as well as examining rising rates of foreclosures;
• Modeled rate scenarios with difference equations and discrete dynamical systems by hand and on the graphing calculator.

3.4.1. Building Towards the Notion of (Un)Affordability

During the 4 days of class leading up to the focal Journal #10, students created difference equations and discrete dynamical systems2 to model simple scenarios first (savings deposits with and without withdrawal), scaffolding up to the mathematics of mortgages. The class collectively determined that the average income earning family in each of their respective communities could not afford the median priced home without experiencing hardship3. The template mortgage they used to determine affordability was a USD 150,000 30-year mortgage at a 6% yearly interest rate.

The class, with teacher facilitation, collectively worked through these problems, with individual students going up to the projector to present different problems throughout the week. Students visually went through the 360 payments of the template 30-year mortgage on the graphing calculator and saw that (1) the initial payment on the loan disproportionately went to interest over reducing the balance (USD 750 compared to USD 58), and (2) after 30 years of payments at the amount a Little Village family could afford (USD 808), they would have paid a total of USD 291,000, with a remaining outstanding balance of USD 92,000. Rico wrote the following equation on the board, representing this real-world relationship: 150,000 − 291,000 = 92,000. He then asked students to “check out that math”, to which students asserted that the bank was taking your money and questioned the legality of this exploitative set up. Students asked “Why is this legal? Aren’t there organizations that can help students?”. “This is capitalism”, Rico asserted, “this is how banks make their money”.

3.4.2. Re-Presenting the Political Knowledge with Mathematics

Two days later, Rico put the same equation on the board [$150,000 − $291,000 = $92,000] and asked students to articulate the meaning of the equation in context, to which students responded that it represented the original loan minus the amount paid over 30 years, equaling the amount still owed. He went on to explain how the capitalist system enables the wealthy to use their money to make more wealth. He then wrote the following equation on the board [1 − 6 = 4]4 and explained that ‘1’ represents the original loan amount (proportionally) borrowed by the Global South from the World Bank, ‘6’ represents the amount they have since paid back, and ‘4’ represents the amount still owed. After explaining what these numbers represented, Rico told students they would come back to the equation, which he asked students to reflect on in Journal #10. I refer to both equations as equations of exploitation.

For the remainder of the class, students returned to completing two things: one, if the median income earning family could clearly not afford the template loan of USD 150,000 at 6% rate over 30 years, what income is required; and two, given the median income that did exist in their neighborhoods, what mortgage could families afford? It is important to note here that Rico asked students to approach the template mortgage from multiple perspectives. For example, for the template mortgage, students figured out three things: (1) paying what is affordable for the median income earner in Little Village would result in paying USD 291,000 over 30 years and still owing USD 92,000, (2) the income one would have to earn to pay off the mortgage in 30 years without hardship, and (3) the affordable mortgage amount for the median income earning family in each of their communities. Some of this work spilled into the following week but I offer this context to illustrate how students were working with a graphing calculator model of the template mortgage and interpreting different variables from the varying case scenarios (what should they earn to pay off the template mortgage, what can they afford given what they earn, etc.). The mathematical knowledge they were building was complex and cognitively demanding and students could not complete it without making sense of it in context.

4. Findings

4.1. Mathematical Knowledge and Political Knowledge (Journal #10)

In Journal #10 (Figure 1), students were asked to reflect on their learning (Q1): what were they learning, was it useful, was it a good week or not. Then students were given the two equations of exploitation as a point of reflection (Q2) and asked to share the meaning and their thoughts of them. I share below their responses with respect to mathematical knowledge, political knowledge, and the dialectical relationship across both questions where applicable.

4.1.1. Mathematical Knowledge (Journal 10, Q1)

Students spoke about the mathematics they were learning from a conceptual and interpretive standpoint, meaning that students were able to make sense of what they were learning in context. They were learning, for example, “how to do the math of getting the interest and the principal over whatever year loan”, as Renee5 remarked. Most students articulated some version of this idea; Jenny believed she could now “find out how many months it will take to pay off your debt [and] how to find the payment for a mortgage of USD 150,000” and Greg could determine “how much interest you will pay over a long period of time.” Students could name the things they were learning with respect to what it meant in the real world, connecting the mathematical terms and equations to real world tangibles.

4.1.2. Political Knowledge (Journal 10, Q1)

Students connected the learning largely from a utilitarian perspective and less so connected to their communities and the structure of capitalism. Students found it productive knowledge for their future selves as potential homeowners, credit card borrowers, and consumers of college student loans. Greg remarked, “I’m glad I learned this because it will help me in the future” and Renee expressed, “Everything we have done in class is very helpful [because] the people in this class are going to grow up and buy a house one day”. Three of the 12 participants articulated a direct connection between the unaffordable payments to foreclosures and debt, particularly for “people of color”, but these were more the exception than the overall pattern. For example, Antoine, an integral member of the crew, articulated in specific terms the connection between capitalist relations and people losing their homes. He connected the specific amount of interest that is frontloaded on a mortgage payment schedule (USD 750 out of USD 808) to show how the banking relationship is both exploitative and disproportionately impacts working-class families (i.e., income to housing payment ratio), noting this as a direct effect of capitalism on families. However, a majority of students (9 out of 12) characterized their learning about the mathematics in relation to loan terms with little articulation to the impact on families.

4.1.3. Capitalism and the Mathematics of Political Knowledge (Journal 10, Q2)

Although a few students mentioned capitalism in Q1, they did so without explicitly describing how the mathematics formats political relationships (i.e., low-income families making unaffordable payments that then cause hardship). However, in Q2, students consistently articulated the connection between the mathematics (USD 150,000 − USD 291,000 = USD 92,000 and 1 − 6 = 4) and the exploitative relationship between lenders and borrowers (the political knowledge). Students linked the equations to profit, lack of affordability, and exploitation in specific terms. This is significant because it supported students’ thinking and reflecting about the politics of mathematical knowledge and the dialectic between mathematical and political knowledge. Students were able to see the mathematization of profitability both at the local and global level and make connections among them. Their responses were clear, emotive, and indignant. Students described these equations as demonstrating how people were being “scammed” and “screwed over” and having to pay multiple times the amount of the original loan. On a personal note, I too remember feeling scammed after signing the paperwork on my own home and seeing that I would pay close to three times the original amount. Students were able to see these relationships visually in the equations of exploitation and connect the impact on their families and communities. Their responses included “the bank makes money off of us” (Gema); “the interest made you pay way more than you was supposed to” (Greg); “the banks profit from using other people’s money” (Minerva); and “these two equations show how capitalism is in the form of math” (Antoine). Tuan conclusively described the political relationship as “certain places say they help others but are actually oppressing them”.

Asking students to reflect and connect how capitalism worked at extreme scales (local and global) helped consolidate for students the political (exploitative) relationship that is formatted between lenders and borrowers. By abstracting the political relationship to ‘simpler’ mathematical terms, the dialectic relationship was consolidated. That is, unpacking the mathematics of mortgages helped inform students’ understanding of family debt and its often-dire consequences. Reflecting on these two equations drove home the exploitative relationships embedded in the lender–borrower relationship and students called it out for what it was: “this is a bunch of bull because there is too much money in the world for people to be having to pay this much” (Carleton) and “this is extremely wrong because America should be a country that helps the poor not the rich” (Monica). Up to this point, students had been working on understanding the mathematics to explain the political configurations. Significantly, in Q2, the representation of the political configurations (1 − 6 = 4) informed the mathematical relationship (the idea that you pay back more than you borrowed and still owe). It should be overstated that this abstraction of the political relations coupled with the objectification in simple, yet powerful mathematical terms supported students’ articulation of the formatting power of the lender–borrower relation. This is the dialectic.

4.2. Towards Reading and Writing the World (Journal #12)

About two weeks after the Journal #10 submission, Rico journaled his reflections from the day. Below is an excerpt:

“I then raised the question of our community presentations…what should we do, how should we do them, etc. Do we have knowledge that we should share with the communities?… People raised a lot of question and there was an interesting discussion of whether or not people would (a) listen to youth, (b) come out if we did not have answers. The discussion (and there was not unanimity) was centered around what was the value of a public presentation. Did we have knowledge that we needed to share. That made it clear to me that I have done an inadequate job in teaching about sub-prime mortgages and what they are/mean and predatory lending, etc. So I need to do this…”

In the days leading up to this day’s session, students continued working on answering different mortgage related questions; they continued working on the mortgage amount both communities could afford, exploring how interest payments change over the life of a mortgage, and collectively finding a closed solution to the recursive equation. Hence, despite students making these strong causal ties between the mathematics of mortgages and families not being able to afford them, they were not convinced that they had anything to share. As evidenced in the above journal reflection, Rico decided students needed to explore sub-prime mortgages (which they had not explored at this point beyond some article readings early on) and he created, with a co-researcher, a Displacement-Gentrification Project, given to students a week later. In this project, students were asked to create three different scenarios with (1) an adjustable-rate mortgage; (2) a pay-option mortgage, where some payments create negative amortization; and (3) a balloon mortgage. Students were given three days of class time to work through these different scenarios with the support of their peers and teacher. After turning in their projects, Rico gave them Journal #12 (Figure 2).6

4.2.1. Towards Writing the World (Journal 12, Part I)

After turning in the Displacement-Gentrification Project, students were more adamant and confident that they needed to and could share their learning with their communities. In their Journal #12 (Figure 2), students were asked to read a New York Times article entitled A Bid to Link Arms Against Eviction (Santos, 2009), that was printed the week prior. The article tells the stories of families across different U.S. cities who had lost their homes due to sub-prime mortgage loans and were finding forms of support among each other, from community organizations, and even Sheriff’s refusing to evict homeowners.

Students were upset and devastated to read about families losing their homes, particularly because they were described as hard-working families who were being taken advantage of because they did not understand the terms of the mortgages they had signed on to. Students used words like upsetting, unfair, devastating, and sad. Students had just developed different scenarios of sub-prime mortgages in their project similar to what the families in the article had been subjected to, and they expressed familiarity with the terminology. In this way, they were able to connect their understanding of sub-prime mortgages to what they were reading, and they noted this. Students displayed compassion and anger in reading stories of hard-working families losing their homes and being exploited by banks due to a lack of information. These stories spoke of real people, stories and losses that cannot be told through numbers. Not all things are quantifiable, and this is an important part of the learning. Students spoke to the resistance described in the story and the agency of those exploited—resistance through the formation of human walls and support by community agencies and law enforcement trying to help.

Students made the obvious connections in the article with what they were learning in class: balloon and adjustable-rate mortgages, impact of lack of information, and ways to fight back. In three of the responses, students made connections with how families and communities can resist and fight these unfair lending practices, of which two of them related it to how they, as a class, wanted to support their families and communities through the sharing of information. Although most of the responses reflected direct connections with what they were learning about the mathematics of mortgages and the exploitation embedded, reading the world in critical ways is a precursor to being able to write (transform) the world (Gutstein, 2016).

It bears noting that in my post-class interviews, all of the students remembered this idea of exploitative lending practices and the role of interest more than any other concept in the class. Gema and Antoine even recalled, respectively, how they used their calculator programs from the class to later determine the best mortgage plan for their in-laws and break down the payments for their own payday loan. Others, like Vanessa, Calvin, and Ann, shared with me how they made strong efforts to either stay away from taking school loans or paying as much as possible upfront and in a timely manner to avoid collecting insurmountable interest (Buenrostro, 2016).

4.2.2. Learning to Do Important Math Together (Journal 12, Part II)

Across the responses, students noted at least two ways they felt supported in their learning. First, many students described engaging with the difference equations as initially challenging but their peers were a critical support, naming specific peers that were key in helping them understand the mathematics. Interestingly, several students characterized the entire class’s engagement and learning as evident: “I think everyone was engaged in this learning process” (Carleton); “a good portion [of the class] was struggling but towards the end most of the people got the idea” (Tuan); “this was good [and] I think that people really understand the math” (Antoine). This idea that students are conscientious about not only their understanding but also the learning of the collective is a testament to the culture built in the class (see Balasubramanian, 2012 for more detail).

A second important aspect of how some students were able to engage with challenging mathematics was the nature of the task. That is, students could see the mathematics through the difference equations and connect the dollar amounts to how and why foreclosures were happening in their communities. They felt empowered to learn about a real-to-my-life issue (Buenrostro & Radinsky, 2019) that could potentially impact them in the future. Jenny, a student who self-identified as weak in mathematics and often expressed her struggles with mathematics historically, shared in Journal #10 how learning about the mortgage math was a “turn around week for [her].”.

“I think that I have been more engaged in the work we’ve been doing in class because I understand it more. The subject that we’re studying is more visible and easier to understand both mathematically and socially.”

Tuan, a quiet student who was relatively strong mathematically, described this math as “math you can relate to”. For him, learning relatable math “makes it harder to forget as you are able to relate to the type of math being done”.

5. Pedagogical Features

I return to my research questions: (RQ1) What trends in focal students’ mathematical and political knowledge emerged from journal entries focused on the mathematics of mortgages? (RQ2) What pedagogical features contributed to students’ ability to read and write the world with the mathematics of mortgages?

Regarding RQ1, demonstrating the formatting power of the mortgage mathematics with the equations USD 150,000 − USD 291,000 = USD 92,000 and 1 − 6 = 4 was key for students to be able to consolidate and objectify their understanding of how mortgage calculations disadvantage low-income and working-class people. That is, families in their communities are more likely to experience hardship given their low and modest incomes. Frankenstein (1983) asserted Freire’s insistence that “‘generative themes’ should be organized and ‘re-presented’ dialectically so that the links between them…their historical context, [and] their relationship to the community” (p. 6) should be made clear. I take the equations of exploitation to re-present such a clarification, characterizing the political relationship formatted through the mathematics of mortgages and in relationship to their families and communities. The ability of the students to connect the equations of exploitation to how banks exploit those in need of a mortgage loan (i.e., certainly most if not all working class families) is evidence of their understanding of the formatting power of mortgage mathematics.

Regarding RQ2, students engaged deeply with the mathematics and from multiple angles, working with real data to determine if they could stay in their neighborhood. Building on the template mortgage case, students approached different questions: Can our families afford this mortgage? If not, what mortgage can our families afford? If the template mortgage case is the going rate, who can afford it? These are all related but different mathematical problems that are not formulaic and require students to make sense of the mathematics in context. One might compare this to the rule of four: the ability to express a mathematical relationship in four different ways—with words, a graph, a table of values, and an equation. Specifically, students need multiple and varied experiences to derive tables from equations, graphs from tables, equations from problem scenarios, and so on. Students’ experiences with manipulating the different terms of the template mortgage case are analogous to this idea, only more complex in having to work with difference equations. The pedagogical practice of approaching concepts, skills, and knowledge from multiple directions engages students with the mathematics that supports flexible and deeper understanding.

Moreover, students’ articulation of the inequity embedded in the lender–borrower relationship was insufficient for them to think they had something to share with their community. Students did not yet feel confident in the mathematics, even if they understood the implications for their communities. The ensuing class discussion after Journal #10 prompted Rico to create a project where they had to create different kinds of sub-prime mortgages—mortgages more complex than the template case. This creation is an important feature of developing mathematical knowledge; it proved challenging but doable for students. Creating space and time for students to work through the mathematics was critical for them to own the knowledge enough to feel confident to share with their communities. This work takes time and faith that students are capable of making sense of their world, even and especially if it involves mathematics.

Finally, the way the class functioned as a unit (on many days) was well under way by the time they began studying displacement; students wrote about this in their journals and raised it in the post-class interviews (Balasubramanian, 2012; Buenrostro, 2016). Working collectively to support one another’s understanding was part of co-constructing the classroom learning space. Rico was intentional about establishing this co-construction through collectivity in class learning and decision-making—when students spoke, he consistently asked them to speak to one another (Balasubramanian, 2012). Members of the research crew served as key peer supports in the class and the political implications of the mathematics of mortgages for their future and that of their families and community also contributed to students’ commitment to push through the intellectual challenge. This is not to say that the teacher did not struggle with learned helplessness, students’ life issues interfering with attendance, in-class engagement, and homework completion rates but Rico relied heavily on his relationships with students and the importance of the topic to re-engage them throughout the class when he felt students falling to the wayside. There were not carrots and sticks involved here, just straight talk, supporting students through tutoring and classroom supports, and being compassionate, but not letting up on their responsibilities to do the work.

6. Limitations and Future Research

Some of the limitations of this study are in the data itself. Notably, there were eight to nine student responses missing from each of the two primary sources (Journals #10 and #12). Notwithstanding, as a participant-observer in the class, the findings are representative of the larger class identities in that the data set contained those who identified strongly with either mathematics, social justice, or both. While the critical mathematics curriculum should constitute topics particular to students’ lived experiences, the following pedagogical features can be translated to other contexts: engaging topics, concepts, and issues from varied and multiple perspectives and finding ways to express reality in multiple forms, even if some of the forms are contrary to conventional structure, as was the case with 1 − 6 = 4. Notably, this class of students went to a social justice-themed high school and participated in a class with an instructor they knew and with whom they had developed political trust (Vakil & de Royston, 2019) over three years leading up to the start of the class. The trust they built over time should not go understated, as this afforded Rico with certain liberties such as starting from day one with the content and context of the topics, raising and discussing difficult topics, and bringing students’ personal testimonies into the classroom, with their permission, of course. He had worked with the research crew who, based on journal responses, played a key part in supporting the collective learning in the class. This is not to say that others cannot recreate similar conditions in other spaces, but trust and credibility are likely to be pre-requisites for undertaking this kind of work; Rico had supported all their previous experiences with social justice math.

Future research can support the field of critical mathematics education to develop the tools needed for teachers and students alike to interrogate and expose the mathematical underpinnings of unjust social, political, and economic relations. In my experience as a secondary mathematics teacher and mathematics teacher educator, there are many challenges and obstacles facing teachers and students. To begin, carrying out such a paradigm shift seems far-reaching given the positivist stronghold mathematics in schools and in the public narrative has had on our imagination of what is both possible and needed. I believe starting with this goal of understanding how teachers might begin to envision a liberatory mathematics education is one productive starting point.

7. Conclusions

A significant part of reading and writing the world with mathematics entails understanding the way mathematics formats our world in significant ways despite the hidden nature of this formatting in plain view. In this analysis, I underscored aspects of Rico Gutstein’s pedagogy that supported students’ engagement with the formatting power of mortgage mathematics in ways that students retained years after leaving the class, more so than other concepts or ideas. This is not completely surprising given that the notion of interest-bearing relationships is both a curiosity for young adults (how do these things even work?) and a likely future scenario given that the average American household debt hovers a bit over USD 100,000 (Streaks & Kane, 2025). Hence, even though they studied mortgages as 17- and 18-year-olds, interest and debt is a pervasive societal construct that they could connect to their current (family and community) and future self. I am not advocating for a kind of financial literacy in the individualized sense but rather a critical numeracy that engages the formatting power of mathematics and exposes the atrocities of capitalism towards marginalized and, quite frankly, all communities.