Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.

—Simone Weil[1]

Writing in the 1930s, Simone Weil’s words presaged the growing alienation that would unfold as a consequence of advancing capitalism and its disregard for the dignity of our humanity. During the last four decades, the regime of neoliberalism has taken center stage in its political economic efforts to prevent the full democratization of society. Through a long-standing belief in the power of absolute measurement, the knowledge realm of mathematics has been, indeed, systematically privileged, as well as colonized as the handmaiden of capital, in the quest to produce a reified world view of binaries and standardizations that work to obstruct the majority of citizens from comprehending, let alone participating within, the structures of power that determine our lives.

Through the process of hegemonic schooling, citizens are individualized and depoliticized, effectively stripped of imagination and curiosity, as they are ushered into the world as technicians of the wealthy and powerful. Traditional mathematics education has been informed by a pedagogy blinded by an ever-narrowing rationality and approach transfixed by the myths of fixed and isolated abstractions. The monstrous ideology of neoliberalism, intent on absolute domination of power and wealth by a few, has declared itself victorious at the expense of our embodied and messy human existence—the same messy human existence from which genuine democratic life must emerge. In essence, the banking approach to education[2] prevalent in mathematics education is the perfect cover-up, in that it not only despises human messiness as irrational, it also blames those who are unable to penetrate the realm of mathematics for their own failure. Hence, the fundamentally unjust values of meritocracy, so endemic to the current neoliberal ethos of schooling, are reproduced, as inequalities are justified and perpetuated.

Reconceptualizing Mathematics Education

Insofar as mathematics is about reality, it is not certain, and insofar as it is certain, it is not about reality.

                                                                                                              —Albert Einstein[3]

Albert Einstein, the consummate scientist of the twentieth century, was more apt than his colleagues of the time to question the absolute nature of mathematics, calling into question the certainty of its relationship to reality. This, of course, did not mean that Einstein did not possess a deep respect for mathematics, but rather than he seemed to comprehend that mathematics, stripped of experience and human life, could not in itself inform our understanding of the world. He recognized that mathematics, like language, is a product of the human mind, expressed as symbols that are created to represent life but are not life. It is a bit like seeing oneself in the mirror. The glass reflects an image of ourselves but in no way is that image the embodied us. Hence, any desire to engage mathematics education critically must begin within the realm of lived experience—the lived experiences of the teacher and the students. Only through such an examination is it possible to not only understand mathematics in a way where power is implicated and social inequalities exposed, but also to consider how critical mathematics education itself can serve as a possible space for the teaching and living of democratic life.

With this in mind, Mathematics Education for Critical Citizenship is an excellent example of the ways that our lived experience can serve as a powerful impetus and strategy for the construction of mathematics knowledge through naming the world, both as an individual researcher and as a collective participant with students/participants, without whom we could not genuinely come to know or appreciate our practice. As such, this volume provides a glimpse into an excellent pedagogical study, where both the author’s life as a critical educator-researcher and his mathematics classroom are utilized as critical sites of inquiry. Through this interrogation, the meaning of citizenship is explored within an educational context where such questions are typically ignored, let alone given primacy.

By so doing, Bülent Avcı centers his study on a few central questions, which focus on the attainability of critical pedagogical practice within the constraints of neoliberal educational conditions, which are essentially in direct contradiction to his larger emancipatory vision of mathematics education. Here, the underlying purpose of the standardization movement’s so-called reform efforts are unveiled, as Avcı critiques the imposition of a one-size-fits-all approach that drives mathematics educational practices. At the heart of this deeply unjust and decontextualized neoliberal strategy is a conservative political drive to destabilize and undo the very meaning and practice of public education and undermine the right to education for all children. Hence, an education that was once (at least in theory) meant to encompass the liberal democratic ideal of citizenship and civic participation has been replaced by an authoritarian top-down tenet, where, by producing efficient and obedient workers, schools can function as economic engines for the nation. Accordingly, public school teachers have been converted into technicians who are expected to enact “best practices” tied to an “evidence-based” or scientific preset curriculum and time frame, indifferent to the lived histories and contemporary conditions faced by students, particularly students from working-class and racialized communities.

Avcı carefully explores the instrumentalizing restrictions imposed by neoliberal policies and their impact on the teaching of mathematics, in the hopes of articulating key dimensions related to his efforts to bring a critical mathematics education praxis to fruition, even within an educational context where the teacher must contend with the limit-situations, as Freire[4] would say, and create counterhegemonic possibilities within an arena of hegemonic schooling. Toward this end, Avcı’s reconceptualization of critical mathematics education, which emerges directly from his critical participatory engagement with students, offers an outstanding contribution to the literature in the field—a literature that has been steadily expanding over the last two decades.

Through the use of participatory nongraded activities, student-generated exams, and a critical mathematics literacy approach, students find classroom space to find their voices, create the conditions for their democratic participation, and build solidarity as they collaborate and learn together. By doing so in a pedagogically conscientious and consistent manner, teacher and students work as revolutionary partners[5] to challenge neoliberal classroom policies and practices rooted in competition, individuality, and instrumentalization, as they transform together the learning environment in the moment. This critical approach also offers students a powerful opportunity to experience embodied democratic participation in ways that not only enhance their understanding of mathematics within the classroom, but also out in their own world. Just as Avcı’s students experienced greater opportunities to learn with one another when engaged through a critical mathematics literacy approach, so too was Avcı as their teacher transformed by the teaching-learning relationship with his students, as together they entered in a critical praxis that dialectically helped to shatter the school/world divide generally conserved by hegemonic schooling. Of this he asserts, “While improving their content knowledge, the students related their learning to a larger society and developed a bottom-up response to neoliberal educational changes. The project helped the students and me to engage in a structural analysis of neoliberal educational policies and implementations. In doing do, we developed and exercised critical mathematical literacy”

In reading Mathematics Education for Critical Citizenship, what is illustrated repeatedly is that the only effective manner to counter neoliberalism’s mania with scientifically packaged curriculum and teacher accountability within the classroom is an unwavering commitment to a critical praxis. However, this requires that teachers engage critically and thoughtfully the conditions within schools, the lives of their students, and the larger social, political, and economic context that informs our lives. In this sense, a critical mathematics approach requires teachers who are prepared to counter the perverted market logic of neoliberalism, steeped in the language of school choice, high-stakes meritocracy, and student surveillance. Hence, critical mathematics as reconceived by Avcı in his study functions as a bottom-up response to the hegemonic conditions produced by the greed and indifference of neoliberal reform.

Certain important key points are made that point to the teacher’s knowledge and the sensibilities that must encompass a critical praxis. The teacher, for example, must have an understanding of class consciousness and how schools reproduce class formation through traditional forms of mathematics education and the instrumentalization and fracturing of the math curriculum. In contrast, a teacher utilizing a critical mathematics approach places dialogue at the heart of the teacher’s engagement with students. This means that the teacher does not expect students to abandon their lived experiences or who they are in the classroom, but rather sees these as sources of strength and significant foundations from which students enter into the process of critically learning mathematics, as well as their coming to understand the emancipatory potential of mathematics in the world. With all this in mind, teachers of critical mathematics, who are intent on challenging neoliberal practices in the classroom, must bring an emancipatory understanding of culture politics, economics, history, knowledge construction, ideology, critique, dialogue, and conscientization, as well as their excellent knowledge of mathematics.

Avcı’s research methodology is worthy of greater consideration and replication, given his uncompromising emphasis on finding or creating spaces within a neoliberal mathematics classroom for critical engagement between teacher and students. His methodology is, indeed, consistent with a critical pedagogical approach to mathematics education in that the themes of his inquiry were anchored in his students’ life-world; the inquiry process welcomed ideas that might be considered unpopular within the mainstream curriculum; the participatory approach was facilitated with the students in order to enable their critical engagement and participation; and the process of reflection and self-evaluation was an effective alternative to traditional banking education. Most importantly, the participatory approach supported the evolution of the mathematics classroom as a genuine community, where relationships were based on horizontal dynamics, cooperation, collaboration, and mutual respect—all key critical principles of democratic communities.

Making the Pedagogical More Political

As critical teachers working in schools, we can make the pedagogical more political….One approach might be to organize a radical pedagogy of citizenship around a theory of critical literacy.

                                                                                                              —Henry Giroux[6]

In Schooling and the Struggle for Public Life, Giroux posits important challenges related to the importance of teachers using their knowledge and insights to thoughtfully redefine the terrain of politics and citizenship within the classroom, as also part of a wider collective struggle out in the world. The sense of teachers making the pedagogical more political and organizing their pedagogy around issues of citizenship and critical literacy is at the heart of Bülent Avcı’s study, where he rightly connects his own critical mathematics praxis to issues of citizenship. Democracy here is directly linked to important pedagogical and political questions about dialogue, citizenship, mathematics literacy, neoliberal ideology, political discourses, and students’ development of critical thought.

Drawing on the writings of Freire and Habermas, Avcı asserts the power of critical citizenship to create spaces for individuals and communities to participate in decisions related to their own lives, despite neoliberal constrictions, through forms of political activism that are informed by a public pedagogy. Here, space is created for dialogue, where there is commitment to remain at the table, despite differences and struggles that may ensue. Critical citizenship also requires civic courage to speak the unspeakable and to listen to what might seem the unlistenable, in an effort to create common ground for work together. At the center of the practice of democratic citizenship must be both a healthy skepticism in order to critically question commonsensical notions, as well as working together to translate our common knowledge into social action for transformation. This also points to the manner in which critical literacy can assist teachers and students discern the changes that occur within the social, economic, and political landscape, so that we can respond together more clearly to the conditions we face within schools and communities.

Throughout this excellent book, Avcı provides well-researched and well-written discussions and conclusions that counter the helplessness often experienced by teachers who feel trapped in the colonizing politics and practice of neoliberal life in schools. This can be particularly the case with mathematics education, given its conservative foundational epistemology. Nevertheless, what is heartwarming and encouraging is the manner in which critical mathematics education, when implemented through praxis of reflection, dialogue, and action, resulted in the promotion of critical citizenship and expressions of democratic life within the classroom that encouraged students to embrace democratic values in their relationships within the classroom and beyond.

Avcı provides a powerful conclusion to this study—the first to undertake a participatory critical inquiry that so eloquently connects mathematics education to the struggle for democracy and critical citizenship. Underlying this excellent treatise are critical moral questions related to our responsibility as educators to genuinely make the pedagogical more political if we are indeed committed to a future where mathematics education is no longer the tyrannical boogeyman used to sort and sift away working-class and racialized populations from opportunities within schools and society. Through his study, Bülent Avcı carves a path toward a living mathematics for democracy—a critical mathematics approach fully committed to the making of critical citizens with the knowledge and skills to both participate in and transform their world.

[1] From “The Power of Words” in Siân Miles (2000), Simone Weil: An Anthology (p. 223).
[2] Freire, P. (1971). Pedagogy of the Oppressed. New York: Seabury Press.
[3] Einstein, A. (1922). “Geometry and Experience.” Speech delivered to the Prussian Academy of Sciences in Berlin and published by Methuen & Co. Ltd. London, UK. Retrieved from: http://www-history.mcs.st-andrews.ac.uk/Extras/Einstein_geometry.html
[4] Freire, P. (2000). Pedagogy of the oppressed. New York: Continuum.
[5] Freire, P. (2000). Pedagogy of the oppressed. New York: Continuum.
[6] Giroux, H. (2005). Schooling and the Struggle for Public Life. Boulder, CO: Paradigm Press.

Reviewer: 

Dr. Bülent Avcı is a public educator in Washington State in the U.S. His research interests include equity and justice in math education, democracy and math education, and the dialogic teaching of math to counter neoliberal hegemony. He is the founding member of Critical Education Network (CEN). He publishes research articles in academic journals and is the author of the book Critical Mathematics Education: Can Democratic Education Survive under Neoliberal Regime? He can be reached at bavci@fwps.org and mjura41@hotmail.com

To cite this book review: 

Bulent, B. (2022). Freire and Mathematics Education [Reading and Writing the World with Mathematics, by E. Gutstein]. Rethinking Critical Pedagogy, p.36-40

Freire and Mathematics Education

This is one of the few books in the literature of critical mathematics education (CME), a new but growing domain of study. The book is based on Eric Gutstein’s classroom teaching experience in a low-income middle school in Chicago, where most of the students were Latino. Gutstein states that his research methodology was practitioner-action research as framed by Anderson, Herr, and Nihlen (1994). While the book under review makes no connection with the research methodology of Paulo Freire, Gutstein does nevertheless draw on other aspects of Freire’s thought. Indeed, the main theme of the book is teaching mathematics for social justice.

There are eight chapters. The first two encapsulate the research and theoretical framework for teaching math for social justice. The others draw on student journals, teacher-student conversations, and classroom observations to show how teaching mathematics can develop a sense of agency and sociopolitical consciousness.

For Gutstein, the larger sociopolitical context is the U.S., specifically, an unjust society that produces a number of injustices in education. The root causes of these injustices are racial inequality and race-based discrimination. In other words, the prime unit of analysis in this book is racial and ethnic discrimination in education.

The book is critical of the National Council of Teaching Mathematics (NCTM). Gutstein argues that the NCTM’s approach to justice and equity is superficial, limited to merely having access to quality mathematics education. The NCTM fails to distinguish between functional and critical literacy, and thereby fails to connect the equity question in math education to the larger society. Gutstein argues that critical mathematics literacy is key to developing a sense of agency and sociopolitical consciousness.

In Gutstein’s view, American society is divided into two parts: whites, who are privileged (the oppressors), and non-whites (people of color such as Latinos), who are unprivileged (the oppressed). He argues math education emphasizing critical literacy can provide students the opportunity to develop a sense of agency and consciousness oriented toward justice and emancipation.

The book is a welcome addition to the CME literature. However, it raises a number of serious issues that cannot be ignored. 

First, Gutstein claims to have been inspired by Paulo Freire. The key ideological-pedagogical point of Freire is dialogic pedagogy. Freire (2013) makes it clear that dialogue is an existential necessity and, moreover, is the opposite of propaganda: “Propaganda, slogans, myths are the instruments employed by the invader to achieve his objectives…. True humanism [and humanizing education], which serves human beings, cannot accept manipulation under any name whatsoever, for humanism there is no path other than dialogue. To engage in dialogue is to be genuine.” (p. 101)

As described in the book, however, teacher-student conversations are far from dialogical. Students are not invited to argue their own thoughts and ideas. Rather, a set of ideas is imposed top-down. It is more ideological indoctrination than dialogical pedagogy.

Second, it seems that the second chapter of the book is not written by the same person who wrote the rest. Chapter 2 puts great emphasis on Freire. The rest of the book, however—and in particular the ethnographic data Gutstein draws upon—reveals no trace of how Freire enacted dialogical pedagogy in teaching. Instead, the book presents yet another version of traditional teaching in which the teacher has pre-made agendas that are duly imposed on students.

Third, it is worth noting that social justice and equity are misunderstood and therefore often-exploited concepts. Neither is neutral: depending on one’s political-ideological stance, they take different and contradictory shapes. The concept of justice is generally based on either liberal or Marxist points of view—the ideologies are drastically different from each other. The author fails to provide a working definition of social justice and equity in the educational context let alone substantiate them through classroom teaching projects.

Fourth, the driving force of social, political, economic, and cultural life for the last forty years has been neoliberal ideology. As such, it is odd that the book makes no mention of neoliberalism or its implications for education. For example, Gutstein appears to have no problem with educational corporate colonization in general or standardization in math education in particular. He wants students to develop agency for justice yet does not see anything in the neoliberal system that brings about injustice in the first place.

Fifth, the author’s definition of class and ethnic identity seems to be based on Max Weber’s (identity politics), and it resonates with neoliberal ideology. Let us assume that Gutstein’s Latino students have developed a strong sense of agency and the consciousness that privileged white people oppress people of color. What are these students to do? Are they going to straighten all white people up?

One does not have to look very hard to see that the U.S. is a class-divided society. Of course, racial discrimination is a big part of justice issue in America. However, class, not race, is the central global concept necessary to explain the human condition, as it encompasses oppression, equality, and freedom (Darder & Torres, 2009). In the U.S., neither communities of whites nor communities of people of color are homogenous. Within each community, there are poor, working-class, middle-class, and upper-middle-class people, as well as some who are super rich. And as long as the capitalist system is around, the America will continue to be a class-divided society.

When Latino students are fully equipped with a critical mathematics literacy and consciousness, how will they account for middle- and upper-middle-class Latinos and people of color? If ethnic background is the main obstacle to success in professional and private life, how to explain the fact that people of color take up important positions in politics, business, and bureaucracy? Among many other examples, the current secretary of education, Miguel Cardona, comes from Latino background. Similarly, if white people are privileged, how to explain the increasing number of poor-white people in the U.S.? Or the number of poor-white students in public schools?

With respect to education, the same holds true. Research from opposite perspectives agrees: the single most important factor in student success is socioeconomic background. Higher socioeconomic status is the best predictor of academic success.

It is not clear in what ways Gutstein’s approach to justice and teaching will lead to a more just and equal societal order. One can foresee, however, that the ways in which he explains justice and equity in his classroom practices, his students may develop a sense of ethnic pride and potentially chauvinism.

Finally, if one claims to be inspired by Paulo Freire, one should internalize Freire’s views. Friere encourages us to find unity in diversity; he reminds us that the things that bring us together and make us human—universal values—are much stronger than the things that separate us. If we want students to develop consciousness, top priority should be given to class consciousness so that poor students (and people) from all racial, ethnic, and cultural backgrounds can come together to fight against the handful of rich elites, and thereby make world a more just, more equal, and more democratic place for all. 

REFERENCES

Herr, K., & Anderson, G. L. (2005). The action research dissertation: A guide for students and faculty. London: Sage.

Freire, P. (2013). Education for critical consciousness. New York: Bloomsbury Academic.

Darder, A., & Torres, R.D. (2009). After race: An introduction. In A. Darder, R.D. Torres, & M.P. Baltodano (Eds.), The critical pedagogy reader (pp. 150–166). London: Routledge.