Democracy and Mathematics Education

Rethinking School Math for Our Troubled Times

Kurt Stemhagen, Catherine Henney

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000378139
• Edition: 1
• Topic: Education
• Subtopic: Education General

In Democracy and Mathematics Education, Kurt Stemhagen and Catherine Henney develop a way of thinking about the nature and purposes of math that is inclusive, participatory, and thoroughly human. They use these ideas to create a school mathematics experience that can enhance students' math abilities and democratic potential. They locate mathematics' origins in human activity and highlight the rich but often overlooked links between mathematical activity and democratic, social practices. Democratic mathematics education foregrounds student inquiry and brings to light the moral dimensions of a discipline that has both remarkable utility and inevitable limitations. For math educators, the book's humanities approach helps to see the subject anew. For philosophers, it provides an important real world context for wrestling with perennial and timely questions, engaging democratic and evolutionary theory to transform school math. This alternative approach to mathematics and mathematics education provides a guide for how to use math to make democracy a larger part of school and wider social life.

2021 Winner of the AESA Critics' Choice Book Award.

PART I

The Problem

1

Introduction

Rethinking Math for Our Troubled Times

Mathematics is a curious discipline. Each of us has a math history and, in all likelihood, a complicated relationship to the subject. Our memories of the math classroom may tell a story of success and delight. Or they may tell a story of frustration, disinterest, or even dread. No other school subject is nearly so divisive. At the mere mention of mathematics, we quickly sift and sort ourselves into categories internalized long ago, probably during our childhood.

How is it that mathematics can mean so much to some and so little to others? Why such widely disparate experiences? And they are indeed wide and disparate. Unequal.

This is by no means a new phenomenon. Historically, math has been cordoned off from the masses and reserved only for the college-bound, particularly for those advancing to quantitative fields such as engineering. This “lack of welcome,” as Francis Su (2020) has described it, has far-reaching injurious social consequences. It is not simply that an exclusionary mathematics is undemocratic; it also works to forestall the flourishing of democracy itself.

While we are not claiming that a non-democratic school mathematics experience is the reason that our democracy is in its current state, at the very least we do see math class as a missed opportunity. We have multiple reasons for writing this book and developing a democratic philosophy of mathematics education and a related set of teaching/learning practices. When one of the authors first started with this line of thinking in the early 2000s, its purpose was primarily to improve school mathematics. Over time, we have come to see implications for this project that go far beyond math class. The center of this democratic mathematics project is the place where thinking about the nature of mathematics, its teaching and learning, and the wider purposes of schooling meet. Stated concisely, our project is about what happens when the math classroom is taken seriously as a place where the civic and democratic aims of schooling are addressed. The potential benefits are considerable for both the learning of mathematics and the health of democracy.¹

A few words about the state of our democracy are in order here. Starting with a look at democracy narrowly construed, it is very troubling that approximately 100 million Americans (roughly 43% of those eligible) did not vote in the 2016 US presidential election. Perhaps more troubling is the lack of faith in institutions crucial for a functioning democracy that has led to the proliferation of questionable information and questionable sources. Newspapers and other media, governmental agencies, and other important sources of the trusted information that make it possible for democratic participants to make sound decisions have been systematically undermined. It started long before the Trump administration but has certainly intensified since the 2016 presidential campaign season and the four years that followed.

This crisis in confidence has made it possible for Americans to be bitterly divided and for many to turn against the very idea of a public sphere. As we write these words, a global pandemic rages and no one knows how it will alter our futures, though we know it most assuredly will. In the US there is a sharp divide between faith (or at least hopefulness) and skepticism about whether scientific and other forms of expertise can or should inform the policies created to combat the COVID-19 virus.

The politics surrounding the pandemic response in the US offer a particularly interesting way to begin thinking about our perception of mathematics, how we teach and learn it, and our wider social lives. Democracy and expertise have always existed in a somewhat uneasy tension. Early efforts at democracy often involved trying to find ways for common folk to know enough to vote, but little else. For example, Thomas Jefferson’s plan to establish three years of public schooling at the taxpayers’ expense (for all free children, both male and female) was designed to ensure that voters would have the knowledge and faculties to elect wise leaders and to participate in the economy. Jefferson also saw these schools as a means to identify future leaders and his plan included continued free education for the “brightest.” He saw this as a way to replace what he called the artificial aristocracy (those who were selected due to their family status and wealth) with a natural aristocracy (those with virtue and talent). That he described his future leader identification system as a way that “twenty of the best geniuses will be raked from the rubbish annually” demonstrates that he had a limited idea of what democracy would come to mean in the future. Jefferson is discussed here not as an exemplar of democratic thinking. Instead his proposed education bill is offered as evidence of the limited scope of what democracy entailed, historically. Historian Benjamin Barber’s An Aristocracy of Everyone (1992) updated and extended Jefferson’s vision of democracy to include concern for the dignity and quality of experience and participation for all.

Contemporary understandings of democracy, at least in theory, tend to be wider and more inclusive. John Dewey, often referred to as the philosopher of American democracy, always highlighted the ways in which voting and the machinations of government were just one part of democracy. To Dewey, democracy connoted the way that we choose to live together, the responsibilities that we recognize toward each other, and the common good. Dewey’s democracy also features the promise that one “return” on our commitment to the common, public good is that these arrangements will also allow for individual flourishing.

Our current moment is one during which faith in the “public” is frayed. Furthermore, the tension between individual choice and expert/scientific opinion, while always present, has been politicized to the point where, to many, expertise is seen as an impediment to understanding and sensible action. The version of mathematics education that we develop in these pages, while certainly not the solution to these problems, works to relieve rather than exacerbate these tensions. We describe a way of thinking about mathematics that leads to a democratized school math experience for students, one that is social as opposed to individual, that values skills of reasoning and judgment rather than just rote learning. It is a way of thinking that develops students’ capacity and eagerness to use math throughout their lives—solving problems, accomplishing goals, questioning and investigating phenomena.

The philosophy and related practice of school mathematics that we develop and advocate for in these pages, Democratic Mathematics Education (DME), is intended to serve as an ingress, not an obstruction, to the wider world. As we envision it, DME seeks to bring about the development of a school mathematics that is not just open to all, but potentially of interest to all, where people see mathematics as potentially theirs and as something that matters in their lives and communities.

We see this moment as providing some great opportunities for democratic education—at the very least there is a great need for it and, in some circles, people are beginning to realize that. The heart of our project involves thinking about how math class can be a site for democratic education and, even more, how this democratic turn can enliven young people’s school math experience, helping them to develop critical faculties and agency crucial to robust civic and democratic participation and the skills and knowledge to meaningfully act on their world.

While taking math class seriously as a space for democratic education is the main focus of this book, there are other benefits to the approach we develop. We are also talking about democratic education in the sense that it is education for everyone, for the people. Labaree (1997) convincingly develops democratic equality as a major purpose of public school. To Labaree, democratic equality means much more than just civic participation; he has his sights set on opportunity and equity. Labaree’s “democratic equality” tightly intertwines participation and opportunity under the banner of democracy. Opportunity, as it currently operates, is in large part a function of success in mathematics. Unfortunately, today’s math class is often used as a sorting mechanism, a decider in the game of who gets to be—by virtue of success in the insular school math competition—thought of as smart and thus given scarce educational and professional opportunities.

This project therefore seeks to stake a claim to mathematics education for everyone,² that is, it is an attempt to think in a new way about mathematics in order to democratize math and math education. We draw heavily on Deweyan progressive/democratic education, in both methods and purpose, to develop the pragmatic/democratic philosophy of mathematics education at the core of this project. This rethinking of mathematics can support the needs of critical and social justice-oriented mathematics educators. We develop a way of thinking about mathematics that aligns with student interests, with issues of the day, that is more engaging and inclusive than the typical ways of thinking about school mathematics. In short, the way we conceptualize mathematics in the following pages has the potential to be a democratizing force in a field that is all too often overly abstract, hierarchical, and exclusionary. This pragmatic/democratic philosophy of mathematics invites broad participation and provides a philosophical foundation for a school math experience that can foster sustained engagement from those who have traditionally been discouraged from striving for success and even possessing interest in school math.

The sorting function of school mathematics happens through a process of continual attrition. Those who succeed and who somehow happen to see the connections between school math and their lives are rewarded: the few, the interested, the successful in math.³ Instead, our hope is that remaking math in a democratic spirit will be democratic not just in terms of teaching the skills of democracy, it will also be democratic in its enactment and in its attention to accessibility, opportunity, and equity. This is a different use of the term democracy, and here we are invoking the version that touts an opening up of a field or area. For example, there has been much ink spilled about the power of the Internet to democratize various enterprises. The democratization of the music industry has, the thinking goes, occurred because—thanks to the Internet—musicians can now sell their music directly to the public, sidestepping the monolithic, capitalist beast called the record company. For now we will leave the problems with this form of democratization untouched other than to say that if the new democratized music model makes it technically possible but highly unlikely that an unknown artist’s music will be heard far and wide, then this is not the kind of democracy we should be looking for. Democratization is marked by a broadening, not a narrowing, of opportunities, a seeking of all that life can offer. Similarly, democratic mathematics education has the potential to open itself to everyone as well as the potential to open everyone to new and varied possibilities.

It should be fairly obvious how improving access and equity in mathematics education can benefit society, as getting more students further along in mathematics has promise to lead to increased expertise, innovation, general math literacy, to name just a few. We also want to call attention to how this democratization, this opening up of mathematics, will be good, not just for wider society but also for the field. Rochelle Gutiérrez (2002) says it well: “The assumption is that certain people will gain from having mathematics in their lives, as opposed to the field of mathematics will gain from having these people in its field” (p. 147). She goes on to point out how many researchers in mathematics education operate with a deficit view of those previously prevented from full participation in mathematics. Instead, she points out that mathematics is in need of change: “Such programs seem to imply that the people being served by the programs need to improve but that the mathematics does not” (p. 147). In the end, it is not just that the people need mathematics, mathematics needs the people.

Mathematics Education’s Untenable Dualisms

Historically, mathematics has been regarded as a bastion of certainty. The characterization of mathematics as objective, logical, and based on objects or truths outside of human involvement has made it resistant to the conceptual shifts that have affected other subject areas. Recent reform efforts that have sought to include social facets of mathematical knowledge within mathematics education have worked against a particularly entrenched understanding of the discipline. Reformers have positioned themselves against these rigid conventions by offering a version of mathematics that is subjective, relative, and fallible. The “math wars” have been raging for several years and show no signs of letting up, pitting traditionalists—those calling for more rigor and a “back-to-basics” approach to mathematics education—against constructivists—those advocating a child-centered, applied approach to mathematics education.

On the surface, there are somewhat similar conflicts occurring in other areas of the curriculum. Certainly, one need not look any further than language arts to see that mathematics is not the only subject area in which a polarized controversy exists. The phonics versus whole language debate, still hotly argued today, seems at first glance analogous to the confrontation at the heart of the math wars.⁴ However, there is at least one important difference. While the phonics versus whole language debate is primarily about teaching methods, the math wars—though certainly concerned with teaching methods—is fundamentally a philosophical confrontation. Disputes about how best to tea...