Performing Math

A History of Communication and Anxiety in the American Mathematics Classroom

Andrew Fiss

• Publisher: Rutgers University Press
• Year: 2020
• ISBN:
  9781978820227
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Performing Math tells the history of expectations for math communication—and the conversations about math hatred and math anxiety that occurred in response. Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers' identities as math students, and the written tests that redefined "student performance." Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety. With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented history of American math education, one that can explain contemporary math attitudes and provide a way forward to reframing the problem of math anxiety.

1

How Math Communication Has Started with Reading Aloud

On Saturday, July 31, 1830, forty-five students were dismissed from Yale because they disagreed with the faculty about how to read from their math textbooks. Many had come from preparatory schools and were descended from established families. One, in fact, was the son of a U.S. vice president. The forty-five said they should be expected to read solutions from their textbook, not develop them from the diagrams printed in the book or reproduced on the blackboard. The new policy, they claimed, made their algebra classes “one-half more difficult” than those of previous Yale students, and conic sections (their current class) was just not possible for them.1

President Jeremiah Day and his faculty responded with dismissal. Not clarifying if the decision was equivalent to expulsion, they still reinforced their action by circulating pamphlets and sending letters to university presidents, professors, and especially parents. The students, they explained, had broken the rules by “enter[ing] into combination” and banding together as a unified body against the faculty. Furthermore, the faculty did their own quantitative study, which did not find, as they said, “greater burdens” in these students’ math classes. Ultimately, though no official expulsion, none of the students could return to Yale, and many found they could not complete a college degree anywhere.2 The forty-five found they had fundamentally damaged their reputations. Why? They disagreed with their faculty about how to read from their textbooks, about how to communicate about mathematics.

Historians have long been fascinated with the story of the Yale Conic Sections Rebellion of 1830. In his history of middle-class professionalization, Burton Bledstein placed it within the context of emerging youth cultures that signaled social change.3 Similarly, Henry Shelden considered it a representative anecdote of changing student life.4 The various chroniclers of Yale University, including Brooks Mather Kelley, Clarence Deming, and William Lathrop Kingsley, have linked the Conic Sections Rebellion to the other Yale protests of the era.5 More recently, math historians Peggy Kidwell, Amy Ackerberg-Hastings, and David Roberts have found it indicative of the blackboard’s pedagogical novelty.6 Chapter 3 will return to the historiographical framing of the Conic Sections Rebellion, arguing for its importance for our understanding of math anxiety as a form of stage fright. For the purposes of this chapter, the Conic Sections Rebellion flags the importance of establishing standards for reading in American mathematics classrooms.

Math classes then—and since—have featured strong opinions about how best to read textbooks. As many historians of primary schooling have recovered, classes in reading preceded those in math; the famous three Rs—reading, (w)riting, and (a)rithmetic—had a particular order.7 First, students learned how to read. Then they learned how to write. Finally, they learned arithmetic. Studies in arithmetic took years because of the framework for memorizing rules for specific types of problems, such as the “Rule of Three.” There were also extensive units about business and commerce, such as the lengthy tables of the monetary systems of England, France, and different parts of the United States.8 Throughout, reading was considered the best way to access arithmetic, as foundational for any math studies.

Day, who chastised the participants in the Conic Sections Rebellion, published textbooks that followed the common practice of beginning with advice about how best to read the book. Day’s Algebra, a central textbook for Yale’s forty-five, included a long, five-page preface along those lines. It began with the problems of the existing, British models: too long and detailed for American students; or too short and sketchy for American classrooms. The implication was that American math needed to be homegrown. British books assumed advanced learners or access to a system of tutors and professors. The United States, without the resources of established British universities or the preparatory schools that supported them, needed a new kind of book. Building on the British models, proudly improving them, Day’s textbook ended its first sentence with a mission and promise: “accommodated to the method of instruction generally adopted in the American colleges.”9 Such a message, with updated language and perhaps substituting “schools” for “colleges,” became common, as did the claim that American schooling necessitated American books. Fundamentally, for Day, the difference in “method of instruction” was precisely a matter of reading.

Reading, for Day, had to do with cultural expectations for instruction. “In the colleges in this country,” he wrote, “there is generally put into the hands of a class, a book from which they are expected of themselves to acquire the principles of the science to which they are attending; receiving, however, from their instructor, any additional assistance which may be found necessary.” In other words, it was distinctly American for math students to be expected to read their textbooks and learn for themselves. “An elementary work for such a purpose ought evidently to contain the explanations which are requisite, to bring the subjects treated of,” he continued, “within the comprehension of the body of the class.”10 A successful American math book, for Day, needed to be so thorough that anyone reading it could come to full “comprehension” with minimal involvement of a teacher—or perhaps none at all. With textbooks good enough, “accommodated” enough, American students could just go off and teach themselves.

The role of reading was further clarified in Day’s continued assertions that American math textbooks should not be “practical.” Yes, he admitted, a lot of people learn without reading. By figuring out what examples fit what situations, workers build careers in occupations related to math: “In this mechanical way, the accountant, the navigator, and the land surveyor, may be qualified for their respective employments, with very little knowledge of the principles that lie at the foundation of the calculations which they are to make.”11 But, Day implied, such workers only act like machines and can be easily replaced. The derogatory use of mechanical (automatic, machinelike, mindless, and soulless) further emphasized that the earlier “practical” was meant as a criticism of learning without reading.

Reading about math was important for Day because he thought it provided a direct link to the mind. As a minister, Day liked to know how to sway congregants, how to persuade them to pursue the right path. The link with math was not about a sort of religious persuasion, at least not directly. Instead, reading about math led to logical thinking, a heightened mind through good reasoning. Not about “practical” skill, “a higher object is proposed, in the case of those who are acquiring a liberal education. The main design,” he explained, “should be to call into exercise, to discipline, and to invigorate the powers of the mind. It is the logic of the mathematics which constitutes their principal [sic] value, as a part of a course of collegiate instruction. The time and attention devoted to them, is for the purpose of forming sound reasoners, rather than expert mathematicians.”12 Compared to British counterparts, the American textbooks had to be the right length and have the right tone so that readers could teach themselves the “logic” in mathematics. Such framing did not communicate exactly how to think like a mathematician and certainly not like a math worker. Undergraduate studies emphasized how to be a lawyer, doctor, minister, or educator instead—and how reading would further all those careers.

Day’s way of explaining math did indicate the specific opportunities and privileges of the imagined audience. Like the chastised son of the U.S. vice president, American college students had tremendous privilege and advantage at a time when less than 1.5 percent of the eligible U.S. population pursued higher education.13 They often were not the same men (Day consistently assumed them to be men) who had to worry about how accounting, surveying, or any other business would bring them money. They could spend some of their time reading math textbooks and figuring out how it would lead to a better mind through “exercise” and “discipline.” They perhaps did not have enough leisure time to become “expert mathematicians.” But they could read a particular kind of textbook, not too long and not too short, not too detailed and not too sketchy. Gathering in classrooms full of white men, they could find out how to be “sound reasoners” by participating in performative, collective read-throughs.

Still, students were not entirely empowered in systems of mental discipline. After all, Day and his compatriots assumed student minds needed “discipline,” even beyond moments of student rebellion. Partially, Day’s view had to do with students’ ages. At Yale, students’ ages ranged widely between young teenagers and thirtysomethings, though the curriculum skewed young. Before high schools became common almost a century later, American colleges catered to a group that some historians (anachronistically) call adolescents.14 As the term makes clear, college students were assumed to be immature and flighty, certainly unable to think clearly. At the time, their reading needed to be carefully monitored and controlled so that it exerted the best, civilizing influence on them. That way, they could become religious and civic leaders, persuading others through their example, their words, and their “sound” logic. Reading, especially about math, seemed the ideal way for educators like Day to instill American values and exert control.

Reading provided a major way of limiting the audience for math textbooks as well. Day’s Algebra and the other books of his series imagine an audience beyond Yale, though only “in the American colleges.” Unlike some of those British textbooks he criticized, Day’s did not assume a general readership, not because of expectations that general readers could not stomach mathematics. Instead, it was a nod to the way that school policy constrained the audience for math textbooks. At the time, most schools and colleges had admission criteria that required all students to be white. The admission of African American students caused a stir in a country that still supported slavery. Similarly, Native American students were rarely incorporated without public outcry and also (often violent) missionary zeal from the educators.15 As many schools and colleges held admission policies based on race, many required that students be male, though some noted how women could be educated for home and family, including family businesses.16 Yale students were likely to be white, male, and from relatively well-to-do families. Within these categories, there was the most variation in social class, though even that was fairly limited. In short, Day’s “American colleges,” imagining from Yale outward, already incorporated implicit links among reading, math textbooks, and expectations regarding race, class, and gender. The Conic Sections Rebellion led to serious consequences because it was not how civilized, white men were supposed to behave, especially if they were truly disciplined, logical thinkers.

It was—and continues to be—important to recognize expectations for reading at the beginning of learning mathematics. The Conic Sections Rebellion included a disagreement about what part of the textbook was supposed to be read during the class time called “recitation.” Though our modern sense of the word might lead us to suspect recited texts were supposed to be memorized, “recitation” here meant reading aloud, in front of other people. Before their peers and tutors, the students were expected to read the words in the explanations included in the textbook, but their professors and textbooks’ authors encouraged them to “read” the diagrams instead.

More broadly than the disagreement about privileging alphabetic strings or visual diagrams, the Conic Sections Rebellion presaged the more complex expansion of reading abilities to quantitative literacy (or QL). According to technical communication researchers Crystal Colombini and Sue Hum, quantitative literacy includes assumptions about exploration, translation, visualization, and expression, touching on information literacy, visual literacy, and tech literacy, among others.17 In other words, reading about math—or as they put it, reading “about data”—involves alphabetic reading ability, along with the ability to “construct meaning” from images and information, usually accessed through digital technologies.18 In the Conic Sections Rebellion, Yale students claimed not to have been prepared for such an expanded notion of reading.

Analyzing the role of reading in math classrooms begins to indicate the performative dimensions of math communication. Teachers, professors, and textbook authors have had certain expectations about students’ minds: how to access them, how to inspire them, and how to discipline them. By setting expectations for reading, past educators created a sense of order as an introduction to learning math: an appeal to reason and logic as a way to exert control. As in the continued use of the term quantitative reasoning (or QR), discussions of reading and math still discuss the project of building “reasoners.”19 Even in appeals to the students’ minds, educators have clarified expectations about students’ bodies. To support a “sound” mind, the body had to be doing something at the time, even remaining calm and still.

This chapter more fully introduces expectations for reading and expectations for students’ minds, especially from Yale’s math professor and president Jeremiah Day. In part, I start with Day because of the legacy of his rules of “mental discipline” for American mathematics classrooms. Furthermore, because performing math involves assumptions beyond abstracted minds, the chapter looks more closely at how math textbooks and their uses have required certain things of students’ bodies: how math books surprisingly promoted early gym classes. The chapter also previews the beginnings of student movements, the seeds of frustration and disobedience within classrooms where teachers preferred extreme control. Throughout, textbooks’ expectations for mental and bodily discipline (clearly expressed with regard to reading) have flagged the performative dimensions of speaking about math in American classrooms.

Read-Throughs of the Mind

As expressed in the case of the Conic Sections Rebellion, Yale’s mathematician-president Day followed strict notions of discipline, and he consistently invoked the ideals of “mental discipline” in his writing and teaching about mathematics. Such a rationale for mathematics education had its roots in Anglo-American philosophies, and it still does exert a considerable influence on education studies in Britain and the United States. The Centre for Mathematics Sciences at the University of Cambridge recently reasserted that reading about math “trains the mind.”20 British statistician Adrian Smith also noted the importance of that rationale in his “inquiry into post-14 mathematics education.”21 Though slightly less common, U.S. sources similarly follow the legacy of Day and others who claimed that math “disciplines the mind.”22 Assuming students’ minds to be naturally undisciplined, these Anglo-American rationales have asserted the importance of mental fitness for professional aspirations and future civic engagement. Under Day, mental discipline showed (implicitly) how students could go out into the world and lead in government, work, and life—all through the power of reading about mathematics.

Mental discipline was already established well before Day went to school, and as he came to know, it already crystallized the intense importance of math in the education of Anglo-American boys. Mental discipline did communicate the sense of mathematics as preparatory for later life; although, in many instances, it was agnostic as to the work that the later life would contain. Rather, in mental discipline, math represented the pursuit of mental perfection through frequent practice. Just as physical exercise allowed the body to acquire superior abilities, so the argument went, the ment...

Table of contents

• Cover
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Introduction
• Chapter 1. How Math Communication Has Started with Reading Aloud
• Chapter 2. How Math Communication Has Been Practiced in Prohibited Ways
• Chapter 3. How Math Anxiety Has Developed from Classroom Tech
• Chapter 4. How Math Communication Has Been Theatrical
• Chapter 5. How Math Anxiety Became about Written Testing
• Conclusion: Math Communication from STEM to STEAM
• Acknowledgments
• Notes
• Index
• About the Author