Tools of American Mathematics Teaching, 1800–2000 (review)

Textbooks, slide rules, and the National Semiconductor Quiz Kid are tools of utopia and novelties of hucksters, mechanical instructors of a space-age polity and torture devices of America’s youth. These are only some of the material influences on the nation’s mathematical heritage as described by Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts. By telling the history of mathematics as the history of things, the authors provide an account of learning not as a progressive march of logic, but rather as ever-shifting constraints and opportunities afforded by sociotechnical change.

Anyone schooled in the American system will recognize the fragmentary gestalt captured in this book—the national directives, pedagogical fads, paltry budgets, and clashing tradition-seeking and inventive teachers. The reader’s sense of disorientation, however, is partially an artifact of the text. The authors employ extraordinary archival materials and include more than eighty illustrations. Eighteen chapters are devoted to artifacts from the abacus to Mathematica, classified by four categories of tools: “Presentation and General Pedagogy,” “Calculation,” “Measurement and Representation,” and “Electronic Technology and Mathematical Learning.” But the authors give only a cursory introduction and offer no conclusion about the collective meaning of these objects; thus the book is read best in units. I found the strongest chapters to be those on blackboards, programmed instruction, cube root blocks, and blocks, beads, and bars.

Historians of technology are not the book’s main audience. Still, scholars for whom the “mute testimony of objects” (p. 22) is more widely accepted will find familiar themes and valuable case studies. Take the blackboard. These classroom stalwarts were copied from England and France independently in the United States’ officer corps and in the trenches of its grammar schools. At West Point, where the new nation imported not just its curriculum but also its instructors, Claude Crozet introduced the blackboard because cadets could not read their French textbooks. By 1831, six of Boston’s eight schools were equipped with blackboards and usage spread as teachers constructed their own, not for lack of language skill but as a cheaper alternative to textbooks. Presence is no indicator of use, however, and many recalcitrant teachers accepted the novelties only after salesmanship and retraining, expedited by the rise of a national education industry in the latter half of the nineteenth century. These seemingly innocuous artifacts, moreover, were imbued with politics. Fearing instructional change, students at Yale demanded they be allowed to consult textbooks in class. When forty-two Luddites rebelled by refusing to perform exercises at the board, they were expelled.

How objects shape human understanding and how that meaning evolves are foundational questions of Thing Theory, a now robust field that includes under its aegis the history of science and technology, book history, anthropology, and English. Given the temporal and material boundaries of Tools of American Mathematics Teaching, perhaps the authors should not be faulted for avoiding synthetic answers to these questions in the realm of mathematics education. The challenges are myriad—sometimes instructional tools emerge from necessity; at other times they embody political philosophies that bind action; always they mediate between visual, tactile, and textual modes of learning. The advent of a transformational medium like digital computing raises further questions about epochal change, impacting even 200-year-old successes like the blackboard, now threatened by smartboards and ELMOs. Moreover, only in rare cases like that of manipulables (described in chapter 9) is there an evidentiary record of the complex interplay of pedagogical theories, manufacturers, government policy, and social change that sheds light on the artifactual politics of education.

The authors do present recurring themes: the gulf between abstraction and embodiment, the promise and failure engendered by technologies, and the drive for standardization wrought by population growth and mass production. Placing students at the core of future research may be the most fruitful path toward an organizing narrative. Sherry Turkle’s Falling for Science (2008)—an anthology of...