How much do you take for granted when you step into a mathematics classroom or lecture hall? Tools of American Mathematics Teaching, 1800–2000, gives the history and impact of the tools used ubiquitously in mathematics classrooms — textbooks, blackboards, projectors, graph paper, and more. Reading this history is especially fascinating right now as many of these tools are starting to be replaced by newer tools. Many college instructors are now using electronic or open-source textbooks. I no longer teach at a blackboard — my lecture notes are handwritten on a notebook computer and projected onto a screen. Many schools are phasing out overhead projectors in favor of computer presentation and document cameras, and graphing calculators and computer programs are much more prevalent in college classrooms than graph paper. As we start to phase out some of these technologies, it is useful to remember how they were introduced to us, why their use became widespread, and how they impacted teaching.
The chapter on standardized tests should be required reading for anyone who wants to engage in the debates around standardized testing in K-12 schools. This chapter traces the beginnings of standardized testing as part of the New York Regents Exam and the college boards. Then, in the late 1800s, an elementary-school reformer and physician named Joseph Mayer Rice observed students in a variety of public schools throughout the US and concluded that there was too much teaching by rote recitation and that teachers were poorly supervised. He devised tests to confirm his observations quantitatively. He started with spelling and later moved on to arithmetic. He urged the development of teaching goals and standardized tests to measure how well these goals were being met. Others took up this call, more tests were developed, and testing became more widespread. But some researchers found that tests did not always measure what educators wanted to measure, and that scores of students fluctuated too widely to make them reliable.
Tools of American Mathematics Teaching also covers tools of calculation, such as slide rules, electronic calculators, and computers. The account of the reception of mechanical and electronic calculators as they first entered schools was an especially interesting read. The book ends with a history of personal computers, graphing calculators, and mathematics software in the classroom, which are all prevalent in college education.
This is a broad survey that covers tools and materials of K–16 mathematics education. It gives a useful background and grounding for many of the debates that are still going on in education today. It is a valuable read for instructors of mathematics and education, as well as for students, particularly those interested in mathematics education.
Angela Vierling-Claassen is Assistant Professor of Mathematics at Lesley University in Cambridge, Massachusetts.