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From the blackboard to the graphing calculator, the tools developed to teach mathematics in America have a rich history shaped by educational reform, technological innovation, and spirited entrepreneurship. In Tools of American Mathematics Teaching, 1800–2000, Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts present the first systematic historical study of the objects used in the American mathematics classroom. They discuss broad tools of presentation and pedagogy (not only blackboards and textbooks, but early twentieth-century standardized tests, teaching machines, and the overhead projector), tools for calculation, and tools for representation and measurement. Engaging and accessible, this volume tells the stories of how specific objects such as protractors, geometric models, slide rules, electronic calculators, and computers came to be used in classrooms, and how some disappeared.
On Parent's Day, in 1952, B. F. Skinner visited his daughter's fourth grade math class. As he watched the lesson, he became increasingly uncomfortable. Almost every principle of effective teaching that he had studied for more than 20 years was being violated in that classroom. Yet it was a typical class. The teacher showed how to solve the day's problems, then gave the students a worksheet to do. Some children began to work readily while others shifted uncomfortably in their chairs, or raised their hands for help. The teacher went from desk to desk, giving help and feedback. Skinner knew what was needed. Each student should be given a problem tailored precisely to his or her skill level, not to the class average, and every answer needed to be assessed immediately to determine the next step. The task was clearly impossible for one teacher. That afternoon, Skinner set to work on a teaching machine. Today's computers have made the mechanical machine obsolete, but the principles of how to design instruction in steps that lead from a basic level to competent performance are as valid today as they were in the 20th century. This book brings together Skinner's writings on education during the years he was most involved in improving education.