This book is an important and comprehensive contribution to the history mathematics education in America as seen through the use of manipulatives. It is in four parts. The first part, Tools of Presentation and Pedagogy, has five chapters addressing: textbooks, the blackboard, standardized tests, the overhead projector, and teaching machines/programmed instruction. The second part, Tools of Calculation, has four chapters addressing: the abacus, the slide rule, the cube root block, and blocks/beads/ bars (e.g. Cuisenaire rods). Part three, Tools of Measurement and Representation, has five chapters addressing: the protractor, metric teaching apparati, graph paper, geometric models, and linkages. Part four, Electronic Technology and Mathematical Learning, has four chapters addressing: calculators, minicomputers, early microcomputers, and graphing calculators/software systems. The first author is curator of the mathematics collections at the National Museum of American History, Smithsonian Institution. She has provided a wealth of photographs of manipulatives from the Smithsonian collection that further enhance an already valuable study. I do not mean to imply that this treatise is simply a dry, laundry list of manipulatives. The authors tell the stories of how specific objects came to be used in classrooms and how some disappeared. As such it provides an interesting and engaging view of mathematics education in the United States in the nineteenth and twentieth centuries.

Reviewer:

Steven C. Althoen (Holly)