On the Shoulders of Giants: New Approaches to Numeracy by National Research Council
	(Illus.) National Academy Press 1990 vi+232pp. 0-309-04234-8 Index C, T, GA **

This report, commissioned by the National Research Council, is intended to stimulate creative approaches to mathematics curricula in the next century. Unlike the David Report (National Research Council, 1984), which examined the state of mathematics research, support for research, and the rapport between mathematics and various areas of application, this report is concerned primarily with the instruction of mathematics in the elementary and secondary grades. It is addressed to teachers, university faculty, the public, and those in positions of public trust. The volume is organized into six essays written by separate authors. These are "Pattern" by Lynn Arthur Steen, "Dimension" by Thomas F. Banchoff, "Quantity" by James T. Fey, "Uncertainty" by David S. Moore, "Shape" by Marjorie Senechal, and "Change" by Ian Stewart. The volume addresses a number of aspects on the problem of innumeracy--the public's general lack of understanding that mathematics is a dynamic discipline and the importance of earlier learning as a prelude to subsequent knowledge both in a historical sense (hence the allusion in the title) and as a mode of instruction so important for mathematics. Most of the examples and illustrations can be understood with a minimum of mathematics, but they also provide a powerful motivation for overhauling and upgrading mathematics instruction. There is a differentiation made between understanding and doing mathematics, and between mathematics as a language and as an exploratory science without deprecating any of these aspects of mathematics. A teacher at almost any level will find some useful ideas and projects as well as a broader grasp of what mathematics is about. The problem that is left unresolved (perhaps because it does not have a simple solution) is not whether to teach fundamentals, but rather which fundamentals to teach. Separately and collectively these presentations show that a massive reorganization of mathematics instruction is required in order for students in U.S. schools to reach the standards we all claim we want them to meet. The traditional separation of arithmetic, algebra, geometry, and calculus is not adequate for the current state of mathematics.

--Reviewed by Donald E. Myers in Science Books and Films, 27/1 (January/February 1991), p. 5-6.