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Essays discuss different methods and philosophies of teaching mathematics, seeking to solve the problem of educational decay.

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A crisis in US mathematical education is widely recognized, but the nature of its cause or cure is the subject of diverging views. Leaving aside such issues as educational funding, teacher competence, or low cultural esteem accorded to mathematical achievement, these essays focus on setting goals for curriculum reform. Indeed, the authors seek a redefinition of numeracy to take account of recent changes in the world and in mathematics itself. One such change is the wide availability of computers and calculators to perform arithmetic, and now graphing and algebra. In the essay "Quantity," James T. Fey describes how calculators may be used in teaching and argues that empirical research in mathematics education supports their use in the classroom at every level. Mathematics, particularly statistics, now finds applications far beyond the realms of science and engineering. David S. Moore's essay "Uncertainty" advocates the teaching of statistical reasoning, as opposed to mere statistical techniques. Other essays, "Dimension," "Shape," and "Change," suggest ways to introduce new ideas from topology, geometry, and dynamics even to very young students. A common thread is that mathematics, to be useful, must be grounded in our intuition and experience of the world. Teachers will find many ideas here to apply, but the formulation of a comprehensive practical curriculum designed to meet these new goals still lies well in the future. Advanced undergraduates and up. -D. V. Feldman, University of New Hampshire