This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus. The calculus considered is elementary calculus of a single variable. The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics. Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you. Topics covered include A history of calculus and how calculus differs over countries today Making sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book) The ordering of calculus concepts (should limits come first?) Applications of calculus (including differential equations) The final chapter looks beyond elementary calculus. Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus. This book is essential reading for mathematics teacher trainers everywhere.
Internationally renowned and award-winning author John Gilbert has spent the last thirty years researching, thinking and writing about some of the central and enduring issues in science education. He has contributed over twenty books and 400 articles to the field and is Editor-in-Chief of the International Journal of Science Education. For the first time he brings together sixteen of his key writings in one volume. This unique book highlights important shifts in emphasis in science education research, the influence of important individuals and matters of national and international concern. All this is interwoven in the following four themes: explanation, models and modeling in science education relating science education and technology education informal education in science and technology alternative conceptions and science education.
This book explains the nature of sound both as a physical phenomenon and as a sensation, how it travels through air and water, and how the hearing system evolved to convert these vibrations into sensations. Drawing on physics, biology, neuroscience, philosophy, literature, history, anecdote, and personal experience, "Now Hear This" is a wide-ranging exploration of the nature of sound and hearing that opens up a fascinating world of sounds from the mundane to the unusual and seeks above all to persuade the reader of the wisdom of John Cage’s advice that “Wherever we are what we hear is mostly noise. When we ignore it, it disturbs us. When we listen to it, we find it fascinating.”
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