Reviving an educational tradition involves a double task. A new generation of students must be taught, and at the same time the teachers themselves must learn. This book addresses the teachers who seek to hand on the quadrivium-the four mathematical liberal arts of arithmetic, geometry, music, and astronomy-at the same time as they acquire it.
Two components run in parallel throughout the book. The first component is practical. Weekly overviews and daily lesson plans explain how to complete the study of A Brief Quadrivium in the course of a single school year, and suggestions for weekly assessments make it easy to plan tests and monitor student progress. The second component is directed to the continuing education of the teacher. Short essays explore the history, philosophy, and practice of mathematics. The themes of these essays are coordinated with the simultaneous mathematical work being done by students, allowing the teacher to instruct more reflectively.
Some users of this book are confident in their grasp of mathematics and natural science. For them, the essays will clarify the unity of mathematical activity over time and reveal the old roots of new developments. Other users of this book, including some parents who school their children at home, find mathematics intimidating. The clear structure of the lesson plans, and the support of the companion essays, give them the confidence to lead students through a demanding but doable course of study.
The British mathematician John Edensor Littlewood remarked that one finds in the ancient mathematicians not "clever schoolboys" but rather "Fellows of another College." This guide invites all teachers of the quadrivium to join the enduring mathematical culture of Littlewood and his predecessors, and to witness for themselves the significance and vitality of a tradition as old as Pythagoras.
"In Teaching the Quadrivium: A Guide for Instructors, the author, speaking as a fellow teacher, offers down-to-earth advice about taking students through the author’s text on the quadrivium. The brief Guide is full of useful wisdom about things like weekly planning, acquisition of basic skills, attention to details, review, and encouragement. The book’s practicality is supplemented by fascinating historical excursions and pointed reflections on topics as diverse as patience, prudence, names, beauty, and death. More than a ‘how to,’ the Guide promotes real thought about the quadrivium in its relation to human experience."~Peter Kalkavage, St. John's College