Calculus Reordered: A History of the Big Ideas

Calculus Reordered explores the history of calculus, why it is credited to Isaac Newton and Gottfried Leibniz, and how its curriculum should be changed to better teach students.

Format: Paperback / softback
Length: 248 pages
Publication date: 04 May 2021
Publisher: Princeton University Press

Calculus, a subject that has evolved over centuries, is the focus of Calculus Reordered. David Bressoud, in this book, delves into the history of calculus, tracing its roots back to seventeenth-century figures Isaac Newton and Gottfried Leibniz, as well as the influence of Italian philosophers like Galileo Galilei. He also discusses how the current structure of calculus emerged in the nineteenth century. Bressoud challenges the traditional curriculum order of limits, differentiation, integration, and series, arguing that a pedagogy informed by the historical evolution of calculus would be more effective in teaching students this complex area of mathematics.

Calculus Reordered explores the journey of calculus from its birth in the Hellenistic Eastern Mediterranean, India, and the Islamic Middle East to its contemporary iteration. It highlights the ways in which this essential tool of mathematics has evolved and been adopted by different cultures and societies throughout history. The book also provides insights into the mathematical principles and concepts that underlie calculus, making it accessible to readers with a range of backgrounds.

One of the key arguments presented in Calculus Reordered is that the traditional curriculum order of limits, differentiation, integration, and series may not be the most effective way to teach calculus. Bressoud suggests that a more chronological approach, starting with the basic concepts of arithmetic and algebra, and then gradually building up to the more advanced topics of calculus, would be more conducive to student learning. This approach would allow students to see the connections between different branches of mathematics and gain a deeper understanding of the subject.

In addition to advocating for a chronological curriculum, Bressoud also suggests that a pedagogy informed by the historical evolution of calculus would be more effective in teaching students. This pedagogy would involve incorporating historical examples and anecdotes into the teaching of calculus, to help students understand the context and significance of the subject. It would also involve using visual aids, such as diagrams and graphs, to help students visualize the mathematical concepts and processes involved in calculus.

Calculus Reordered is a valuable resource for anyone interested in the history and development of calculus. It provides a comprehensive and engaging account of the subject, and offers insights into the challenges and opportunities that arise in teaching and learning calculus. Whether you are a student, teacher, or mathematician, this book will help you deepen your understanding of this fascinating area of mathematics.

In conclusion, Calculus Reordered is a must-read for anyone interested in the history and development of calculus. By challenging the traditional curriculum order and advocating for a more chronological and historically informed pedagogy, David Bressoud offers a fresh perspective on this essential subject. This book will help students deepen their understanding of calculus and its applications, and will also inspire teachers to explore new and innovative ways of teaching this complex area of mathematics.

Weight: 366g
Dimension: 154 x 236 x 18 (mm)
ISBN-13: 9780691218786