Bressoud, David M. (Author)
How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change. Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus’s birth in the Hellenistic Eastern Mediterranean―particularly in Syracuse, Sicily and Alexandria, Egypt―as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus’s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order―integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities―makes more sense in the classroom environment. Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
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Book
Auvinet, Jérôme;
(2013)
Charles-Ange Laisant: itinéraries et engagements d'un mathématicien de la Troisième République
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Article
Bellhouse, David R;
(2014)
The Deification of Newton in 1711
(/isis/citation/CBB001420038/)
Book
Wardhaugh, Benjamin;
(2012)
The History of the History of Mathematics: Case Studies for the Seventeenth, Eighteenth, and Nineteenth Centuries
(/isis/citation/CBB001251196/)
Article
Sun, Xiao-li;
(2006)
Leibniz and the debate of inventor's right of calculus
(/isis/citation/CBB000780273/)
Article
Wang, Youjun;
(2009)
Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics
(/isis/citation/CBB001032848/)
Chapter
Rudolf Sträßer;
(2014)
History of Teaching Vocational Mathematics
(/isis/citation/CBB225382036/)
Article
Kidwell, Peggy Aldrich;
(2009)
Computing Devices, Mathematics Education and Mathematics: Sexton's Omnimetre in Its Time
(/isis/citation/CBB000953072/)
Chapter
Livia Giacardi;
Roberto Scoth;
(2014)
Secondary School Mathematics Teaching from the Early Nineteenth Century to the Mid-Twentieth Century in Italy
(/isis/citation/CBB733044844/)
Article
Gao, Hongcheng;
(2014)
Textual Research on the Date of the Master Copy of Daiweiji Shiji
(/isis/citation/CBB001214105/)
Article
Giuntini, Sandra;
(2009)
Gabriele Manfredi e l'insegnamento della matematica a Bologna nel XVIII secolo
(/isis/citation/CBB000933196/)
Article
Blanco, Mónica;
(2013)
The Mathematical Courses of Pedro Padilla and Étienne Bézout: Teaching Calculus in Eighteenth-Century Spain and France
(/isis/citation/CBB001211889/)
Chapter
Luciana Zuccheri;
Verena Zudini;
(2014)
History of Teaching Calculus
(/isis/citation/CBB284930360/)
Article
Günhan Caglayan;
(2019)
Theory of Polygonal Numbers with Cuisenaire Rods Manipulatives: Understanding Theon of Smyrna’s Arithmetic in a History of Mathematics Classroom
(/isis/citation/CBB942427938/)
Article
Mason, John;
(2007)
Bartering Problems in Arithmetic Books 1450--1890
(/isis/citation/CBB000831582/)
Article
Caroline Ehrhardt;
(2018)
A Locus for Transnational Exchanges: European Mathematical Journals for Students and Teachers, 1860s–1914
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Article
Sonja Brentjes;
(2019)
Pourquoi et comment étudier l’histoire de l’enseignement des mathématiques dans les sociétés islamiques entre 750 et 1500
(/isis/citation/CBB767421224/)
Chapter
Gert Schubring;
(2014)
On Historiography of Teaching and Learning Mathematics
(/isis/citation/CBB213855058/)
Article
Paola Magrone;
Ana Millán Gasca;
(2023)
Children shall know what lies at the heart of genuine mathematical science: The Lectures on the logic of arithmetic (1903) by Mary Everest Boole
(/isis/citation/CBB542582796/)
Article
Lawrence, Snezana;
(2011)
Dee and His Books: Lessons from the History of Mathematics for Primary and Middle School Teachers
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Book
David Lindsay Roberts;
(2012)
American Mathematicians as Educators, 1893--1923: Historical Roots of the "Math Wars"
(/isis/citation/CBB489861601/)
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