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.
