Vita Mathematica: Historical Research And Integration With Teaching (mathematical Association Of America Notes And Reports, No. 40)

Vita Mathematica will enable teachers to learn the relevant history of various topics in the undergraduate curriculum and help them incorporate this history in their teaching. It contains articles dealing not only with calculus, but also with algebra, combinatorics, graph theory, and geometry, as well as more general articles on teaching courses for prospective teachers, and describes courses taught entirely using original sources. Judith Grabiner shows us how two important eighteenth century mathematicians, Colin Maclaurin and Joseph-Louis Lagrange, understood the calculus from these different standpoints and how their legacy is still important in teaching calculus today. We learn from Hans Nils Jahnke why Lagrange's algebraic approach dominated teaching in Germany in the nineteenth century. Wilbur Knorr traces the ancient history of one of the possible foundations, the concept of indivisibles. This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but in fact deserves a central role. This book brings together papers by scholars from around the globe on the historiography and history of mathematics and their integration with mathematical pedagogy. Of the three articles in Part 1, "Historiography and Sources", one identifies research trends in the history of mathematics, the second discusses the centrality of problems, and the third uses drama to recreate moments of mathematical discovery. Part 2, "Historical Studies: From Antiquity to the Scientific Revolution" and "From the Scientific Revolution to the Present", offers a range of scholarship in the history of mathematics, including mathematics education, from antiquity to the present. Part 3, listed under two titles: "Integration of History with Mathematics Teaching: Fundamentals and Selected Cases" and"Origins and Teaching of Calculus," includes papers on the topics of reasons to include the history of mathematics in mathematics education, Ethnomathematics, networks for sharing historical mathematics information, and a mathematics history course. (MKR) During the last twenty years, historical studies devoted to various aspects of mathematical knowledge and activity have greatly increased.