The Use Of Primary Historical Sources In Mathematics

As a way of incorporating the history of mathematics into the mathematics curriculum, Barnett describes the use of primary historical sources in teaching concepts in linear algebra and abstract algebra, as he suggests that “the use of original sources is among the most thrilling for the insights and the challenges it offers for students and instructors alike” (p. 722). The author utilizes a guided reading approach for students in reading the primary sources. However, unlike the method most frequently used with guided reading in which students read a selection followed by the consideration and/or discussion of questions about the text, students perform various “tasks [that] require students to engage actively with the mathematics as they

One challenge in incorporating primary sources lies in choosing selections or excerpts that are not too advanced for the specific group of students that would result in a high level of frustration instead of increased understanding. Another consideration in choosing primary sources is whether the terminology or principles match that currently used or do not contain such significant differences that would confuse students. Because of these considerations, the excerpts by Peirce appear after that of Boole and Venn to allow students to gain understanding of set theory terminology and to develop preliminary skills in Boolean algebra before encountering the formal and sophisticated proofs as developed by Peirce. Additionally, the project incorporates “the award-winning 1938 paper ‘A Symbolic Analysis of Relay and Switching Circuits’ in which Claude Shannon (1916–2001) first applied Boolean algebra to the design of parallel and series circuits” providing student tasks in a concrete context (p. 728). The project concludes with tasks associated with primary sources incorporating the work of Arthur Cayley (1821–1895) on the theory of permutations and his abstract theory of finite groups, that of J. L. Lagrange (1736–1813) on polynomial equations and that of Augustin Cauchy (1789–1857) on permutation theory

62). Geometric interpretations of complex numbers by mathematicians such as Wessel, Buee, Argand, and Gauss in the early 1800’s led to the widespread acceptance of complex numbers among mathematicians (p. 63). Undoubtedly, a purely arithmetic representation of complex numbers confused the average scholar then just as it might confuse today’s students without a visual representation such as that depicted by “the Argand diagram displaying a point z = a + bi on the complex plane” (p. 69). By visualizing a complex number either in Cartesian coordinates or polar coordinates on the Euclidean plane, students requiring multi-sensory instruction and concrete examples, such as the author’s son who is dyslexic, may form more meaningful and lasting conceptualizations of complex numbers. As such, Grosholz concludes that “the reason why the geometric interpretation of complex numbers moved mathematical research forward historically and why it aids students pedagogically is because it gives us a repertoire of modes of representation” (p. 71).