Janet Heine Barnett
A 1995 -1996 fellow at the MAA Institute for History of Mathematics and Its Use in Teaching (funded by the NSF), my scholarly interests have long included mathematics history and its use both to promote mathematical understanding and as a vehicle for promoting teacher reflection on pedagogical issues. Through my collaboration with faculty at New Mexico State University under two prior NSF grants, I have developed seven primary source projects to date: three on topics in graph theory, another three on boolean algebra and its applications, and an extensive project on elementary group theory based on papers by Lagrange, Cauchy and Cayley. Writing and teaching with these guided reading projects has allowed me to witness at first hand the many ways in which working with primary sources allows students to develop their own robust understanding of the mathematics in question. Beyond this, primary sources offer students experiences with and insights into the processes that mathematicians employ as they attempt to solve outstanding problems, refine their existing theories and abstract new concepts from their efforts. These experiences and insights in turn support students’ ability to develop and reason with ideas on their own. For the TRIUMPHS grant, I plan to write two full length projects for upper division mathematics courses. The first will be a two-part project on the theory of rings and ideals featuring works from Dedekind, Noether and Krull. The second will be a project for introductory analysis that will utilize excerpts from Darboux and Peano as a means to refine students’ intuitions about continuity, differentiability and their relationship, and to introduce them to the concept of uniform continuity. Both projects will also seek to foster students’ ability to read and critique modern proofs, thereby enhancing their understanding of current standards of proof and rigor in mathematics more generally. I also plan to write two mini-PSPs for analysis, four mini-PSPs for use in second semester calculus and another three mini-PSPs on topics to be determined based on site-tester interests.