Teaching and Learning With Primary Source Projects: Real Analysis, Topology, and Complex Variables
Recent pedagogical research has supported Abel's claim of the effectiveness of reading the masters. Students exposed to historically based pedagogy see mathematics not as a monolithic assemblage of facts but as a collection of mental processes and an evolving cultural construct built to solve actual problems. Exposure to the immediacy of the original investigations can inspire an inquiry mindset in students and lead to an appreciation of mathematics as a living intellectual activity.
TRIUMPHS (TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources) is an NSF-funded initiative to design materials that effectively harness the power of reading primary historical documents in undergraduate mathematics instruction. Teaching and Learning with Primary Source Projects is a collection of 24 classroom modules (PSPs) produced by TRIUMPHS that incorporate the reading of primary source excerpts to teach core mathematical topics. The selected excerpts are intertwined with thoughtfully designed student tasks that prompt students to actively engage with and explore the source material. Rigorously classroom tested and scrupulously edited to comply with the standards developed by the TRIUMPHS project, each of the PSPs in this volume can be inserted directly into a course in real analysis, complex variables, or topology and used to replace a standard textbook treatment of core course content. The volume also contains a comprehensive historical overview of the sociocultural and mathematical contexts within which the three subjects developed, along with extensive implementation guidance. Students and faculty alike are afforded a deeper classroom experience as they heed Abel's advice by studying today's mathematics through the words of the masters who brought that mathematics to life.
American Mathematical Society
Providence, Rhode Island
pedagogy, teaching, undergraduate mathematics, primary sources, historical sources, topology
Analysis | Curriculum and Instruction | Geometry and Topology | Higher Education