Connecting History to the Mathematics Classroom

Submissions to Convergence are required to further the journal’s mission of using the history of mathematics to teach mathematics in undergraduate institutions and schools (specifically, for mathematical subjects in the K–16 curriculum, with a particular emphasis on topics studied in grades 8–14). Although Convergence authors often share materials that they have employed in their own classrooms, the editors recognize that pre-submission field testing is not always possible. Thus, some submitters may need help articulating potential classroom applications for the historical concepts addressed in their articles. Although the realm of possible classroom connections is infinite, the list below offers several of the most common ways in which Convergence articles bring together the history of mathematics and the teaching of mathematics, along with examples of how these connections were realized in existing publications. Again, a submission to Convergence must include a well-defined discussion of when, where, and how the historical content of the article can be used in a practical way in the mathematics classroom.

Some possible approaches to classroom applications:

• Guided readings of primary sources
  • A Series of Mini-projects from TRIUMPHS: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources, by various authors
  • The French Connection: Borda, Condorcet and the Mathematics of Voting Theory, by Janet Heine Barnett
• Self-contained classroom lessons
  • Apportionment: What's Your Fair Share? – An Activity for Liberal Arts and High School Students, by Jeff Suzuki
  • Things Certain and Uncertain, by Michael P. Saclolo and Erik R. Tou
• Exercises from historical treatises or textbooks
  • Helping Ada Lovelace with her Homework: Classroom Exercises from a Victorian Calculus Course, by Adrian Rice
  • Mabel Sykes: A Life Untold and an Architectural Geometry Book Rediscovered, by Maureen T. Carroll and Elyn Rykken
• Explorations inspired by or related to historical material
  • Mathematical Mysteries of Rapa Nui with Classroom Activities, by Ximena Catepillán, Cynthia Huffman, and Scott Thuong
  • Need the Area of a Triangle? The Pope Can Help! by Betty Mayfield
• Alternative ways of thinking about a mathematical concept when the “traditional” 21st-century textbook approach isn’t clicking with students
  • An Analysis of the First Proofs of the Heine-Borel Theorem, by Nicole Andre, Susannah Engdahl, and Adam Parker
• Course outlines and experiences
  • A Mathematical History Tour: Reflections on a Study Abroad Program, by R. Abraham Edwards and Marie Savoie
  • Discovering the Beauty of Science, by Christine Latulippe and Joe Latulippe
• Discussion prompts and out-of-class essays
  • A Writing Intensive General Education History of Mathematics Course, by Amy Shell-Gellasch
  • Numbers, Infinity, and Reality: An Interdisciplinary Undergraduate Philosophy of Mathematics Course, by Kevin DeLapp and Jessica Sorrells
• Descriptions of potential student research projects
  • Building a Book: HathiTrust, Ancestry.com, Serendipity, and Lifetime Interests, by David Lindsay Roberts
• Construction of replica historical objects
  • Bridging the Gap Between Theory and Practice: Astronomical Instruments, by Toke Knudsen
• Tools for identifying and utilizing primary sources in the classroom
  • Online Museum Collections in the Mathematics Classroom, by Amy Ackerberg-Hastings and Amy Shell-Gellasch
  • The Educational Times Database: Building an Online Database of Mathematics Questions and Solutions Published in a 19th-Century Journal, by Robert M. Manzo
• Processes for incorporating history into the professional practice of one’s teaching techniques, methodology, or philosophy
  • Euler and the Bernoullis: Learning by Teaching, by Paul Bedard
  • Why History of Mathematics? by Glen Van Brummelen
• Informative background articles that enhance an instructor’s understanding of a specific course; may include general suggestions that can be infused into one’s teaching but that may not have been designed for direct use with students
  • Recreational Problems in Medieval Mathematics, by Victor J. Katz

For additional examples of classroom connections, see Convergence’s Classroom Resources Index.