Connecting past to present: An approach to teaching topology and more via original sources

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Connecting past to present: An approach to teaching

topology and more via original sources

Nicholas Scoville, Janet Barnett, Kathy Clark, Daniel Otero, Diana White

To cite this version:

Nicholas Scoville, Janet Barnett, Kathy Clark, Daniel Otero, Diana White. Connecting past to present: An approach to teaching topology and more via original sources. History and Pedagogy of Mathe-matics, Jul 2016, Montpellier, France. �hal-01349226�

CONNECTING PAST TO PRESENT:

An approach to teaching topology and more via original sources

Nicholas A. SCOVILLE, Janet Heine BARNETT, Kathleen CLARK, Daniel E. OTERO, Diana WHITE

Ursinus College, Collegeville, PA, USA nscoville@ursinus.edu

Colorado State University-Pueblo, Pueblo CO janet.barnett@csupueblo.edu

Florida State University Tallahassee, FL, USA USA kclark@fsu.edu

Xavier University Cincinnati, OH, USA otero@xavier.edu

University of Colorado Denver, Denver, CO, USA Diana.White@ucdenver.edu

This one-hour workshop will introduce participants to a guided reading approach for bringing history to the classroom in the form of “Primary Source Projects” (PSPs). Each PSP consists of excerpts (in English translation) from original sources that are historically related to core topics in today’s curriculum, interwoven with exercises to guide students’ active engagement with the mathematics in each excerpt. PSPs also contain commentary on the historical authors and the problems they wished to solve. At appropriate junctures, students are introduced to present-day notations and terminology, and asked to reflect on how today’s definitions evolved to capture concepts that arose from attempts to solve those original problems.

Workshop participants will experience this teaching avenue by putting themselves in the role of the student as they work in groups on a specific PSP: Connecting connectedness. This 1-2 day PSP begins with a discussion of Cantor’s efforts to determine the nature of a continuum. Students then wrestle with Cantor’s original 1883 definition of connectedness, a definition which appealed to a metric. They next carefully examine Jordan’s more nuanced understanding of connectedness, still with a metric. Finally, students encounter the first purely set-theoretic definition, given by Schoenflies, before arriving at the current definition provided by Lennes in 1911. By tracing the concept of connectedness and its evolution over a 30 year period, this PSP exposes students to the original motivations behind the esoteric concept of “connectedness” in a way that makes this concept both more meaningful and more accessible to them. Following this opportunity to grapple with original sources within a guided reading format, workshop participants will discuss classroom implementation issues. An overview of the pedagogical benefits of this approach will also be provided.

Workshop facilitators are members of a seven-person grant team with funding from the US National Science Foundation (NSF). A collection of PSPs from two prior NSF grants that supported the development of this approach is available at www.cs.nmsu.edu/historical-projects/. Through the current Transforming Instruction in Undergraduate Mathematics via

of undergraduate mathematics topics, will be created and tested. A list of new PSPs to be developed is located at http://digitalcommons.ursinus.edu/triumphs/.