David J. Pengelley
Professor Emeritus
Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003, USA
davidp@nmsu.edu
David Pengelley


******The document Evidence-based teaching: how do we all get there? contains issues, discussion questions, and resources from the AMS Committee on Education Guided Discussion held at the Joint Mathematics Meetings 2019.******

Here's my
detailed vita, which lists all my publications.

How efficiently can one untangle a double-twist? Waving is believing! (with Dan Ramras), preprint and animations, in The Mathematical Intelligencer in 2017.

I have extensive web material on Teaching with Original Historical Sources in Mathematics, which includes versions of quite a number of my joint publications in this area.

Classroom teaching methods for student active learning via reading in advance, writing, and warmup exercises, as alternatives to lecture:

Beating the lecture-textbook trap with active learning and rewards for all, a condensed piece in the Notices of the American Mathematical Society in 2017.

From lecture to active learning: Rewards for all, and is it really so difficult?, an extended piece, preprint.

Video and slides of my 2017 presentation From lecture to active learning: Rewards for all, and is it really so difficult? in the MIT Electronic Mathematics Education Seminar.

Video of my plenary presentation How to beat the lecture/textbook trap, and then throw them both away! to the 2013 Legacy of R.L. Moore Conference.

And here are some suppporting materials with details:

Translations of primary historical source materials:

Excerpts on the Euler-Maclaurin summation formula, from Institutiones Calculi Differentialis by Leonhard Euler (pdf), or in (dvi format), also at the Euler Archive.

Excerpt from a letter of Monsieur Lame to Monsieur Liouville on the question: Given a convex polygon, in how many ways can one partition it into triangles by mean of diagonals?: Lame's elegant geometric solution to finding the one step recursion relation solving Euler's decomposition problem, leading to the factorial formula for Catalan numbers.

A few preprints (separate from topology research (see vita) and joint publications on Teaching with Original Historical Sources in Mathematics):

  • The bridge between the continuous and the discrete via original sources, in Study the Masters:
    The Abel-Fauvel Conference, 2002 (ed. Otto Bekken et al), pp. 63–-73, National Center for
    Mathematics Education, University of Gothenburg, Sweden, 2003
  • A graduate course on the role of history in teaching mathematics, in Study the Masters:
    The Abel-Fauvel Conference, 2002 (ed. Otto Bekken et al), pp. 53-–61, National Center for
    Mathematics Education, University of Gothenburg, Sweden, 2003
  • Arthur Cayley and the first paper on group theory, in Using Recent History of Mathematics in Teaching Mathematics (ed. Amy Shell et al), MAA Notes Series, Mathematical Association of America, 2005
  • Did Euclid need the Euclidean algorithm to prove unique factorization? in American Mathematical Monthly, 2006
  • Dances between continuous and discrete: Euler's summation formula (pdf) or (dvi), in Euler at 300: An
    Appreciation (ed. Robert E. Bradley et al), Mathematical Association of America, 2007, pp. 169-–190
  • Teaching With Primary Historical Sources: Should it Go Mainstream? Can it?,  opening keynote address at HPM 2008, the quadrennial international meeting of the International Study Group on Relations Between History and Pedagogy of Mathematics, Mexico City, 2008
  • "Voici ce que j'ai trouv�": Sophie Germain's grand plan to prove Fermat's Last Theorem (January 2010 revision), in Historia Mathematica, 2010
  • Sophie'�s Diary, by Dora Musielak, book review in the Mathematical Intelligencer, 2010
  • Mathematics Emerging: A Sourcebook 1540-–1900, by Jacqueline Stedall, book review in Notices, American Mathematical Society,2011
  • Quick, does 23/67 equal 33/97? A mathematician's secret from Euclid to today, in American Mathematical Monthly, 2013
  • The Pedagogy of Primary Historical Sources in Mathematics: Classroom Practice Meets Theoretical Frameworks, in Science & Education, 2014
  • Prime Mystery: The Life and Work of Sophie Germain, by Dora Musielak (book review), MAA Reviews, 2015.
  • What does `less than or equal' really mean? in American Mathematical Monthly, 2015
  • Enticement to College Mathematics via Primary Historical Sources, in The Courses of History: Ideas for Developing a History of Mathematics Course, eds. Amy Shell-Gellasch and Dick Jardine, MAA Notes Series, Mathematical Association of America, to appear.
  • Capstone Mathematics from Primary Historical Sources, in The Courses of History: Ideas for Developing a History of Mathematics Course, eds. Amy Shell-Gellasch and Dick Jardine, MAA Notes Series, Mathematical Association of America, to appear.
  • Teaching Discrete Mathematics, Combinatorics, Geometry, Number Theory,
    (or Anything) from Primary Historical Sources
    , in The Courses of History: Ideas for Developing a History of Mathematics Course, eds. Amy Shell-Gellasch and Dick Jardine, MAA Notes Series, Mathematical Association of America, to appear.

  • OK, here's a photo taken at the 1999 Boulder conference on homotopy theory.  On the left is Italian algebraic topologist Luciano Lomonaco, on the right is me.

    You might find another photo of me playing badminton at NMSU.



    Page maintained by David Pengelley, davidp@nmsu.edu
    Last revised on Oct. 17, 2018.