David J. Pengelley
New Mexico State University
Las Cruces, NM 88003, USA
Here's my detailed vita, which lists all my publications.
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:
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
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:
- Further philosophy, my evolution, logistical details, and
personal experiences of the classroom
dynamics of teaching this way.
- An explanation just of my grading
and daily logistics of handling several units
simultaneously with these assignment parts.
- Homework guidelines for students, a
handout for day one, about how assignments will be designed to
foster an active classroom without lecture.
- Homework 0, due on day two, gives me
student input for designing the course and explaining to them
how the pedagogy is tailored to their learning. The main thing I
usually get from their Homework 0 is that they say they learn
best by practice and doing (not lecture), and they say
they can best demonstrate what they've learned by
teaching/showing someone else (not by taking timed exams); I
endeavor to make any exams be untimed. So only on day three do I
give them a detailed course overview handout, informed by their
- My qualitative grading rubric for
A/B/C/D/F grading (see classroom dynamics).
- I also ask students to give me me some written information about
themselves in class on the first day, to build a sense of
connection and familiarity with students.
- An example overview handout for a
sophomore discrete mathematics course of how I present this
pedagogy to students.
- Example assignments for
courses in discrete mathematics and calculus, showing reading
questions, warmup exercises, and final exercises.
- An actual assignment handout for
students, showing the different things I expect them to do.
Translations of primary
historical source materials:
the Euler-Maclaurin summation formula, from Institutiones
Calculi Differentialis by
(pdf format), or in (dvi
format), also at the Euler
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::
bridge between the continuous and the discrete via original
graduate course on the role of history in teaching mathematics
between continuous and discrete: Euler's summation formula (pdf)
and the first paper on group theory (appeared in "Using
recent history of mathematics in teaching mathematics", ed. Amy
Shell et al, MAA Notes Series, Mathematical Association of
Euclid need the Euclidean algorithm to prove unique
factorization? (appeared in the American Mathematical Monthly)
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,
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.
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, firstname.lastname@example.org
Last revised on November 20, 2017.