Professor Emeritus

Mathematical Sciences

New Mexico State University

Las Cruces, NM 88003, USA

davidp@nmsu.edu

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.**

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:

- 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
Homework 0.

- 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:

Excerpts
on
the Euler-Maclaurin summation formula, from Institutiones
Calculi Differentialis by

Leonhard
Euler
(pdf format), 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):

Mathematics Education, University of Gothenburg, Sweden, 2003

Mathematics Education, University of Gothenburg, Sweden, 2003

(or Anything) from Primary Historical Sources, in

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.

Last revised on Sep. 2, 2018.