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, including all topology research.

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:

Evidence-based teaching: how do we all get there? is an article in the August/September 2019 FOCUS news-magazine of the Mathematical Association of America, on challenges and opportunities for shifting our pedagogy toward evidence-based active learning methods that substantially improve student success, emerging from the AMS Committee on Education Guided Discussion held at the Joint Mathematics Meetings 2019.

Evidence-based teaching: how do we all get there? is a summary report containing issues, participant responses to discussion questions, and resources from the AMS Committee on Education Guided Discussion held at the Joint Mathematics Meetings 2019.

Evidence-based teaching: how do we all get there? contains our slides displaying evidence and professional calls taken as given, issues, discussion questions, and resources from the AMS Committee on Education Guided Discussion held at the Joint Mathematics Meetings 2019.

Maximizing Student Outcomes in Flipped Classrooms: How Do You Ensure Student Buy-in? contains my slides for the Project NExT workshop at the Joint Mathematics Meetings 2019.

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

From
lecture to active learning: Rewards for all, and is it really so
difficult?, an extended piece in the College Mathematics
Journal in 2020.

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.

- More
examples of reading questions. In this folder is an
overview.pdf file for a course on introduction to proofs, logic,
etc., for mathematics majors, along with all the reading
questions used in the course, found in files labeled ht*.pdf and
hw*.pdf. This should give the best sense of what I choose for
reading questions.

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 and video presentations (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